PoS
How did you become familiar
with the problem of second-order phase transitions?
Patashinski
The problem was known in
Landau's school for a long time, and was frequently mentioned. Andrew
Borovik-Romanov and Yury Sharvin mentioned this problem in their lectures
for our low-temperature physics group. We were told that Landau theory does
not assume singularities in Landau expansion, and there may be
singularities. An example was
the Onsager solution of the 2D Ising model. Ginzburg and Levaniuk published papers and demonstrated
that some kind of singularity appears in perturbation theory due to
fluctuations, and there were other statements and papers stating that
singularities may be present.
PoS
Patashinski
Probably. I was too young at that time, and not an active participant in public
discussions. I had a talk with
Landau when I was working on Feynman diagram singularities and realized
that there are no interesting next steps here. I told Landau something like: "You are my official scientific
advisor, and this seems finished, so could you give me a new problem to solve?"
Landau looked at me with a smile (as he always did) and told me:
"Sasha, if I knew something which I felt worth recommending, I would
do this by myself. I don't provide topics to scientists. Attend the
seminar, read the literature, participate in discussions, and try to find
something for yourself. Then, come to me and we will discuss it."
I told him that there are two things I would like
to work on. One is the behavior of scattering amplitudes at extremely
high-energies; that was along the line I already worked. The second problem is singularities
in second-order phase transitions. Landau again looked at me with a smile, and told me that "you
are right in guessing the two most important problems for the future."
PoS
Would one of these problems be
considered more fundamental than the other one?
Patashinski
I am not sure I remember the words,
but I remember well this conversation, and the sense of the words. I was a student, and
what I said was rather a brave gesture, maybe too brave and too
self-confident. I was imbedded in a medium where ideas and problems were in
the air, and I was responsive. I simple-mindedly took two of the
highest-level problems around, without any clear ideas how to solve them. I
had some gut feelings that these
two things are connected. Some features of Feynman diagrams I played with, jumps
in singularity positions, some mathematical behaviors like the Stokes
phenomena in Bessel functions were in my imagination somehow related to
phase transitions. And the answer of Landau was -- I can't now remember the
exact words, but very close to what was said is, "these are really the
crucial problems, the rest is marginal."
PoS
Were you aware at the time that
Landau himself had spent six months or so working on the problems?
Patashinski
In this conversation, Landau
mentioned a much longer time. At the end of the conversation, he advised
that I rather do doable things and first get my PhD, a good salary, and
other material things, but think about these problems before going to bed,
and only once I comprehend those things should I start really investing time in these
great problems. He even added,
probably to encourage me, that maybe I will be the one who will push at
least one of these problems from the stagnation point, but there is no solution
in sight, and maybe no solution at all. "Well," I said, "but what about the Landau theory of
Phase Transitions." And here,
he said something that, as I had proven later, nobody had heard him saying:
"Oh, this is only a dirty speculation. I spent seven years trying to go beyond this speculation
and failed."
I never actually worked with
Landau on a day-by-day basis, it was probably impossible. Landau worked by
himself, not showing anybody that he's working hard. His method was based on his
unbelievable ability to concentrate, and get results by applying rather
elegant and nontrivial logic than brute force calculation. This, of course, was a hard job,
but he liked to show results as if he obtained them easily, and just a moment ago. He was not a person ready to show
you his sweat. We had many
talks in 1960-61, but mostly he would listen and make remarks, or tell
things and give advice about life.
PoS
How much did you know about
Onsager?
Patashinski
Very little. Only the main fact
of singularity in free energy, not the mathematics. The fact that there is
a solution of this two-dimensional problem, and there is a logarithmic
singularity in the heat capacity.
PoS
Did you know of the kind of
work that Voronel was doing?
Patashinski
Not at the time of this talk
with Landau, but in 1963, when we started the study of the lambda-point
in He-4. Voronel was an old
friend, from Kharkov times, of Pokrovsky. The experimental situation in critical
points, and Voronel's results, were frequent subjects of everyday discussions
I had with
Peter Alexeevich Strelkov. Strelkov was the Head of the Thermodynamics Department
in the Thermophysics Institute of the Siberian Branch of the Academy of
Science of the USSR. It was Strelkov who offered me my position there when
circumstances forced me in 1960 to search for a better-paid job, and
Strelkov took care of my needs. Strelkov probably was Voronel's scientific
adviser, or it looked to me this way. It was Strelkov
who turned my attention from high-energy to phase transitions. You can't
stay uninvolved when discussing a challenging situation on a daily basis.
PoS
But in 1962 Voronel already had
his experiments which indicated that--
Patashinski
In 1962, maybe, if one believes
in his experiments (some people had strong doubts, as I remember). The talk
with Landau took place, probably, in 1960, or maybe early in 1961.
PoS
But he didn't want to share any
of the speculation with you?
Patashinski
No, not at all. What he said
was like this: It can take at least five years before you could see a
result. But if somebody did not get any interesting results in five years,
he becomes neurasthenic, and then he will get no results at all. So, as your adviser, I urge you only
think about these problems at bed time for the next three years, and work
on something which has a solution, make your career, get your PhD, get a
salary, establish a position, then return to these problems. This advice was
kept in my memory, it was kind of a blessing and an obligation to return.
After the quasi-classics job was done, I still had things to do: to write my
PhD thesis, and the rest on Landau list. But, three years after the conversation almost passed, and
probably this moved me to make my declaration to Gorkov and Abrikosov. With all the discussions with
Strelkov, this was the next problem I wanted to attack, without having a
good idea of how. I was young and very much confident that, sooner or
later, I could find a solution of any problem.
PoS
When was your declaration?
Patashinski
This was at the end of 1962,
probably in December. I made my declaration to Gor'kov and Abrikosov, and
Khalatnikov could have been nearby -- I can not clearly see now the entire
scene in all the
details. I remember I felt like a victor at that time: we found the
solution of a challenging problem, and I kind of confirmed my class as a
theoretical physicist. Before that time, it was only Landau's
recognition -- the Feynman diagrams activity was not too popular with other
in the Kapitza Institute -- and I got many friends only because of Landau
being on my side, not because they appreciated what I did. Now, we were
selling a problem known to many. My statement about phase transitions
was first met with some kind of smile and laugh, but then it was taken more
seriously, and probably somehow pushed a decision that a Second School of
Theoretical physics would be organized in Odessa in May of 1963. The First
Odessa School took place a year or two earlier and was concerned with Debye
screening in high charge density systems and Bruckner-Sawada theory. The
aim of the Second School was to review, point by point, all mayor
achievements in second-order phase transitions.
PoS
And can you tell me who was the
institutional sponsor of this summer school?
Patashinski
There were no sponsors in the
American sense. Odessa
University was glad to host a meeting of practically all active theoretical
physicists, and did the organizational part. The logistics and program committee included local
Odessa people and people from Moscow, Leningrad, and Kharkov. You see, the Landau School worked
like one body and without formal assignments. Gor'kov and Abrikosov, and Pitaevsky, Dzyaloshinskii and
Khalatnikov were members of the Theoretical Department headed by Landau. Unfortunately, in 1963 there was no
Landau as a scientist. [Landau's catastrophic automobile accident took
place in January of 1962.]
PoS
But between 1961 and 1962
when you made your
declaration...
Patashinski
One reason why I actually
wanted to work on this problem, and not, say, on high-energy physics
problems, was my position in the Thermodynamic Laboratory. Peter Strelkov invited me on
weekends and weekdays to talk on physics matters and the research agendas for the
Thermodynamics Department, and what topics the PhD's who were working
experimentally should study. Voronel's work
came into the discussion, and other results and ideas. I saw a very, very current problem
where a step had to be made in understanding that could be chosen as the
direction for this institution work.
PoS
But your publications are still
not in high energy physics?
Patashinski
Sure. I was free to do whatever
I wanted. Strelkov was the Head and a very interesting person in his own
right. He actually was the one who was sent by Kapitza to bring home Landau
from prison, and he was a close ally to Kapitza in the Institute. He headed
a branch-off of the Kapitza Institute in Siberia. I started as a high-energy-oriented physicist -- at that
time Landau was working in high-energy, Sudakov was in the Institute of
Theoretical and Experimental Physics, a high-energy Institute, with
Pomeranchuk and Okun and others surrounding me during my diploma work, all
excited by high energy problems, and I became part of high-energy
community. In my institute in Siberia, I became a member of a condensed matter
community, with phase transitions and critical phenomena as a top problem
in the field. It was time for
me to work on this problem in order to help Strelkov and my new colleagues.
But, to be clear, I had no idea of how I would solve the problem, I simply
wanted to solve it, and this was the declaration.
PoS
What were you learning between
1959 and 1963 specifically? Were you studying liquid helium?
Patashinski
I learned all kinds of things. You
attend seminars, you talk to people, you read papers, you listen, mostly,
and discuss. I'm not a good reader, I like listening and discussing when
I am
interested. I had learned a
lot from Valery Pokrovsky in the course of our work on the quasi-classical
problem. Valery is a
universally educated scientist with extended knowledge in many branches of
mathematics and physics, and he is very good at teaching, maybe the best
teacher I ever
saw. I am sure I have not taught him as much as he has taught me. As for
helium, I had a lot of lectures, and a cryogenics practice as a student.
PoS
Were there some things that
were particularly important or influential to you even though you were
studying everything?
Patashinski
My curiosity, and some
education in experimental physics, resulted in frequent talks with
experimentalists, and I was frequently asked to help to understand this or
that experiment. Once, such an
experiment attracted the attention of Jakov Abramovich Zel'dovich, and
discussions of this experiments started good relations with Jakov
Abramovich who later became my very good older friend.
PoS
When you say an experiment,
which experiment?
Patashinski
Oh, the experiment was rather
of little importance. It was found that in silicon, diamond, and some other
dielectric materials, the thermal expansion coefficient becomes negative in
a limited range of temperatures, and the question was why? Well, I was in Moscow at the time
(1961), and after the Landau seminar I discussed this with Zel'dovich who
had shown vivid interest and seemed to intend to work on this effect. I came home and started working, and
soon I came out with a simple solution. In one of the next seminars, I met
Zel'dovich again, and explained my solution. Soon after, I got an offer to
join his team (he worked at that time on a very classified project). The offer
could give me good conditions and possibility to work with Landau and, of
course, with Zeldovich. I
would probably have accepted it, but Abrikosov gave me strong
counter-advice, mentioning selling my soul to the devil, and I walked away
from this offer.
PoS
Did you discuss superconductivity
with Abrikosov and Gor'kov during this period?
Patashinski
Never. And I had not studied it,
I have only one publication on superconductivity, with Pokrovsky and
Batyev, related to critical fluctuations, although in my first years in the
MFTI David Schoenberg's book on superconductivity was one of my favorite
readings. It probably was the decisive factor for my acceptance in the
Low-Temperature group.
PoS
In part because he's so
concise?
Patashinski
Yes, and well written, too.
PoS
Patashinski
Liquid helium was at the center
of our education in the Kapitza Institute, with special lectures and lab
work in different aspects of liquid helium, including how to produce the
liquid.
PoS
But you saw Ilya Lifshitz in
Moscow, and not Gor'kov, or what?
Patashinski
Ilya Michailivich Lifshitz
lived in Kharkov but frequently visited Moscow. He played an important role in my life. When Landau left the scientific
scene, Ilya Lifshitz and Zel'dovich were the top authorities for me, sometimes
very supportive when I needed support. I felt much better with the generation of physicists that
included Landau, and Eugene and Ilya Lifshitz, and Zel'dovich, and Leontovich,
and Ivan Obreimov, and Rumer, and Strelkov, and many other great people and
my friends, than I did with the next generation. It was a huge difference in
stance between this old generation of titans, and younger colleagues.
PoS
In 1962, did you know of
Buckingham and Fairbank's results?
Patashinski
We (Pokrovsky and I) had known their
papers, at least in 1963. We
knew Buckingham and Fairbank's work very well, and this played a rather
negative role in our work, because Buckingham and Fairbank's result was a
logarithm in heat capacity, and looking at the 2D Ising model logarithm
found by Onsager. We were mesmerized by this logarithm, and when we finally
got a logarithm we were satisfied -- too early, I would say.
PoS
How about Boguliubov and all of
this?
Patashinski
Of course we knew Bogoliubov's
work. We had the book on
Matsubara Green's Functions, written by Abrikosov, Gorkov, and Dzyaloshinskii,
and we had known the Belyaev technique for Bose-gas with condensate. As for
personal relations, I met Boguliubov a few times in my life. And I had
good relations with Shirkov.
PoS
At some point in the 1960s,
Shirkov tried to start an Institute of Theoretical Physics.
Patashinski
Yes, he headed a Theoretical
and Mathematical Physics Department in the Institute of Mathematics in Akademgorodok,
and I was a frequent quest in this department. Shirkov volunteered as an
opponent in my Candidate final defense.
PoS
I actually meant Boguliobov's
work on liquid helium. I mean, when do you get in?
Patashinski
Probably before we started
phase transitions. I knew this theory, this is kind of a canonical text in
theoretical physics. Before I really started working, I read the book of
Abrikosov and Gorkov and Dzyaloshinkii, but with no clear understanding of
what use I would have from these techniques.
PoS
This is when it comes out
[1961], or later?
Patashinski
I bought the book in Moscow and I
still have it; this was before we started working on phase transitions.
PoS
Well, there was also an earlier
review article which was--
Patashinski
There were many sources on
Green's functions. At the
beginning of our study, there was some strange idea of how to start this
phase transition stuff, a false model which was around. After my
declaration but before we started, when we came back to Akademgorodok, I
still had a lot of stuff to do, I had to get my PhD, and it took some time
to write down the thesis. In March of 1963, I defended my PhD thesis. Pokrovsky,
too, finished some formal stuff. Then, in few weeks, we decided "let's
start."
PoS
And his position at this stage?
Patashinski
Pokrovsky is six years older
than I am. He was head of a theory lab in a Radiophysics Institute, with
Rumer being director of the Institute. In 1962, the Novosibirsk Scientific
Center
was at the beginning, Pokrovsky
had a temporary office in one of the apartment buildings in Akademgorodok,
not too far from my apartment. The quasi-classics and the He works were done
there. We started the study of the lambda-point,
and very soon we were completely absorbed by this problem. We usually spent,
I think, about fourteen hours a day working together. At that time, I
had problems with my lower back, and there
was no time to go to a physician. Every day, I hobbled to the office, and
then we would start working and I would forget about my pain. About the
beginning of May, probably,
when it was time to go to Odessa, we had a rather unusual and strange
solution for Green's functions in a non-ideal Bose-gas at the lambda-point.
PoS
Patashinski
We had what was later published
in the 1964 paper, and earlier, in 1963, as a local publication. It was an attempt to solve all the
problems in one step, kind of--
PoS
Patashinski
Yes, and this problem was very
complex, there were so many details to understand and tie together and
adjust to other details. The first thing is to test that if you have a Hamiltonian
of an interacting field scalar, and calculate the statistical property of
it, this is enough. This was not clear enough. We tried at least to understand how this can happen
mathematically. We had studied
the problem in terms of Matsubara Green's functions, and found that the omega-equal-to-zero
terms are probably responsible for the singularity, and with this
assumption, we derived and analyzed the equations for the singularity using
Feynman-Matsubara diagrams. In
this part, my experience in Feynman diagrams appeared to be helpful. Then, after
many unsuccessful attempts of balancing the equations, we found this
strange construction.
PoS
I'm sorry to interrupt you, but
when you started working on theory of phase transition, what do you consider
is the problem to be solved? Deviation from mean field theory, or--
Patashinski
The goal was to get correlation
functions and then thermodynamic quantities by summing up the singular
parts of Matsubara diagrams. Matsubara technique was a well-developed
apparatus.
PoS
Patashinski
To explain, to calculate what
happens to Green functions that are the correlation functions for
fluctuations, and to thermodynamic quantities like heat capacity,
compressibility.
PoS
Because you knew that mean
field theory didn't work, I mean.
Patashinski
We tested this as hard as we
could. It was a common expectation
in part of the community, maybe from Voronel's experiment, certainly from
the Onsager solution, that somehow the Landau theory does not predict
the
actual behavior. And, as we learned later, about that time or slightly
later, there was an activity in fitting experiments with critical exponents,
and experimental work which favored the idea of some singularities. Ginzburg
and Levaniuk found arguments that there is a mechanism, related to fluctuations,
that can
destroy the Landau theory. One
thing that has to be mentioned here: at that time, there was a mathematical
technique, popular in the Landau School, of how to handle and sum up the
main singularities in series expansions like the Feynman diagrams. This
idea was used by Landau, Pomeranchuk, Ter-Martirosian, Sudakov, and others
to get what is called the Moscow Zero. A more compact but merely equivalent
way to do the same thing is provided by Renormalization Group, but this
technique was
developed later.
PoS
This is the summing of leading
coefficients?
Patashinski
Of leading singularities. You expect
to have a singularity that is defined by some funcion, but the only form
for this function you have is a series expansion. The idea of Landau was
that you have two variables, or parameters to look at, the one, say, alpha,
the fine constant of electrodynamics, and the other is a diverging integral
that you make finite by introducing a cut-off. In electrodynamics, the two quantities are alpha and the
logarithm of cut-off energy. Alpha by itself is a small parameter, but it
may come multiplied by a logarithm (in quantum electrodynamics) or
powers (in phase transitions) that diverges with the cut-off length vanishing
(or cut-off energy increasing). The idea is that your function can be
re-written in terms of new variables, one being alpha times log (in QED)
and the other simply alpha. Alpha times log may became large, so you cannot
use the expansion in this parameter, but you can expand in the alpha at a
given alpha times log. Landau
and the School developed a technique how to do this. Later, an equivalent
but somewhat less intuitive method was provided by the renormalization
group, the Gellman-Low equations or other techniques. I think that both
methods use the same assumptions, but the RG approach is easier to teach,
and it looks more like a closed theory, with less art and more regular science. When we started our study, the
Renormalization Group and the Gellman-Low equations were not too popular
with the School, it was considered that Boguliubov and Shirkov had done a
boring job by explaining something that can be obtained in a more intuitive
and physical way. You would be better off by resumming series. This was the
background for our attempt. We had actually used and extended this idea of resumming, reexpanding,
and so on. This was how we tried to solve the singularity problem.
PoS
So if I understand you
correctly, in 1964 when you get started--
Patashinski
We started about March of 1963.
PoS
The paper is submitted in
August of 1964.
Patashinski
As far as I can recall, it was
submitted in 1963, and published in 1964. And a preprint (an official form
of local publication at that time) was published in 1963 by the Siberian
Division. Then, it came to a long and mostly
unfriendly discussion, and it was a general rejection of these ideas by
some part of the scientific community. The most active foe of the ideas was,
probably, Abrikosov. We had many discussions inside Russia, and Russian
publications were slow to appear, usually about a year. Basically, in May
of 1963 the theory was done, and brought to the Odessa School. This Conference
started in a usual
way, participants analyzed most important papers like Onsager, Lee and
Yang, probably Buckingham and Fairbank. When the time came, Pokrovsky went
to present our theory; at that time, my style of presentation was known
to be
hard to follow, so Valery has to be the speaker for us. He made the presentation,
with very active questions asked, and statements made, and the smooth
passage of the
conference broke up. The conference stopped. No more lectures. One participant
even got a stomach problem during the presentation. The rest of the
conference was a bitter struggle for and against the theory.
PoS
What was the opposition, what
was the point?
Patashinski
The main force opposing the
theory was Abrikosov.
PoS
Patashinski
For me, yes it was. He was one
of my teachers, I had passed exams with Abrikosov as examiner. The other
thing is that he was close to Landau. It was a strong and restless opposition,
kind of ideological rejection. He expressed this
at some point, saying that there are assumptions in this theory which you
have to accept or not accept, you cannot prove or disprove them. He added: "I
do not accept." The self-similarity of fluctuations at different scales
(later, Kadanoff coined the term scaling for this property). This
self-similarity was actually the main, the core of our construction, and
we had come to this picture not without hesitation, so to say, because this
was a very dangerous statement in our apparatus. By resumming all diagrams
that we were able to resum, we derived integral-differential equations for
the correlation functions (the zero-frequency Green's functions), with the
right-hand part in the form of a series of expressions related to
irreduceable diagrams, each diagram containing only physical correlation
functions, and not the so called "bare" terms that are rather mathematical
artifacts but appear in the perturbation theory. When we attempted to balance
the
left-hand and the right-hand parts, we came to a difficult situation. The
power-law singularities and the homogeneous form of the dependence of Green
functions on distances (or momenta in the Fourier-representation) was our
ansatz that had to be justified. With this ansatz, each expression in the
right-hand part was singular. We tried to see the relations between the exponents
in different Green functions. It appeared
that assuming some form of the relations, we got the result less singular
that we need for consistency, or, for other relations, more singular. Only
for one special choice of relations was it possible to have a balance of
exponents, but in this case
all terms in the infinite series became equally singular. So, this was the
only possibility to have a power-law behavior and not to have imbalance at
the level of
exponents. This was, of
course, not a proof of existence because, except for exponents, the
homogeneous functions were to be matched, and this was not technically possible
to prove. The homogeneous form
of correlation functions, assumed from the beginning, was an expression of
similarity of fluctuations at different scales; with the special relations
between
exponents this became the now well known scaling relations in terms of
correlation functions.
The paper we sent to publish was
written in the Russian style of the time, brief and without considering general
relations not used at the end. In our talks and presentations, the special
values of critical exponents would appear at the very end. First everything
was done without specifying the binary correlation function exponents, and
only the relations between exponents for different order correlations were
used. It was meant that these basic
exponents have to be found from the solution of the equation. Then, an
additional assumption about the behavior of the four-point vertex resulted
in an exponent 3/2. The right
value, found later by Wilson and others, is only a few percent smaller that 2,
so our result here was of a very rough approximation. Much later, one of
my students, Mark Pal'chik, showed that one obtains these 3/2 terms in a
Wilson-like approximation starting from a conformal-invariant ansatz in
three dimensions (Wilson and Fisher made calculations extrapolating from
four to three dimensions). Besides
this, our theory had a general framework of how to simplify the math and reduce
the problem to that of a classical field, and some understanding of
universality of this reduction: the theory appeared insensitive to details
of the initial Hamiltonian. Later, in 1964, we found that in a superconductor, if you take into
account the interactions besides pairing, you'll get exactly the same
equations for the singularities as in the Bose-liquid.
PoS
...you mean the "Phase
transition in superconductors" [Sov. Phys. JETP 19 (1964): 1412, with
E. G. Batyev and V. L. Pokrovsky]?
Patashinski
Yes. This work has, probably,
to be redone, because we kept the 3/2 idea, but most of important results
are independent from the value of the exponent.
PoS
You demonstrate the equivalence
of phase transitions in superconductors and--
Patashinski
Superfluids. This paper was published a few
months later than the paper on Bose-liquid, and as in the first paper,
everything was fine except for the additional assumption of how to actually
calculate the critical exponent. In diagrams, logarithmic terms appear with our values of the
exponent. The additional assumption was a mechanism of cancellation of
these logarithms due to a kind of super-screening at the small-distance
length-scale. It can be now
understood that this assumption probably violates the renormalization symmetry. However, I believe (I still
believe) that the assumed mechanism will, at some point, help in understanding
why the fundamental non-dimensional constants (like the fine structure
constant) have their values. This mechanism of a precise screening is a
very rich idea in how a highly non-linear field-theoretical system
determines a non-dimensional physical charge. I thought at that time, apart
from phase transitions, that this mechanism may determine the fine constant,
because for wrong values of alpha some non-compensation of singularities makes
it impossible to have a self-consistent theory. To be frank, practically nobody understood, not to say
accepted, this idea in our first work, so we tried to find examples
and additional arguments in an Appendix to the first paper. In 1963, one outstanding scientist
understood this perfectly, and I was very impressed. In the fall of 1963, an All-Russian,
All-Union Conference on Solid-state physics was called in Moscow. This Conference become an
International meeting due to a representative American delegation that
included John Bardeen, David Pines, Paul Martin, and Leo Kadanoff. I'm not sure that there were no
other members, I met only with these mentioned.
PoS
Now, this is 1966, isn't it?
Patashinski
PoS
Patashinski
Yes, I am sure it was about
fall of 1963. At this time, our
situation in the scientific community we belonged to was really difficult.
As I realized later, there was an opinion that we were claiming results
we didn't have, and we were kind of paranoid on
this, so the best way to deal with us is to politely avoid any
discussion. This was adhered
to strictly; personal relations became cold. For me, it was even worse; I
had only an entry-level position in Siberia, and less past achievements
than Valery had. Fortunately,
the organizer of the conference was Ilya Lifshitz. We were invited. At the
day preceding the conference, my close friend from student times Theimuraz
Melik-Barkhudarov, who was at
that time a PhD student of Gor'kov, had to bring the American delegation
from the airport to the hotel. I went with him to the airport terminal. When
we went back to the hotel, there was little free space in the car (a Volga,
the full size Russian car),
with four Americans, Theimuraz, me, and the driver. It was a large car, but
still it was dense, and I remember that David Pines, who was more delicate
in construction, was sitting on somebody's lap.
PoS
Was Luttinger part of that
delegation?
Patashinski
I can't recall. I remember only
these four. On our way, and in
my really very bad English -- I hadn't spoken English at all, but I had
read a few English papers -- I tried to explain to David Pines and probably
to Bardeen, who listened a little bit, the essence of our theory. This appeared to be enough to
excite the curiosity of Americans. Then, the day came for Pokrovsky to
present our theory, and in a comment to his presentation we were publicly
declared wrong and paranoid --
PoS
I'm sorry, declared you wrong
and?
Patashinski
Well, something like "the
authors are paranoid in insisting on a wrong theory." Surprisingly, the
next to comment was Paul Martin. He took the scene and said that he was very
glad to listen to the talk and these ideas. "We ",-- I can still recall his
words—"we tried to do
something similar, but stopped short on a much earlier stage. He kind of
praised us for interesting ideas and achievement, and this was so important
to heal our
wounds, and kind of exonerate us. But this was not all. At the end of the
day, we were asked whether we would agree to give a seminar for the American
delegation. We agreed.
The seminar was long. John
Bardeen, and David Pines, and Leo Kadanoff and Paul Martin, all of them sat
on a sofa, in a seminar room. I remember well this room and our guests but
I cannot recall the building, it may be in the place where the conference
took place, or in Kapitza Institute. Pokrovsky was the presenter, and from
time to time I turned in giving short comments. We tried to show all the
details, and to offer argument and
counter-argument for all this stuff. John Bardeen had a huge pad to make
notes, and silently made notes on every point of what was told, but with
no words. The really active
listener was Kadanoff, who asked many questions and wanted to know details
and arguments and so on. This was up to the point when Pokrovsky started
to explain the idea of self-cancellation of accumulating logarithms. This
point was, as we were aware,
difficult to follow. This
appeared the only point when John Bardeen broke his silence and in a cracking
voice spoke loudly to the audience: "A non-linear eigenvalue
problem." Exactly what it was. I understood at this point that he understands
everything we are talking about, he simply had no questions because he
immediately got all the ideas. During our talk, which was very long, a
work-day conversation, our colleges who obstructed us came in and out, looking
if they're still sitting, these famous and well-respected Americans. Then
it was over,
and at the end of the meeting, John Bardeen took us by the shoulders and
told us something like : "I see you have troubles (I can't recall the exact
words but only the idea of what he had said) with your colleagues here. Don't
be upset, you are on a right track. In America, we are not afraid of new
ideas." I was glad of
this support. It was no Landau – as Abrikosov said earlier that Dau
(Landau) would either order us to shut up with this theory, or tell the rest
to
listen to us.
About two years later, during a
many-body conference in Akademgorodok, I asked David Pines why our theory
still had no recognition, and David told me something like, "There are not
many people in the world who can work on or discuss this theory. In Russia,
there are Gor'kov and
Abrikosov, but they don't accept your ideas. In America, it's probably only
Martin and Kadanoff. Martin is
probably too old, and Kadanoff is too young, but this is a matter of time.
PoS
So if I understand you
correctly, what you've explained to them was that you can demonstrate
scaling relationships in different systems.
Patashinski
This talk was a very detailed
analysis of the future 1964 publication. It was in 1963, before the paper
appeared, but the presentation was much more detailed than the publication.
All sides of mathematical construction for a complex scalar, with how to
derive this and that, and how to handle the problem of self-consistent
treatment of fluctuations in conditions of a singularity.
PoS
That was what I was going to
comment on.
Patashinski
Our theory had the new equations
and scaling relations and understanding of the role of irreducible
correlations of all orders, which is actually what is called scaling now.
But the assumption we used to get the critical exponent was wrong. On our
way back home to Moscow we had a lengthy talk
with Isaak Jakovlevich Pomeranchuk, one of the authors of the Moscow Zero.
And he told us: Guys, we dealt with the same mathematical situation in a
four-dimensional space-time,
and at the end we got a zero interaction and a free field. So what's different
in your case? After some
analysis, we found the answer, which was described at the end of the first
paper.
[break]
Continue reading part III of the
interview.
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