Under the Spell of Landau

The following sections are included:

• CONTENTS

• INTRODUCTION

• FROM THE EDITOR

The following sections are included:

• Landau's Theoretical Minimum

• Landau's Seminar

• Stories of the Creation of Some Works

• Landau's Personality

• The Leaflet

• References

The following sections are included:

• An “Ardent Communist”

• Landau as I Knew Him

• References

The outstanding theoretical physicist Arkady Benediktovich Migdal was one of the pioneers of theoretical nuclear physics in the Soviet Union, the founder of a major scientific school, a man of diverse gifts and irresistible personal charm. A. B. Migdal was born on March 11, 1911, in Lida (Belarus). In the 1920s his family moved to Leningrad. Migdal produced his first scientific work at age 17. He then enrolled at the physics department of the Leningrad State University (LSU), but studied there only a short while: arrested, he spent over two months under investigation, then was released (releases were still granted sometimes then). From 1931 to 1936, while working at the factory “Electrical Appliance,” he produced several scientific works. At this time he managed to recover a place at the LSU extension division. After graduation in 1936 A. B. Migdal enrolled in graduate school at the Leningrad Physical-Technical Institute, where he formed his research interests and his own research style. His thesis adviser was M. P. Bronshtein. [Note: See footnote, p. 171.] Despite the briefness of this contact with Bronshtein – in 1937 Matvei Petrovich was arrested and executed – this bright, talented and deep person played a major role in Migdal's scientific development…

In 1947 I became a second-year student at Moscow State University's Physics and Engineering Department, where a part of the week's classes were taught at base organizations. Our group's base was the future Kurchatov Institute, at that time known as the mysterious “Laboratory ,” and later as LIPAN. . Besides group lectures and practical work at the experimental laboratories, we also had access to the general seminars which Igor Vasilyevich Kurchatov tried to hold, with Leonid Vasilyevich Groshev filling in when he was absent. At the seminar, theorists spoke as welcome co-presenters and commentators. In 1949 I felt ready to approach A. B. Migdal to ask if I could transfer to his theoretical sector. In response, he suggested a number of simple qualitative problems, which I then successfully solved. (Incidentally, AB used the very same “introductory problems” for screening many generations of students.) So I wound up among AB's students. From 1952 on (for 10 years) I also served as an employee of the Migdal Sector. My memoirs here are mainly inspired by these years of constant communication with AB. After my departure for Novosibirsk in 1962, although our meetings still took place, they became occasional.…

The following sections are included:

• LAST CONVERSATION

• WHAT MIGDAL LOVED

These notes record things that live in my memory connected with Arkady Benediktovich Migdal. He entered my life when I was 17, and became my teacher…

I had the good fortune to be a student of A. B. Migdal – AB, as we called him in person or in his absence – and to work in the sector he headed at the Kurchatov Institute, along with his other students and my friends, including Vitya Galitsky, Spartak Belyayev and Tolya Larkin. I was especially close with AB in the second half of the 1950s, the years most important for my formation, and AB's contribution to this formation was very great. To this day, I've often quoted AB on various occasions, as it's hard to put things better or more precisely than he did; I tell friends stories heard from AB, because these stories enhance life as AB himself enhanced it; my daughter is named Tanya after AB's wife Tatyana Lvovna, and so on. In what follows, I'll recount a few episodes in my life in which AB played an important or decisive role, and then will share some other memories of AB…

Certain questions have long concerned me: how sure is the flow of life? In what way does it depend on the decisions we make and the paths we choose? This dependence almost always seems weak and short-lived, however much pride we may take in our foresight. But there are also special points when the line of our fate leads in multiple directions and choice decides everything…

I will always remember my first meeting with YaB . In the autumn of 1951, after my graduation from Moscow State University, I ended up as a teacher of physics and mathematics in a high school in a village called Belousovo in the Kaluga Region, 105 km from Moscow. Sitting in the evenings at dinner with the old peasant woman who kindly took care of me, and in whose izba (loghouse) I lived, I looked at my university notes and, listening to the rain beating on the window, beyond which was pitch darkness, I consciously bade farewell to the scientific activity for which I had prepared at university.

The following sections are included:

• Mother and Father

• "Scat" and the Family Name

• Brothers and Sisters, Children and Grandchildren

My father Yakov Abramovich Smorodinsky (Ya.A. hereafter) was born on December 30, 1917 in a small town of Malaya Vishera located about 100 miles south-east of St. Petersburg. His mother Roza Smorodinsky (Fitingof) originated from a big family. She married a young railroad engineer and a dance competition winner named Abram Smorodinsky, who died of typhus in 1921, when little Yakov was four years old. So, he was brought up solely by his mother…

Ya. A. Smorodinsky studied at the Leningrad State University from 1934 to 1939. When he entered the Department of Physics at the Leningrad University, this was the only department of physics in the Soviet Union, and continued as such for some time…

Yakov Abramovich Smorodinsky… memory brings me back to those far-off days when we first met in March 1952. We saw each other for the first time at the Hydrotechnical Laboratory (GTL) of the Academy of Sciences of the USSR, , where I obtained a position after graduation from The Physics Department of Leningrad State University. Already a well known professor, Yakov Abramovich (Ya.A.) was only eleven years older than me, a beginning physicist. Today, I would say that we were almost of the same age. We immediately liked each other, and worked closely together for 18 years until I moved back to St. Petersburg, at that time Leningrad, of course. I learned a lot from Ya.A. during those years: his intrinsic desire and ability to share his knowledge was a peculiarity of his talent…

This is a very brief contribution reflecting my intervention at the Conference on Symmetries in Physics dedicated to Yakov Abramovich Smorodinsky, held on March 27-29, 2008…

Shortly after its foundation in 1956 the Joint Institute for Nuclear Research in Dubna became an important training place for young physicists from Eastern-European countries. In those years I, too, was much younger than now, and from the late 1950s until the mid-1980s visited the Laboratory of Theoretical Physics many times for a few weeks. Discussions with Yakov Abramovich about particle physics and field theory were always interesting and instructive. When flavor SU(3) symmetry was discovered, his Dubna reprint review on the subject for me – and I think not only for me – proved to be a very helpful handbook during many subsequent years. Let me also tell you about an episode which I remember with gratitude…

Next to my parents, Yakov Abramovich was the person who had the greatest influence on my life. I would like to use this opportunity to say a few words about this influence, and mainly about him and his work…

I first heard of Yakov Abramovich when (being a student of the Leningrad State University) I read his papers written with Pomeranchuk and Landau [1]. Later, in my last year at the university, thinking about a possible future working place, I met G. Domokos who at that time was a researcher in Dubna. He gave me the advice to go to Dubna for a while and look for the possibility to work with Professor Smorodinsky who was the broadest-minded physicist he had ever met…

I knew Yakov Abramovich mostly as a child. That is to say, I was a child; Yakov Abramovich was over sixty. Years later, when I had to take charge of constructing my own intellectual environment, I realised what a luxury it had been to socialize with the adults who populated my childhood and for whom substantive conversations had been the norm, not an exception worthy of celebration. Among the many intellectual lighthouses who surrounded me, Yakov Abramovich was one of the brightest and most constant…

One can say that Karen Avetovich Ter-Martirosyan was one of the stars in the brilliant constellation of theoretical physicists dating back to the golden era of Soviet physics: a disciple of Yakov Frenkel and Lev Landau, he was one of the creators of the theory of (soft) strong interactions at high energies…

I was never a student of Karen Avetovich (Karen, as everyone called him behind his back) and never collaborated with him. I've never worked on Reggeistics – the area of high-energy physics that was close to his heart. For an understandable reason – a thirty-year age difference – I couldn't be his close friend. And yet I decided to write a few kind words about Ter-Martirosyan for a reason which will soon become clear…

Karen Avetovich Ter-Martirosyan was a remarkable physicist, one of the creators of the great ITEP theoretical physics school. He was a teacher of many brilliant theorists. The most known of them are probably three Alexanders: Alexander Polyakov, Alexander Migdal and Alexander Zamolodchikov. He was also one of my teachers and it is an honor and pleasure for me to write these notes…

Karen Avetovich Ter-Martirosyan (K.A.) was at once my teacher, scientific adviser, and collaborator. My communication with K.A. enormously influenced my life and career; he helped me to establish the basic values and principles that I try to follow in my everyday life and research activities…

Karen had tons of amazing students, and it's unfortunate that they could not contribute to this collection. They would have a lot of marvelous stories to tell, since they spent so many days and nights at Karen's house, enjoying Bella Artemievna's hospitality and kindness. Karen was a difficult person, with many eccentricities, but at the same time he was very kind and forgiving. When people he knew had troubles, he always did whatever he could to help them. I should add, however, that due to the many tragedies he had experienced in his family life, Karen's threshold for what counted as troubles was unusually high, and what others perceived as major problems struck him as the minor complications of everyday life…

A remarkable theoretical physicist, Russian Academy of Sciences corresponding member David Abramovich Kirzhnits (1926-1998) left us a multifaceted and brilliant scientific legacy. Basic to his scientific vision was an understanding of the unity of physics as a reflection of the unity of nature. “…This unity,” he said in his lectures for upper-level students at the Moscow State University department of physics, “emerges not only in the existence of general laws of nature, whose scope of action covers the widest range of scales – from 10⁻³³ cm (the submicroscopic world) to 10²⁸ cm (the Metagalaxy)… Moreover, it turns out that Nature also successfully uses specific physical mechanisms concurrently in the most diverse types of phenomena … such as the ‘superconductor’ mechanism for forming the masses of elementary particles”…

The following sections are included:

• A little about my parents

• Where the city of Chelyabinsk-40 will rise
  • Extension school
  • The “Collective Farmer” radio
  • German radio
  • Conversations by the radio
  • The Thirties

• The East Ural Radioactive Trace

In the mid-1950s, a new staff member appeared at the Theory Division of the Physical Institute of the Academy of Sciences (FIAN): David Abramovich Kirzhnits. A Moscow State University alumnus, after graduation he had been assigned to a large defense plant in the city of Gorky, where he had worked for several years as an engineer. He was “liberated” from there by Igor Evgenyevich Tamm, our department head, who managed to transfer him to FIAN. Igor Evgenyevich knew D. A. Kirzhnits – they had met in Moscow before Kirzhnits finished university. At that time Kirzhnits was performing thesis work with professor A. S. Kompaneyets as academic adviser. At his adviser's suggestion, D. Kirzhnits consulted with I. E. Tamm on questions pertaining to the thesis topic. I. E. Tamm took a great liking for the diploma student, and he even wanted to recruit D. A. Kirzhnits for the Theory Division immediately after graduation. But at that time (1949) this proved impossible for several reasons. First, D. Kirzhnits was, as they say, an “invalid of the fifth group” – a Jew – which during those years of violent struggle against cosmopolitanismb often proved an obstacle in looking for work. Second, during the years of mass repressions D. Kirzhnits' father had been arrested on treason charges (according to the charges, he had wanted to sell the Far East to Japan). After intensive investigation his father was released, but he lived only a little longer. Reports of this also could have impeded his acceptance. Third, Igor Evgenyevich didn't have enough weight in officials' eyes at that time and so was unable to overcome “first” and “second.”…

My parents recently found an old letter I had written them shortly before finishing the graduate program at the Physical Institute of the Academy of Sciences (FIAN) and which I myself had long since forgotten. My work was going well, but the future was unclear. I wrote that after graduate school maybe Zeldovich could offer me a job with him, but that “It'd be better if I went to the Food Institute but worked with Kirzhnits.”…

Gribov was an outstanding theoretical physicist, a deep thinker. His profound insights and results, powerful theoretical constructions lie at the heart of theoretical description of soft particle collisions at high energies. They continue to be used all over the world, both by theorists and experimentalists…

V.N. Gribov was incapable of sparing himself. All his life he has acted as passionately, as intensely as he did in his youth when he worked with Landau and Pomeranchuk and led the Theoretical Physics Department of the Ioffe Institute, and later of the Nuclear Physics Institute in Leningrad. For him “leading” meant simply hiring the most talented students to join the institute and then engaging in merciless, endless but fruitful discussions with them on the problems they worked on. He did not care who was right, he cared only about the right answer. Incidentally, only in physics did he push tirelessly to reach a decision. In conversations about literature or politics as a rule he argued mildly and kindly. Not that he did not have thoughtful and firm opinions about many questions, but because he seemed to realize that in these matters different standpoints were arguable…

This article is intended to make the physics world aware of the loss it suffered on August 13, 1997 when professor Vladimir Gribov passed away, all of a sudden, in Budapest where he was steadily recovering after a mild stroke…

Vladimir Naumovich Gribov was undoubtedly the greatest theoretician of the postwar generation in the USSR. Even a short list of his major scientific achievements is impressive: the theory of threshold multiparticle reactions, Gribov–Froissart projection; shrinkage of the diffraction cone at high energies; Gribov–Pomeranchuk factorization of the contribution of Regge poles; Gribov–Morrison selection rules; Glauber–Gribov theory of diffraction scattering on nuclei; Gribov Reggeon diagram technique; Abramovskii–Gribov–Kancheli rules; the Bjorken–Gribov paradox and Gribov generalized vector dominance; Gribov-Pontecorvo neutrino oscillation; the theorem of bremsstrahlung at high energies; the Gribov–Lipatov evolution equations of structure functions; Gribov copies, and much else besides…

It is really hard to write about Volodya. There are no words that can express my admiration for his talent and the charm of his outstanding personality. Time cannot soothe the pain of his untimely death. The passage of time only makes it worse, especially for the scientific world…

Anatoly Ivanovich Larkin – Tolya to his friends and colleagues – was born on October 14, 1932, in the small town Kolomna in central Russia. Later Larkin's family relocated to Novosibirsk and then to Moscow. At the age of 17, Tolya was admitted, as physics major, to Moscow Mechanical Institute which in 1953 became Moscow Engineering Physics Institute…

The following sections are included:

• Tolya's Parents and Teachers

• Tolya's remarks and jokes

• Remarks of his students, friends, and colleagues

• Our joint work began

• Larkin-Fest

• Anatoly Larkin's talk at Larkin-Fest

• Albert Schmid. Anatoly Larkin's Poster

• Sources

I write this note as a tribute to my good friend, Tolya Larkin, who left this life so suddenly and much too soon. Perhaps, some readers of this book would be interested in his personal traits and some of the events in his life that demonstrated his understanding of his place and mission in this world…

I first got the chance to study with A. I. Larkin in 1961, on the recommendation of V. B. Berestetsky. At this time Larkin worked under A. B. Migdal at the Institute of Atomic Energy and concurrently at the Moscow Institute of Physics and Technology's department of theoretical physics, which V. B. Berestetsky headed then…

I initially got acquainted with Anatoly Larkin at the first Odessa theoretical school, probably in 1959. Amid the brilliant company gathered in Odessa (Abrikosov, Khalatnikov, Gorkov, Keldysh, Perel, Pitaevsky), he astonished me at the time with his fundamentality, the soundness of his judgment and the ease of his receptiveness to new ideas. Later in Novosibirsk, where I lived then, Roald Sagdeev told me A. B. Migdal, Tolya's research supervisor for graduate work, had invited Tolya to move with him to Novosibirsk, to the Budker Institute of Nuclear Physics, with the promise of a fast-track academic career. Tolya refused, and then A.B., who held Tolya's opinion and collaboration in high regard, also decided to stay in Moscow…

Knowing Anatoly Ivanovich – Tolya for his friends and colleagues – for years I can't recall him ever writing mathematical expressions on a sheet of paper as he was usually solving problems in his head. Tolya was Homo Sapiens in its true, literal sense of this word. A side observer would hardly notice his mastery and deep understanding of modern methods of theoretical physics and mathematics as there were no piles of paper speckled with math symbols on his desk. But there was a blackboard in his office, all covered with fragments of problems he was discussing with various coauthors. He was famous among his students and coauthors for “falling asleep” in the chair in his office and then writing the solution on the board immediately after awakening…

The Institute I've been a part of since 1990 is unusual even for the U.S., with its whirlpool of foreign postdocs and researchers from all over the world. Out of six permanent members, only one – Keith Olive – is a genuine American. The rest of the faculty came in the early 1990s from the former Soviet Union, toward the beginning of a Great Exodus of physicists and mathematicians from the collapsed Soviet Empire. Our high proportion of researchers with Soviet back-ground came about as a matter of timing. The Institute officially came into existence in 1987, but its faculty search didn't start in earnest until 1989, when Larry McLerran was appointed Director…

Alexei Andreevich was born on July 1, 1934. During the war, he was evacuated to Kazan. In 1951 he enrolled at the physics department of Leningrad University. He graduated with honors in 1956 and then enrolled at the Ioffe Physical-Technical Institute. Among the teachers who influenced him most, in his view, were K.A. Ter-Martirosyan, I.M. Shmushkevich, L.D. Landau (with whom he once entered into a scientific dispute. more on this below) and of course his older colleague V.N. Gribov, with whom he did many joint works…

Alyosha and I kept up a friendship for a quarter of a century and were very close, although we lived in different cities – he in St. Petersburg, and I in Moscow. When I moved to America, we didn't see each other for years, but our closeness and understanding endured despite the distance. We met several times in America, at Princeton, and always started talking again as if in mid-word, as if our previous conversation had ended only the day before…

My story, you might say, reminds everyone of the well-known fairy tale about Cinderella: a provincial girl from Irkutsk winds up in Leningrad, where she meets…

It happened that our careers in physics – that of Boris Lazarevich Ioffe and mine – started almost simultaneously at the Institute of Theoretical and Experimental Physics (ITEP) in Moscow. Half a century later, my memories of this time are still vivid…

Now, when I am writing down these recollections, I can clearly see Bruno Maximovich arising in front of me, quite alive, with his invariable smile, humor, interest in people, craving for knowledge, his tact and profound democratism, owing to which he could speak equally freely to people of the highest positions and workers in a workshop, with his intolerance of any falsity and, especially, of ignorance in science, his readiness to give all support to new interesting experimental explorations…

The following sections are included:

• Glimpses of ITEP

• Seminars

• Ambassadors

• Students

• “Making physics”

• Penguins

• References

The following sections are included:

• Window to Freedom

• Gribov's Circle

• Physics and the Struggle for Truth

• Physicists and the State

• Contacts with the West

• References

One of the most prominent physicists of the 20th century, Lev Davidovich Landau, was at the same time a great universalist who made fundamental contributions in diverse areas of physics: quantum mechanics, solid state physics, theory of magnetism, phase transition theory, nuclear and particle physics, quantum electrodynamics (QED), low-temperature physics, fluid dynamics, atomic collision theory, theory of chemical reactions, and other disciplines.

The following sections are included:

• Introduction
  • Phase transitions
    • Spontaneous symmetry breaking, the mesoscopic description, universality
    • Classification of phase transitions; order parameters
    • Fluctuation theory
    • Dynamics of critical fluctuations

• Landau levels
  • Landau levels and the diamagnetism of metals
  • Magnetic oscillations: Shubnikov–de Haas and de Haas–van Alphen effects
  • Quantum Hall effect

• Landau–Zener transitions
  • History and formulation of the results
  • Applications
  • Development of the theory

• Acknowledgments

• References

The following sections are included:

• Introduction

• The Basis of the Theory
  • The Pomeranchuk theorem
  • Regge poles
  • Moving branch-points

• Two-body Processes

• Multiparticle Production Processes
  • Multiparticle structure of the Pomeron
  • Meson-cloud model
  • Cutting rules for Reggeon amplitudes
  • Space-time interpretation of Reggeon diagrams
  • Diffraction processes
  • Deep-inelastic processes

• Quantum Chromodynamics and the Pomeron

• Pomeron Interaction

• Conclusions

• Aknowledgments

• References

The Gross–Neveu model comprises quantum field theory of N Dirac fermions interacting via four-fermion interaction in one spatial and one time dimension. It was introduced in 1974 (shortly after quantum chromodynamics was discovered) by David Gross and André Neveu [1] as a toy model which mimics two crucial features of quantum chromodynamics: asymptotic freedom and spontaneous breaking of a chiral symmetry. The model is based on N Dirac (i.e. complex two-component) fermions, ψ¹, ψ², …, ψ^N. The Lagrangian of the Gross–Neveau model is

Two fermion fields are considered in a space of one dimension (and in time), with interaction of each field with itself and of the two with each other. The first term in the expansion of the vertex part in an asymptotic series of well known form is obtained. It is shown that within certain limits the renormalized charge can have an arbitrary (nonvanishing) value.

The following sections are included:

• INDEX