Prof. V. Balakrishnan in conversation with Prof. Suresh Govindarajan

On behalf of the Heritage Centre, Professor Balakrishnan,

I would like to welcome you to this informal chat.

[Prof. Balakrishnan] Thank you. [Prof. S. Govindarajan] And, the idea is that we go over the history,

your history and your association with IIT Madras.

And so, we'll start with your life before IIT Madras.

So, maybe you can tell us something about

where you lived, where you studied and worked.

Well, I went to school at, primarily in Bombay and Pune.

After matriculation, I had a year of pre-university science

at the University of Pune

and then my father got transferred to Delhi.

So, I joined Delhi university in the Physics Honours Programme

in 1960 and '63, I finished my Physics Honours.

And, in '65 M.Sc. programme and then went abroad

to Brandeis University for a Ph.D.,

returned to India in late 1970

and then spent 3 years at Tata Institute in Bombay

and then joined the then new Reactor Research Centre at Kalpakkam

in the Materials Science division,

I mean what was then the Materials Science lab.

And, after 6 years there, I moved to IIT

and joined in 1980, and then of course,

[Prof. S. Govindarajan] So, RRC is now called IGCAR right?

[Prof. Balakrishnan] RRC is now called IGCAR;

after Indira Gandhi passed away, the name was changed

and it's the second research arm of

the atomic energy department after BARC.

Since you actually had a permanent job

at IGCAR or RRC as it was called,

how did you end up at IIT Madras?

Well, a combination of circumstances,

some intentional, some accidental,

happy accidents in some sense for me.

I always wanted to teach and in fact, in 1976

Professor R. Srinivasan

who was the Head of the Physics Department

invited me to come over here from Kalpakkam 3 days a week

and give a new course on the quantum theory of solids,

which I did during the January to April semester.

And the next year he repeated the experiment.

So, I realized that I really liked teaching.

So, when the opportunity arose I thought.

I would apply and I did and then I came here.

So ... it's true that I did spend

the first decade in a pure research institution,

but I felt always that something was missing, a crucial ingredient.

And then after coming here I realized

it was the presence of young students -

that's generally missing in research institutes

except for a few research scholars or very young scientists.

But being in an institution with

undergraduates and postgraduate students

and a large number of them is a different feeling altogether.

[Prof. S. Govindarajan] So, in 1982 which is probably a year or two after you joined IIT Madras,

I joined IIT Madras as an undergraduate

and by then you were already a legendary teacher.

And I mean it was my great regret that you were not teaching my class

because you were teaching alternate batches.

So, the odd years had you and your team teaching,

but how did you be ... I mean, have such a huge impact

in, I think a year or two?

I don't know if it was an impact,

but you have to remember that in 1980,

'81, the first 4-year batch - B.Tech batch - started,

till then it was a 5-year stream.

So, after I came over, there was this effort to rewrite the Physics curriculum

to compress all Physics so, to speak in 3 semesters.

Professor Indiresan was the Director

who recruited me and I remember even asking him

saying, because, I had been told by people in the Physics Department

that prior to that in the 5-year

stream they actually had Physics for 10 semesters.

So, I even asked him:

how do you expect all of Physics to be compressed in 3 semesters?

And his reply was: that's the mandate, you have to do it;

now everything else depends on how you do it

and surely you can communicate the essentials of a subject

to potential engineers in 3 semesters,

if you can't, it means something is wrong.

So, he was categorical about it, he said you should be able to do it.

So, a team of us: Professor R. Srinivasan who was taking the lead

and then Dr. Swaminathan, Ramabadran and myself,

we handled the first few batches of the new 4-year stream.

And, we wrote out the syllabus,

a curriculum which was used for many years

and we - our philosophy was roughly to say,

we avoid details and focus on principles

and we talk about single particle

or small number of degrees of freedom systems

in the first semester along with ... vector calculus.

So, essentially you are doing mechanics in vectorial form.

In the second semester, we went on to fields

electromagnetism specifically, with a little bit of optics

and in the third semester we looked at

a very large number of degrees of freedom.

So, after a brief introduction to Hamiltonian, Lagrangian mechanics

we did elementary statistical mechanics and ended up with

the fundamentals of quantum physics.

So, that was a very neat package

indeed, in 3 semesters

which kind of summarized what Physics was all about.

And, I must say that the students,

a much smaller number in those days,

I believe that in the early '80s the number was only about 240 or 260.

[Prof. Balakrishnan] Even less - 220 to 230, I think. [Prof. Balakrishnan] Yes.

And then it, of course, has grown since then

but they were split into 4 batches and the 4 of us handled these batches

more or less in synchrony.

And in - in fact, I would say in strong synchrony

because we discussed things beforehand.

And the students were deeply interested, many of them;

as you know very well, including yourself, many people went on

to form in - to careers in science and mathematics.

So, it did make some difference.

Even though I did not have you as a lecturer,

[Prof. S. Govindarajan] I got access to you know cyclostyle notes. [Prof. Balakrishnan] Yeah.

Your legendary cyclostyle notes

and can you tell us something about that?

Well, I - when I joined here, I had a room, an office room

which clearly was a temporary room because

it had a cyclostyling machine at one end of it which was not used

and it had apparently been junked or whatever

and it was still in working condition as far as I know

and there was a technician who would occasionally run things off on it.

And after a while I got this idea that

we could do this stencilling and type and cyclostyling ourselves.

And question papers in those days were cyclostyle,

220 copies made for the quizzes,

for the final exam and so on, and stapled.

So, we set up a kind of assembly line to do this

and I had an old typewriter with me.

So, we'd type on those old stencils, fill out all the equations

using those stencils and then run off;

I even learnt how to use that cyclostyling machine, how to run it off.

And then once that happened, it became easy to

you know distribute handouts, notes, and so on;

because things are much easier,

now we do it by just forming an email group and then

sending out PDF files or whatever.

But...those early days I think it did help

that students had access to notes

because we didn't, in this curriculum it was so mixed

that we didn't really use a single textbook

[Prof. Balakrishnan] and that caused - [Prof. S. Govindarajan] Actually, there isn’t one till today.

And, that caused a lot of difficulty because a lot of complaints

that there wasn't a single textbook from which we were teaching;

unlike the other IITs, I - I guess.

And we insisted that this course was so broad-based

that a single textbook couldn't do justice to it,

it was certainly at a much higher level than

Resnick and Halliday for instance or Bizer or anything like that.

And ... years later, I had opportunity to

compare this syllabus that we had laid out with

corresponding syllabus at Caltech and Cornell and so on

and to a great surprise it was -

there was a very very high degree of overlap.

So in that sense, we had actually modernized the physics curriculum

well before many other places did.

[Prof. S. Govindarajan] One of the funny things is

that with regard to laboratory duty it’s sort of

in - in the Physics Department - as you know most people are assigned

1 session or 2 sessions of lab.

And ... I mean you were assigned a few times,

but then it was decided that it was better not to give you lab duty.

[Prof. S. Govindarajan] Can you tell us what happened? [Prof. Balakrishnan] Might be

you know, realistic assessment of my talents as an

experimentalist which is less than negligible.

But I think for many years through the '80s,

I actually handled 2 theory courses every semester.

And one memorable semester in 1984,

I had 3 and with a little bit of - for a few lectures

I also handled a few lectures of, you know, 4th course

in the same semester.

I wouldn't want to repeat that experience again.

[Prof. Balakrishnan] Because it was a very heavy load. [Prof. S. Govindarajan] Yes.

But 2 was fairly routine and so on

[Prof. Balakrishnan] and then - [Prof. S. Govindarajan] Which is definitely more than most people

because it's usually 1 lab.

[Prof. Balakrishnan] Yeah, 2 and [Prof. S. Govindarajan] And 1 course.

one of them a 4 credit course - it takes takes away some time,

but towards the end in the late '90s,

I did get assigned lab courses, etcetera.

But... I think they found me more useful,

they found it more useful if I gave lectures on error analysis

and statistics and how to analyse data than to

actually go there and supervise experiments,

which I could do, you know, no differently from anyone else.

And one of the big surprises for me at least

is that you know a lot of stuff about materials science

and it is not something you work on day to day,

but I know that you know so much.

Oh. When I - my - my thesis is on elementary particle physics,

theoretical high energy physics of those days

S-matrix theory and field theory, trying to bring them together.

So, that is as abstract as you could have got in those days,

but then when I moved to TIFR, I slowly shifted

to many body theory and did work on the Heisenberg ferromagnet

and statistical physics and so on.

And then when I got this job at Kalpakkam,

it was specifically in the materials science lab.

So, the mandate was to try to understand

from a physical point of view,

fundamental properties of materials, specifically metals.

So I had to learn a little bit of metallurgy

and materials science to be able to work there

and contribute to the research programme.

So, that - my - initially I felt, I mean

this is a subject which would be totally uninteresting to me.

But as I got into it, I realized that it is

a fascinating subject and that sort of ... interest,

cultural interest has stayed with me, you know.

And among the many things you already mentioned that

you were very actively involved in setting up the

physics curriculum for the new 4-year programme in the '80 -'81,

but - but you kept introducing new courses.

So, can you tell us something about the course

called Classical Mechanics II which became Classical Field Theory?

Oh. That was again a bit of an accident,

the very first course that I taught here was in the January -

apart from the '76, '77 brief interlude.

This was a course on Classical Mechanics II

as it was in the M.Sc. syllabus then

and it was from January to J - April or May of 1981.

The class was small and what I didn't realize then was that

it had some exceptionally good students

including some B.Tech. students who were sitting in on the course.

And in all my innocence I went and asked them

what textbook they'd used for Classical Mechanics I

and they said Goldstein.

And I said how much of Goldstein?

And they said all of it

and I was surprised by this

that they had actually covered this entire course,

I found out later that that was a little bit of a hyperbole.

But...I decided that if they had done all of Goldstein,

then the next thing to do was to do - start practically at the last

chapter of Goldstein which is continuum mechanics

and then I looked at it

and said: continuum mechanics is kind of boring;

so, let us make it relativistic.

And then I gave this course on classical field theory.

One of the great advantages of academic freedom is that you could kind of

distort the syllabus in this fashion as you pleased,

the students seemed to like it.

So, I introduced special relativity and tensor calculus

and then did classical field theory.

It went down well, I even wrote a set of notes on it

and distributed it and then in the next few years

occasionally one would come back and give this.

I think it got formalized as classical field theory only much much

later after all of you came in and then

introduced a lot of general relativity and

really made it a proper course on classical field theory.

But I was happy to be able to do things

like spontaneous symmetry breaking

and the Higgs mechanism and so on,

way back then in the context of basic classical field theory.

And ... one course at least for me it’s memorable by its name

and it gave, I - I did not know what that was about;

it was called synergetics.

Can you tell us?

Oh. In the '80s,

when people were beginning to look at complex systems,

what today known as complex systems,

specifically Hermann Haken in Germany, he coined,

I think he coined the name 'synergetics' for this course;

where you have a large number of

effects coming together to produce -

causes coming together to produce an effect,

something like what we would call emergent phenomena

or complex dynamics and so on, today.

And there was a whole series of monographs published on

synergetics with collections of articles in by Springer.

And, I found that one of the lacunae in our M.Sc. syllabus

curriculum was that there was no room for critical phenomena

or phase transitions, the modern period of critical phenomena

nor was there any nonequilibrium statistical mechanics.

And...there was nothing on dynamical systems per se,

although chaos and non-linear dynamics had become quite

popular and they were very very actively

being pursued in the late '70s and '80s

and I thought why not put these together and offer an elective for it?

Strictly speaking it should have been 3 electives,

but the hassle of going through the Board of Academic Courses,

getting permission for all the courses would have been too much

and 3 would have been too much to float at one - one shot.

So, I put the 3 together into 1 syllabus in a little bit of

sleight of hand and called it synergetics.

And, it was approved by the departmental committee and the Board

of Academic Courses and then the course was floated as an M.Sc. elective.

So, for several years to successive batches of M.Sc. students as well as

senior B.Tech. students who'd opted for this course,

I ran this course by focusing on one of these three main topics.

So, it was three kind of different courses but under one umbrella.

Then of course, today we have separate courses on all these subjects.

So, I mean, actually, you have been involved in

creation of dynamical systems.

[Prof. S. Govindarajan] Now, that's two courses, there is advance. [Prof. Balakrishnan] Yeah, there is an advance.

And, then more recently you added two more courses, you know,

which in some sense, seems to have its origins in synergetics;

[Prof. S. Govindarajan] one is Physical Applications of Stochastic Processes... [Prof. Balakrishnan] Yes. Yes.

And Nonequilibrium Stat Mech.

[Prof. S. Govindarajan] And - and in fact, you have actually given NPTEL courses on this. [Prof. Balakrishnan] Right. Right.

So, can you tell us how your NPTEL courses came about,

especially the first two which I think are

wildly popular, I mean to say the least.

For entirely accidental reasons, as usual,

this was around the time that I was actually retiring from the department

formally, a little later in fact, when I was already on ...

[Prof. S. Govindarajan] But your classical physics and quantum physics was given to a real class.

[Prof. Balakrishnan] Yes. [Prof. S. Govindarajan] You were still. They were all.

Yes, they were given as courses

as you know we had a minor stream

which Professor Ananth had proposed early

and the minor stream started off by saying

the physics minor stream, the proposal was 4 courses;

all 4 generally M.Sc. electives.

So, for a few years it was a little chaotic

because different people who would take

different courses or float different courses among the electives,

depending on the interest of whoever taught the course.

And the course wasn't receiving its

due attention from the undergraduates,

it wasn't being opted for as a leading preference.

So, the department decided to do something about it

and then they revamped it,

there were only 3 courses, I think, now...

[Prof. S. Govindarajan] Now, it is 3 but it started off as 4 [Prof. Balakrishnan] Right.

[Prof. S. Govindarajan] with 2 core. [Prof. Balakrishnan] Right.

So, my suggestion at that stage was

to formulate two new courses altogether for the minor stream

and then have the remaining course of two courses

taken from the list of M.Sc. electives.

And the two basic courses would be an overview of classical physics

and an overview of quantum physics, that was agreed to.

And, then I wrote - helped write the curriculum,

the syllabus for these courses

and then it was suggested that they could perhaps be recorded,

that I could give the courses for the - when they were given the first time

and they could be recorded and that was done.

And that was intended entirely as a recording for the local area network,

for internal circulation alone.

They got recorded and I get these series every day and then I decided

just give it to the student representative

which was done and I forgot about it.

And, then when NPTEL came along a few years later,

I was asked whether these courses could be put under part of NPTEL

and I readily agreed because, I didn't see why they shouldn't be.

The only thing is I didn't edit them in any way because, I realized

that to edit an hour of lectures takes 4 hours of work

and that was too much.

So, I said warts and all, let it be there and then, of course,

if there are mistakes in it, it will be detected by the students

and kind of self-corrected and that is how it's remained.

I did do one or two more courses of that kind and then

the last few were recorded, even them -

all the courses I have given there have been

[Prof. Balakrishnan] courses to actual classes. [Prof. S. Govindarajan] Yes.

They happened to have been NPTEL courses which were recorded,

[Prof. Balakrishnan] but they... [Prof. S. Govindarajan] Except for the series you have for high school students

[Prof. S. Govindarajan] Yes. [Prof. Balakrishnan] which is different in character.

[Prof. Balakrishnan] Can you tell us something about it? [Prof. S. Govindarajan] [inaudible] together.

The mandate there was to do half-hour modules on 11th standard physics

and on 12th standard physics in two different courses

and they were supposed to be half-hour modules.

Hm...I was able to do the 11th standard,

but I still haven't been able to do the 12th, yeah.

And ... you started writing articles for this

nice journal of education called Resonance

which is started by the Indian Academy of Sciences

and I really like this series called What Can The Answer

Be and I think of it as vintage Balakrishnan.

In some sense can you tell us a little bit about What Can The Answer Be?

Well, Resonance started in 1996

and they were looking for articles at that time

and one of the thoughts I had was supposed to be pedagogical articles,

supposed to interest students in science and mathematics.

And ... I was on the editorial board at that time

and one of the thoughts I had was why not

put down some of the useful tricks

that one uses in teaching these courses,

kind of heuristic arguments which could be made rigorous subsequently

after you guess the answer into a systematic set of articles on this.

So, I started by writing 1 and then it grew to 2 and 3 and then 4

and then went on for a few more and I titled it What Can The Answer Be?

The idea being - the philosophy being that you

[Prof. Balakrishnan] use very general arguments such as linearity, superposition, [Prof. S. Govindarajan] Isotropy.

scaling, isotropy, homogeneity, dimensional analysis,

order of magnitude estimates and so on;

all the tricks of the trade of a professional scientist

trying to guess the answers to questions.

And then show that it is indeed the the rigorous answer or whatever.

You can move this up to a point, but I found to my great surprise that

you could illustrate fairly sophisticated concepts like

the reciprocal basis for crystallography

not just in 2 and 3, but in n dimensions.

You could then go on to infinite dimensional

Hilbert spaces, vector spaces,

you could talk about basis sets and change of basis

and the idea of completeness and over-completeness, etcetera.

So, fairly sophisticated concepts could be brought in

from very elementary considerations and that's how this series grew.

I must say I regret not having contributed

more towards that set of articles

but they are sort of time-consuming.

Though, I must admit that some of my lectures

now are titled What Can The Answer

Be and the lecture ... proceeds in

[Prof. Balakrishnan] I - I - don't know where I got that - [Prof. S. Govindarajan] a fashion imitating yours.

I don't know where I got that title from - it may not -

it may not be an original thought at all.

So, I always tell them we are going to imitate 'Professor Balki' as you are called,

we are going to imitate Professor Balki today,

[Prof. S. Govindarajan] we are going to say What Can The Answer Be? [Prof. Balakrishnan] Of course, the greats in Physics have always used such arguments.

[Prof. S. Govindarajan] Yeah. [Prof. Balakrishnan] As you know, the Feyn - Feynman and Fermi and so on are legendary

figures who have used such arguments.

Fermi is famous - back of the envelope calculations -

and Feynman’s heuristic way of arguing even complex ... problems...

[Prof. S. Govindarajan] Yeah. [Prof. Balakrishnan] problems out, their object lessons and how to do this.

So, can you tell us a little bit about your family?

I know that your - both your kids, your son and daughter, studied at IITM

and so, I would like your -

you to tell us a little bit about your family and your

influence in them getting into IIT, influence or lack of influence.

Well, my wife is a theoretical physicist.

We were students together at Delhi university

and then at graduate school at Brandeis

and she worked at IMSC till her retirement.

And when our children grew up,

we have a son who is 7 years older than our daughter -

and when he grew up, well, he went to KV IIT here.

One of the things I realized very early on is that

I simply didn't have the patience to be able to teach him anything.

It's just that I think many parents have this problem

with at least the first child.

They think they can download all their information and experience

at several Tera-whatever-it-is -

TeraFLOPS per second into their children instantaneously

and get impatient if they don't absorb all of this at once,

that doesn't work.

It doesn't work that way at all.

So, my wife was very sane about it and she said, well,

let’s give inputs to the kids only when they ask for it

which of course, was not very often

and this this turned out to be very helpful.

So, we really didn't, you know, interfere in any way or

pressure in anyway: as long as they were doing ok, it was fine with us.

It’s only when Hari- that's my son’s name - when he got to about

maybe the 10th standard or something, that he

showed some interest in problem solving in mathematics and so on.

He got into these various quizzes and

then these Olympiad kind of

problem solving with some friends, he had some very good friends.

And so, he wrote the IIT entrance exam and got in here

into the Computer Science programme.

Long after he graduated, my daughter who went to a State Board school,

and we didn't expect that she would be interested in anything scientific at all.

So, she said - she - one fine morning, she told my wife that

she would like to take the IIT entrance exam.

And then - mean - by this time long before, this promise

had been extracted from me that I won't interfere in any way whatsoever

which I was all the more true in her case.

No, but I remember one legendary story

is that you came proudly and announced

to me and Professor Lakshmi Bala

over a tea that you taught -

tried to teach your daughter complex analysis.

[Prof. Balakrishnan] Well - [Prof. S. Govindarajan] and you should tell us your wife’s reaction to that.

[Prof. Balakrishnan] Yes, I - I must say that residue theorem, residue theorem [Prof. S. Govindarajan] Yeah.

it was - it was a mistake because I felt that -

she was probably in her 7th or 8th or something like that -

I felt that talking about real numbers was meaningless without

introducing complex variables.

So, I tried to do that geometrically

and the poor child was totally confused.

[Prof. S. Govindarajan] To do, yeah, equation of a circle in ... in polar coordinates. [Prof. Balakrishnan] Yeah. Right.

So, I said the equations of common curves in

in terms of a complex variable become very simple.

For example, a circle becomes mod z equal to a

very obvious and then of course,

this totally went over her head and it was a disaster.

So, then, I decided to follow my wife’s advice

and not interfere in this matter at all.

I think she told you to stick to being her chauffeur.

Yes. Indeed.

So, I think it's a good - good idea not to interfere till help is asked for

and then to stick to just that.

The other thing I learnt by

getting involved with them was you shouldn't...

it's true you should explain the basics,

but very often they want an instant answer to

whatever the problem is at that moment.

And if you start going too far back and starting from their basics

then they feel their foundations are shaken completely

and then they don't know which way to move,

they don't have a mooring,

so, it's important not to destroy that, you know.

One more thing which I would like to discuss now

is the evolution of the Physics Department.

So, around the time you joined, I remember it was mostly

a department of experimental solid-state physics.

And, today it's evolved to being one of the largest departments in

IIT Madras and having a wide spectrum

of - of topics, I mean it's probably, one couldn't even argue

that it's one of the better Physics Departments among all IITs.

[Prof. S. Govindarajan] So, could you just - [Prof. Balakrishnan] I - I'd go further and say it's the best.

Okay. So - but I know that you were also involved in this

sort of slow but sure shift.

So, could you tell us something?

Well, clearly, historically, the department started with

emphasis in experimental solid-state physics

or what was then solid-state physics of a particular kind;

specifically, things like colour centres and

you know conventional band structure calculations and so on

and Professor Srinivasan had set up very early on

an extremely successful low-temperature physics programme;

cryogenics and low-temperature physics experimental programme

that must - it must be said that

that was one of the country’s first such programmes.

[Prof. S. Govindarajan] That we had a helium plant, right? [Prof. Balakrishnan] There was the helium plant

[Prof. S. Govindarajan] Working helium. [Prof. Balakrishnan] which arrived here, I believe in 1970 or '71

and which was a kind of one-of-a-kind facility

in this part of the country at that time,

apart from maybe BRC or TIFR.

So, that was a very significant achievement of the physics department,

but after that, it focused essentially on one subject,

one part of one subject.

And it was not even geared to

other developments in condense metaphysics such as

the whole theory of critical phenomena and

even the experimental study of critical phenomena and stuff like that.

But then over the years it started slowly expanding

as it should, as it must, inevitably,

and more and more people came in very slowly at first

and then a little faster later on in recent years.

Till today, I think we have a reasonably healthy balance,

certainly the experiment to theory balance was skewed in the early days.

No one knows what the ideal balance is in the Physics Department,

but certainly 2 to 1 ratio would not be too bad.

Which is what it’s roughly now I think.

Which perhaps is what it is now 2 to 1 or even maybe,

you know, 5 to 2 or something like that would be alright.

But that wasn't attained in those days and it did

it - it was a luck, you know, and that I am very happy to say that -

see that it's been kind of addressed.

We have very good people now

and I think the institute as a whole of course,

and then the department in particular is certainly on an upward trajectory.

I would go so far as to - I said this to the review committee when they

came and of course, I'd retired by then

but I said so, I could say this in a very

casual and irresponsible way and perhaps the review committee felt

a little taken aback by this, they smiled.

When they said the department was a good one,

I said it's the best one among the IITs

and then of course, maybe that is arguable.

But I - I would say that we certainly have today

an extremely vibrant department which is extremely

active both research and teaching-wise, yeah.

You are very well known as a teacher but

personally, I think you are even more remarkable as a scientist.

And so, let us just talk a little bit about your research,

I also know that it's not like you be - you worked on one topic,

your thesis was on S-matrix theory high - you know,

theoretical high energy physics.

And, then promptly in your first post-doc you were doing many body theory

and it evolved over the years.

So, could you tell us a little bit of the kind of problems you worked on

and the evolution of your research?

It - I kind of fell into these problems out of curiosity

... more or less by chance, in some sense.

So, when I ... was in TIFR, I slowly shifted out of high energy physics

which had gone in a different direction then

and the reason was that the gauge theories had just come in,

electroweak unification had just been demonstrated,

't Hooft's papers had just come in.

And I didn't have enough field theory

background to be able to follow this

and contribute in terms of research

but by that time I had also found an interest

in many body theory and statistical physics.

So, I did some work on the Heisenberg ferromagnet

Green's functions for it, low temperature properties and so on

and then slowly moved out. When I went to Kalpakkam,

the shift was to materials science

and we set ourselves the task of doing something new

which is to understand mechanical relaxation

using linear response theory.

[Prof. S. Govindarajan] So, that's how you got into linear response theory. [Prof. Balakrishnan] That's right.

[Prof. S. Govindarajan] Through mechanical relaxation. [Prof. Balakrishnan] Through mechanical relaxation,

because there's a well-established

theory of dielectric relaxation and magnetic relaxation

and the idea was there should be a parallel in mechanics and there is

except that it is for very low strains

and it's things like anelasticity and linear viscoelasticity

which are not of direct interest to metallurgists.

It didn't take long for me to realize that the really hard problems in

metallurgy are non-linear,

intrinsically extremely complicated non-linear complex systems.

But as a baby step, one could look at the linear regime,

the time-dependent elasticity in the linear regime.

And sure enough it turned out

that if you looked at the dynamics of defects

using stochastic as well as statistical methods,

you could formulate ... an approach to mechanical relaxation,

things like anelastic creep and stress relaxation and so on

on the same footing as that for dielectric and magnetic relaxation

and you had the same role played by fluctuation, dissipation theorems

in both the first and second ones in this.

So, we developed that for a few years,

that kind of got me interested in random processes

and stochastic processes

and after coming here I looked at the

problem of hydrogen diffusion in metals

which is a very complicated diffusion problem,

its got mixing of classical and quantum properties here, diffusion here.

And that led me to looking at random box

and random box has stayed a kind of recurring interest for the last

35, 40 years now, many years now.

So, that's one aspect of it.

My first students here we did things on random box

and diffusion and generalized diffusion, anomalous diffusion,

continuous time random box, first passage times and so on

for several years through the decades in the '80s and into the early '90s.

So, you were actually being very productive

at a time when you were teaching 2 to 3 theory courses.

Yeah, surprisingly the semesters

I had the maximum teaching load, I also felt

obliged to do the maximum amount of research

because I felt guilty that I wasn't, you know, spending enough time on that.

So, yes, I think when you're kept busy, then you tend to work harder,

when you when you have a lot of things to do.

Then in the '90s, I slowly switched to dynamical systems

and had a few papers on non-linear dynamics,

got into chaos and stuff like that.

And then a little later into - back to quantum physics

to isospectral oscillators, generalized coherent states, things like...

These were all tailored toward students were on at the time and

what their thesis topics would be like.

[Prof. S. Govindarajan] And, now you are working on quantum dynamics. [Prof. Balakrishnan] on quantum dynamics

because there's this fascinating world of quantum optics

and atom optics and kind of coming together of

fundamental quantum mechanics, operator theory

in the behaviour of -

in a nutshell the behaviour of quantum mechanical systems

which show all the normal complexities of quantum physics

like entanglement and multipartite systems interacting with each other,

along with the fact that classically, these are chaotic systems.

So, signatures of chaos as they translate into these systems,

signatures of non classicality

in mainly in photonic systems, etcetera.

So, it’s a hotchpotch of many things,

but there's an underlying method in the madness -

is a theme which Professor Lakshmi Bala

and I have been exploring for many years

which is to understand using expectation values

of physical observables and their higher moments

and the expectation values of - and correlators

and things like that in quantum systems

And your ideas of recurrence from the early days

is coming back in some sense.

Yes, yes, there are deep connections between

revival phenomena in quantum physics,

wave packet revival phenomena,

fractional revivals, full revivals on the one hand,

and recurrences in the Poincaré sense in classical dynamical system.

So, I have got some papers on recurrence statistics,

recurrence time statistics and different kinds of chaotic systems

including intermittent systems and then

ranging all the way from quasiperiodic

to chaotic fully developed chaotic systems.

And, each of them has their own peculiarities

for the recurrence time distributions

and the idea was to explore if

there are connections with revivals and fractional revivals

in the corresponding quantum counterparts to this

and we have some interesting results.

So, the whole idea is to see to what extent

phase-space descriptions can play a role in quantum mechanics.

As you know on the one side,

you have the Wigner distribution and its generalizations,

but on the other side you could also take a more naive approach

and look at expectation values

of observables and their higher powers and cross correlators and so on,

treat them as dynamical variables in some effective phase space

and see what the plots look like

and what signatures of quantum physics they carry here.

That’s been a kind of general programme,

ongoing programme for about 2 decades now.

One feature of your research which I personally

like a lot is the fact that

you come up with exact solutions,

exact by mean there are no approximations

to ... to illustrate non trivial behaviour.

And maybe you can tell us about a couple of them so that -

Well, I think it's just a personal

like in some sense because I'm not very strong in numerics

or in computation - the students are

and I rely on them entirely for this purpose -

but at the same time, I've always felt that if you have a model

which captures some of the essential features that you want to explain

for more complicated systems,

then it’s worth solving the model as exactly as possible

because any reliability that you place on the

results from this model

shouldn’t be dependent on the approximations that you made.

On the other hand, if you start with a model

which is already a caricature of reality,

or a real physical system,

and then you make further approximations to it and they get uncontrolled,

then any results that you get you have no way of deciding

whether it's an artifact of the approximations

or whether the model has captured whatever you wanted to do.

There's this uncertainty and it's difficult to decide

what to do in such a case.

So, it - it would be good to have analytic solutions to simple models

but of course, what happens in most cases is that

these analytic solutions occur for models

are possible only for models which are extremely simple

and oversimplify the real situation.

So, the trick is to find systems which are not oversimplified,

but which at the same time can be analytically solved

like one dimensional models, for example, very often are solvable

but they may not have real features that you may want to capture.

Just to give you an instance, not something I worked on,

even if you know that the one-dimensional Ising model

does not have a phase transition in the standard sense,

you'd still like to understand correlation functions

or the renormalization decimation procedure

from these one-dimensional models,

where it can be implemented exactly.

So, they still have valuable lessons to give

for more complicated systems.

Ok. So, the last part we will just...you've been writing books over the years.

In fact, your first book was written when you were at ... in Kalpakkam.

So, can you just tell us

something about the various books that you've written?

The first book was not written - it was written with -

[Prof. S. Govindarajan] You were already in IIT Madras. [Prof. Balakrishnan] I was already in IIT Madras when it was published,

it was a Springer for book on the Solid-State Sciences.

We had, in Kalpakkam, looked at topological defects in condensed matter

a little bit, didn’t do much original research on it,

but we looked at what kind of arrangements could -

how you could understand the structure of glass.

So, it was basically a disordered system

and there were ideas floating around at that time

due to the French school particularly,

that maybe there are regular tilings in curved spaces and when

projected onto Euclidean space, they looked disordered the way they do.

That’s an oversimplified idea

but in that connection there were proposition,

there were suggestions to have

quote unquote Gauge Theory of Glass,

using the Gauge theory of defects and

dislocations and disclinations which had been developed

by people in continuum mechanics.

Now, that programme didn't really go too far at that time

but we decided to write a short monograph

explaining in very simple terms, the notions of symmetry, broken symmetry,

broken ergodicity

and then give an introduction to gauge theories in this context

and that was the Springer book which came out in '89,

it's called Beyond the Crystalline State,

because it dealt with things beyond the normal lattice dynamics of crystals.

We even included a little bit about quasiperiodicity,

incommensurate phases, Penrose tiling and so on.

Later on, much later, I wrote this book on Nonequilibrium Statistical Mechanics

based on the courses I have given here, basically [inaudible].

[Prof. S. Govindarajan] This was after retirement or - [Prof. Balakrishnan] Book was published in 2008,

but I had the, yeah, in the last year or two of retirement,

I had already started collecting material on this.

It was a set of notes that I had written when I was in Kalpakkam

as a report and then that got elaborated

and the book should have been written earlier but I just didn’t do it.

And then after 2010, I started collecting material

which I had been giving in earlier courses in Mathematical Physics

and it was - that book has been published this year,

late last year - early this year, that was a major effort.

It took me more years than I thought it would,

I thought I'd finish it in 2 years, it took me 4 times as long

or three and a half times as long.

And I know that you are working on

many more book projects and

so, what is your - what are you currently working on?

... When I started this Math Physics book seriously

I put on the backburner a book on problems

and solutions and non-Linear dynamics

which in all these books I wanted to have a - a point of view

before one would start writing a book.

And in the case of this Non-Linear Dynamics book,

the point of view is that I'd like to lay equal emphasis on

Hamiltonian or conservative systems as on dissipative systems

and equal emphasis on discrete time dynamics

as on continuous time dynamics.

So, maps and flows - with that view, I have several chapters already;

I'm well into the book I'd say about - it’s about two-thirds complete

and I hope to finish it fairly soon.

And what are the other projects in the annual?

Well, there are several research problems

which I should pay more attention to,

for which every now and then I get scattered away from it,

there's a kind of desire to write another book of problems and

solutions on conventional statistical physics.

I have the material ready, it's just got to be [inaudible]

I haven’t done that and then it has to be expanded

and that would be one thing which I...

I have a couple more distant dreams

but I am not sure whether - one at a time I think.

[Prof. C. S. Swamy, off-camera] Excuse me, by the time you joined, the Physics Department had

stopped doing demonstrations [inaudible] the first year students.

[Prof. S. Govindarajan] No. [Prof. C. S. Swamy, off-camera] The Physics Lecture Theatre, Chemistry Lecture Theatre,

they used to conduct the

[Prof. C. S. Swamy, off-camera] first year class because they had to show the demonstrations. [Prof. Balakrishnan] Oh yes, yes, oh yes.

[Prof. Balakrishnan] Well, even after I joined, this went on for many years and [Prof. S. Govindarajan] Even in 2014.

[Prof. S. Govindarajan] I actually had demonstrations. [Prof. Balakrishnan] Yeah.

[Prof. C. S. Swamy, off-camera] You had, is it? [Prof. S. Govindarajan] Yeah.

[Prof. C. S. Swamy, off-camera] Ah, because professor - from the time of Prof. Koch, [Prof. Balakrishnan] Yeah.

[Prof. C. S. Swamy, off-camera] And [inaudible], it had started. [Prof. Balakrishnan] Yeah, they...

[Prof. Balakrishnan] And in fact, they used to have the classes only in those days, that's the thing. [Prof. Balakrishnan] Yes.

the - the Lecture Theatre was built specifically

so that they could actually illustrate mechanics.

They had a lot of very beautiful demonstrations equipment,

piece of equipment from Germany

and in particular, they had this huge turntable

on which you could place 2 chairs

and then you could have a rotating frame of reference, illustrate

[Prof. Balakrishnan] all the non - inertial forces and angular momentum. [Prof. S. Govindarajan] Rotating wheel.

Yes, it’s a pity that these went out

partly because I think the curriculum got abbreviated,

got foreshortened; it was assumed.

I remember distinctly that in the '80s,

it was specifically stated almost that

students had already read those who got into IIT had already absorbed

what was in Resnick and Halliday.

And therefore, there was no reason to repeat

elementary mechanics anymore

and it got an early - you know, it - it - it was discouraged to some extent,

the curriculum didn't have space for this and then

[Prof. Balakrishnan] gradually the number of... [Prof. S. Govindarajan] But still there were demonstrations.

We still have and I think it -

[Prof. S. Govindarajan] Few times. [Prof. Balakrishnan] wherever it's possible it should be revived,

but in the presence of - in the availability of

[Prof. Balakrishnan] very good animation and things on - [Prof. S. Govindarajan] And YouTube.

On YouTube, this has become a little per se

but I still think that a live demonstration - nothing like it, I mean.

I remember not too many years ago going to a school and then

they had issues with understanding

the 12th standard electromagnetic waves:

the idea that you have transverse waves

with electric and magnetic fields in perpendicular directions

oscillating and then a propagation in the third direction.

We have a beautiful piece of equipment where you have rods in

two perpendicular directions coloured differently and you rotate a

wheel and there's this beautiful wave

motion which appears to propagate

and that single piece of equipment is worth

dozens of pages in textbooks and explanations,

because all you have to do is to rotate this wheel

and students understand instantaneously

what polarization is and what transverse waves are.

So, in that sense, I think that these demonstrations should be

to the extent possible, revived;

unfortunately, the classes are extremely large now.

And also my experience from 2014

was that we had 850 students

and so, PHLT can hold 200.

So, what we did -

we broke them up into 4 batches

and turns out that many of them were not interested because

attendance was not compulsory.

And ... the - when I mentioned this to

students who graduated maybe you know

6, 7 years ago; they said: sir, we used - may have bunked classes

[Prof. S. Govindarajan] but we never missed the demonstration. [Prof. Balakrishnan] Yeah.

Also you get chocolates, you are asked questions

and you you get chocolates and that was you know they said

you know I remember PHLT would be filled

and people sitting in the stairs,

you know not just - seats were not enough.

And ... but times have changed in some sense.

[Prof. C. S. Swamy, off-camera] I have another question, your notes for the NPTEL.

This is meant at the - for M.Sc. standard, Master's standard

or is it at the - the engineering students only,

the books - I mean, the lectures you are doing under NPTEL.

The courses on overview of classical physics

and overview of quantum physics

were specifically undergraduate courses,

they were part of the minor stream.

On the other hand, I did introduce topics especially

in the second course on quantum mechanics

in - in the course on quantum physics.

I did introduce some topics which were little more advanced

and the notes do contain some material which

is more advanced on operator theory and so on.

The courses on Mathematical Physics and Stochastic Processes.

[Prof. S. Govindarajan] Non-Equilibrium. [Prof. Balakrishnan] Non-Equilibrium Statistical Physics,

these are M.Sc. courses.

Those are M.Sc.-level courses.

Although in all the courses that I have taught throughout my career at IIT,

they've always been open to undergraduates,

I've always given consent of teacher for whatever

to whoever wants to attend these courses.

Although, undergraduates maybe in the first

year or two may not be able to -

wouldn’t have enough background material to take these courses.

But in the third and fourth years I have had large numbers of undergrads

taking these courses as electives.

[Prof. C. S. Swamy, off-camera] The reason I asked you was, you know, Ramakrishnan, Venki.

He talks about the Berkeley lectures which

[Prof. C. S. Swamy, off-camera] he learnt in Baroda University. [Prof. Balakrishnan] Yes.

And of course, IIT Kanpur they were talking about Richard Feynman’s lectures.

And two volumes you know.

So, those are meant for the Bachelor’s level or at the Master’s level?

[Prof. C. S. Swamy] Feynman’s or. [Prof. Balakrishnan] Ok.

[Prof. C. S. Swamy] The Berkeley lectures. [Prof. Balakrishnan] Yeah. Let me take the Feynman lectures first,

he gave them in the early '60s to undergraduates.

But, as is well known from what he has said in - in the book itself,

as the lectures went on, more and more undergraduates dropped out

and more and more graduate students

and faculty members attended the lectures.

So, they were learning.

So, clearly Feynman’s viewpoint was so original

and things were so beautifully meshed together and brought in,

that it's only people who already had a knowledge of

the subject at some basic level could appreciate this.

So, it's like you know an exquisite music concert

and the lectures themselves apart from the

first volume's initial lectures reflect this

because the topics are absolutely eclectic.

Everything is brought together,

you see this incredible unity of the subject,

but it's not a textbook for beginners, certainly.

On the other hand, the Berkeley physics course was a deliberate effort

to have a 5 volume set of books

accessible to undergraduates

and it's my personal opinion that to this day, they remain the very best

set of textbooks for undergraduate physics.

Book 1 is on Mechanics, book 2 is on Electricity and Magnetism,

book 3 is on Waves and Oscillations.

4 is on quantum physics, 4 is on statistical physics

and 5 is on quantum physics or vice versa.

They're all written by extremely competent people,

very very good people and the textbooks are brilliant in their own way

[Prof. Balakrishnan] and they are at a lower level. [Prof. S. Govindarajan] Purcell's introduction.

[Prof. Balakrishnan] Purcell's introduction ... absolutely. [Prof. S. Govindarajan] of magnetism is.

So, each of the books is a gem

[Prof. Balakrishnan] Reif’s book on Statistics Physics is an absolute gem; [Prof. S. Govindarajan] Statistical Physics.

if a student reads - goes through those books,

he or she doesn't need anything else for undergraduate physics.

I would say B.Sc. Physics Theory you have.

Absolutely and I would say good part of the Master's too,

except for specialized subjects.

And in that sense I think the Berkeley Physics Course

which is available in an inexpensive edition in India today

is a great help and you know I very strongly recommend it to colleges,

to students everywhere in the country.

[Mr. Kumaran Sathasivam, off-camera] Professor Balakrishnan, can I ask you about the connection. [Prof. Balakrishnan] Yes.

that you mentioned with Professor Srinivasan, which brought you to IIT.

Can you tell us about that?

How did you brief [inaudible] about that?

I'm not very sure exactly, I don't recall exactly when I met him first.

There was in this of course, I came here in '76 and '77 as I mentioned

and Professor Srinivasan by that time already was well-known

to be the leading expert in lower temperature physics.

So, people in Kalpakkam were interested in this year.

And, on trips to Madras I have visited IIT during that time,

we'd come in a minibus to do various things in - in Chennai.

And, I've spent days in IIT and looked at the lower temperature lab

and got to know him then, we have a working helium plant, I mean.

It was fascinating absolutely.

And I got to know him then and Professor Srinivasan and my old

boss at Kalpakkam, Dr. G Venkatraman, a very well known

physicist from the Atomic Energy Department, they were close friends.

They are contemporaries and close friends,

I believe they were even college mates

maybe not...within a year or two of each other I guess, Presidency College.

And they knew each other very well.

So, I got to know Professor Srinivasan through Dr. G. V. as we call him.

And then he suggested that a course on Quantum Theory of Solids

kind of modernizing solid-state physics be framed

and taught in IIT and I think Dr. G. V. suggested my name for it.

[Mr. Sathasivam, off-camera] Was that for the - I mean, there were only M.Sc. students right?

There were only M.Sc. students in that course.

So, I started giving that course here,

I would come 3 days a week in the minibus

and then give the course and spend the day here and go back in the evening.

And, as the course got given, it - I - I had a full room

of people and they were not all the M.Sc. students,

there were many research scholars here

and there were students from the theoretical Physics Department

at I - at the University of Madras

because Professor Matthews heard that this course was being given

and he suggested I [inaudible].

It was not a credited course.

It was an M.Sc. elective.

So, I didn’t take care of the administrative part of the course,

since I was not a faculty member here. Yes.

So, I do not know who graded the course and who gave, you know,

who gave the grades and so on,

but it was an M.Sc. elective at that time... Oh, it was.

and... But you mentioned university students, how did they

how did the university students - Professor Matthews,

he is a contemporary of Professor Srinivasan and G. V.’s.

So, he heard about this course, I guess

and then he suggested that some of his students attend it here.

[Prof. S. Govindarajan] Just auditing, I guess. [Prof. Balakrishnan] They they would audit, they audited the course.

So, the notes that I made for this course, I did a lot of reading up and so on,

I wrote as a reactor research centre report, a big report

and sent it out to various people.

And I didn't take their suggestion,

people suggested that I should make it into a little book

and I should have done it at that stage, of course.

But the notes, the - the report was quite popular; many

copies were distributed to people and so on.

And then, in the second year in '77, Professor Srinivasan said

I should repeat it since people - it had been favourably received the first time.

And after that...he was - he expressed interest in my coming to IIT.

He said I should really come here and you know teach

and the opportunity didn't present itself till 1980 or so,

and then when I did, I did take his advice and applied.

It’s good for IIT sir,

I - I would like to also ask you about the colleagues

you had in those early years, in the 1980s

and about the facilities of the department at that time.

I'm pretty sure the facilities were nowhere near what they have now,

that's very obvious... As far as

I was concerned since the only facilities I needed were

[Prof. S. Govindarajan] Cyclostyling machine. [Prof. Balakrishnan] Paper and pencil and a waste basket.

So, I didn't feel the need for, you know, I didn't feel any lack of facility,

there was plenty of academic freedom here.

And... Professor Indiresan was the Director

and he essentially I think

had a lot to do with the the credit-based semester system here,

in this institute and he gave complete academic freedom to people

and... he introduced - I think he introduced relative grading,

I wouldn’t know because I don’t know

what the system was before I came here

but the very first courses that I taught in Physics-I, I still remember

we had to fit a Gaussian to it and then there was a...you gave

[Prof. C. S. Swamy, off-camera] Yeah, Gaussian. [Prof. Balakrishnan] You - you put cut-offs and then those who had

[Prof. Balakrishnan] full attendance were shifted into... [Prof. Swamy] Yeah, yeah.

[Prof. S. Govindarajan] That extra marks you had, right, [Prof. Balakrishnan] they were given a little extra thing

[Prof. S. Govindarajan] if you had at- [Prof. Balakrishnan] to move them to - if you were within a certain range.

So, it was an elaborate exercise.

I have one story to tell about

may not - my memory may not be totally accurate

to tell about the grading: the very first course that I taught

in in the undergraduate programme in '81.

It was Physics-I in the semester July to December of 1981

and out of the total number of students who took Physics-I,

the grades in those days were not S, A...

[Prof. S. Govindarajan] Just A B C D E. A B C D U. [Prof. Balakrishnan] A B C D E.

[Prof. Balakrishnan] There was A B C D and F. [Prof. S. Govindarajan] U

[Prof. S. Govindarajan] U for fail. [Prof. Balakrishnan] For fail if I remember correctly.

Yeah, there was an F for fail

and we drew this - I drew this histogram, there were four of us teaching it

and myself, Professor Srinivasan, Ramabhadran and Swaminathan

and we went strictly by the book.

We drew this graph, it was a beautiful Gaussian,

there were 240 students in the class and we gave this.

[Prof. Swamy] It was very difficult to get the Gaussian in this [Prof. Balakrishnan] Yes but the number of days

[Prof. Swamy] Small number. [Prof. Balakrishnan] given in the course was a handful,

like 6 or 7 out of 240 -

this created some comment because they said

I still remember being told this: they said,

well, the number's much larger in Chemistry,

it's much larger in Computer Science,

much larger in Mathematics.

How come it’s so hard in Physics? It’s impossible.

So, I...you know, I kind of shrugged my shoulders and said that’s what the

that’s what it says here, because if you did

1.2 times the standard deviation and you went beyond it

and gave A grades, that's the number and you,

by definition you've said A is outstanding or excellent,

B is very good, C is fair and D is marginal and E...F is fail.

So, I take that literally and the matter was taken up

and then I had to explain that...

I was asked whether physics was different in any way

to which I kind of said maybe intemperately I said: yes, it’s different.

And I was asked how, how it's, why is it so different?

Then I kind of tried to explain that while Mathematics was

something which, there was a set of rules

of calculus or whatever they were teaching, Real Analysis,

and if you mastered those rules, you mastered the subject.

Chemistry likewise, Chemistry they did not try to

explain the Quantum Theory of valence which is very hard.

They said there is this element, has this valence

and this valence and so on and that was the end of it

and Computer Science also was a set of rules.

But Physics was a situation where according to the syllabus we had,

you took a physical system and you changed,

you formulated a physical phenomenon in mathematical terms,

solved the equations that arose using mathematical tools

which the students who were just learning

and then reinterpreted the solution back in physical terms

and this two way translation is hard enough for professionals,

much harder for young students.

So, that's why Physics at that level is more difficult

than Chemistry or Mathematics or Computer Science;

at least so I thought, that is how I felt.

And in any case, this apparently had reached Professor Indiresan’s ears.

[Prof. S. Govindarajan] Wasn’t his daughter part of that class? [Prof. Balakrishnan] Pardon me.

[Prof. S. Govindarajan] His daughter. [Prof. Balakrishnan] I am not sure if she was also in that class.

She was. She was. She was in that class.

[Prof. Balakrishnan] Might have been. [Prof. S. Govindarajan] She is 1 year my senior so,

But in any case the grades

fell where they fell and

Professor Indiresan casually met me one day near the Ad Block

and by this time I realized post facto that it had gone to him

and so on because you know I stuck to the grades

and we - we as a team stuck to the grades and so on.

So, he said: it appears that you are very harsh in grading.

I said - I was taken aback and then he added as he passed by, he kind of said, "but fair."

So, it's ok and then he went off.

I still remember that and...

[Prof. S. Govindarajan] So, Professor Balakrishnan, thank you so much. [Prof. Balakrishnan] Thank you.

For giving the Heritage Centre your time.

[Prof. S. Govindarajan] Thank you very much again. [Prof. Balakrishnan] My pleasure, thank you.

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