The Life, Genius and Perseverance of Lev Davidovich Landau

Genius, that power which dazzles mortal eyes, Is oft but perseverance in disguise.
Henry Austin, Perseverance Conquers All

In 1962, the Nobel Prize in physics was awarded to Lev Davidovich Landau for his ground-braking theories concerning condensed matter, especially Helium. However, he could have easily obtained this honor in any number of subjects that his genius graced. His contributions to plasma and high-energy physics are substantial. He lectured on everything from superconductivity to Fermi liquids with a fervor and enthusiasm few could maintain, and with mathematical genius fewer still could match. He was one of the more influential and renowned experts in the relatively new quantum mechanics and nuclear theory. However, his substantial contributions to physics and science in general aside, his life as a man is equally as interesting against the tumultuous historical background in which he lived. Growing up in Russia through the revolution and horrific civil wars that followed, surviving the purges of Stalin's Soviet Empire, the subsequent Nazi invasion of the USSR, and the cold war that followed are but some of the events that obstructed Landau in his rise to prominence and eventual greatness. One must consider the remarkable personal triumphs along with the scientific achievements of Lev Davidovich Landau (Dau as he was affectionately known to his colleagues and friends), when examining his remarkable life.

A Raw Youth: The Adolescent Landau

Landau was born on January 22, 1908, in Baku, a central Russian city in what is modern day Azerbaijan. He was born into a family of scientists. His father worked as an engineer in the petroleum industry and his mother was a medical doctor. His only sibling was an older sister, who subsequently became a chemical engineer. Lev was an awkward child who disliked physical activities. With a scrawny frame, uncontrollable hair, and a large overbite, Lev was naturally shy and avoided socializing with peers his own age. Furthering the gap between him and other children was the fact his extraordinary intelligence was realized at an early age. He enjoyed the company of adults and eagerly sought conversation with them on any subject science to politics (this was the time around the Russian Revolution). Even from any early age, he was a firm believer in the ideals of the revolution and saw Marxism as the savior of humanity. His true gifts, however, remained in math. He was constantly working through geometry and algebra problems in his spare time. He completed all his high school math requirements by the age of seven, and completed high school itself by the age thirteen.

Being too young for the University, his parents opted to send Lev to a technical school, where he was expected to study economics. However, he hated the subject with a passion and a year later was allowed to leave for Baku University. He was there for two years under a chemistry/physics double major before leaving for the Department of Physics at the University of Leningrad (modern day St. Petersburg). It was here, at the tender age of 18, that landau had his first article published. It was on the theory of spectra of diatomic molecules and showed scientific refinement far beyond his years. The following year, 1927, he completed his studies at University of Leningrad and had his second paper published on the subject of the damping problem in wave mechanics. This was to be one of the trademarks of Landau's scientific work. Although he only put out 60 scientific papers in his lifetime, small by many standards, the material covered was thorough and was ranged from theories about stars to superconductivity, without any evident pattern. He would only publish a paper if it were thorough and well thought out by his tediously high standards.

A Most Fruitful Pilgrimage

Although his travels abroad lasted only a year in a half, they were so important in Lev Davidovich Landau's development as a theoretical physicist that it is necessary to mention it in some depth. When Max Born visited Leningrad, Landau made a very good impression on him. Through the recommendations of his professors and Max Born, Landau was given grant money and allowed to study abroad. He spent only a few weeks in Göttingen, where Born taught, but Landau quickly developed a reputation as someone never afraid to answer a question or donate his opinion. After his stay with Born, he moved on to Leipzig, where he took classes from Werner Heisenberg. Again, although he did not stay in Leipzig for very long, his stay was marked by many (often times, vehement) discussions with one of the fathers of quantum mechanics, a man who would win the Nobel Prize a few years later.

His final and longest stop on his European tour was in Copenhagen, where he worked under Nobel Prize winner, Niels Bohr. This would be the most fruitful tenure in his pilgrimage. In Lev, Bohr found a student of remarkable potential who he quickly grew to like despite their many differences. Bohr's influence on Lev was notable. Niels Bohr was a legendary teacher who gave a lot of attention to Landau. Although Landau had had several professors, both in Russia and abroad, Bohr was the only one that Landau considered his teacher in theoretical physics. Lev held on to this assessment all his life.

Because of what he felt as the illogical nature of shyness, Landau overcompensated, becoming a terribly condescending, aggressive speaker. In general conversation, he would almost become hostile rather than recede into the awkwardness he experienced throughout his youth. Although his determination, outspokenness, and confidence impressed many of his peers, it would be the same confidence and lack of restraint that would get him in trouble latter in his life. However, spending time with the legendary Niels Bohr had softened, if only slightly, Landau's ego for the better.

After a short stint at Cambridge studying under Dirac, funded by the Rockefeller foundation, Landau traveled to Zurich to work with Wolfgang Pauli. They had met previously at Bohr's school. Their meetings usually consisted of them yelling at each other till they were out of breath and exhausted. It was here that he came up with an extremely thorough analysis of diamagnetism, which would prove to be one of his most significant findings.

It was soon after this short, but productive trip that Landau published a paper on the diamagnatism of metals in the Journal of Physics he had postulated about while abroad. The paper focuses on the fact that up until that time, magnetic properties of electrons, excluding spin, were still related through binding in atoms. For free electrons, the result of solving the Hamiltonian involved is independent of magnetic field. Both of these require that quantum effects are ignored.

He starts by working on the Hamiltonian of a free electron in a magnetic field.

make up the velocities of the electron. By making p3 a constant corresponds to a Schrödinger function. In stead of solving the equation from the sum of the two independent terms, he uses a commutation relationship of

This reduces further to reveal the Hamiltonian of a linear oscillator. The eigenvalues of such a system are

E = (n + ½) eh/mc H

which the motion in the z direction is then added once more,

p₃² /2m

This equation now represents the translational motion of the electron. In order to solve for the eigenfunctions of this system, Landau eliminates one of the coordinates . Because the resulting equation in thus independent from the eliminated term, the equation can be written as an exponential equation.

Once again the corresponding Schodinger equation is akin to the harmonic oscillator. Setting the equilibrium point of the oscillator yields the complete eigenfunction, which is denoted by

d²Phi_n/du² + (2n + 1 - u2)Phi_n = 0.

It is important to note, that when a finite space in substituted for the assumed infinite space, the equation agrees with the Bohr Correspondence Principle, which Bohr had presented twelve years earlier in 1918. It simply shows in the limit that as the magnetic field, H, goes to zero, the equation reduces to that of classical mechanics or the usual eigenvalue distribution for free motion.

Zurich would be his last stop before returning to the Soviet Union. The years that lay ahead would prove to be both productive and trying for Lev Davidovich Landau.

A Time of Insight through Turmoil

The period nineteen thirties were a tense time for Landau, as for most of Russia. Following the death of Lenin, Stalin had usurped power from the other members of the communist triumvirate and began his horrific purges and five-year plans. Science in the Soviet Union, up to that point, had been ignored because of the political and social turmoil. However, this is when communist officials became more watchful that scientific findings and ideology coincided with political ideology. The theories expressed by Heisenberg and Bohr stated that there could be no strict determinism in quantum physics, which was deemed as totally contradictory to the political philosophy of the party leader who were trying to save the world through dialectical materialism. The jailing and exiling of many legitimate scientists took place because they did not conform to party ideal and many less than brilliant "scientists" were highly honored for what could be considered laughable work. During this time, Landau was working as the head of the Theoretical Department in Physics Technical Institute of the Ukrainian Academy of Sciences. He was given his doctorate without having to defend a thesis. This period saw the most production from Landau on papers from superconductors to theories of stars. This is also were he met his future wife, Concordia Terentievna, a young Ukrainian chemistry student.

By 1937, the Soviet Union had all but clamped down on its scientists as extremely valuable assets and restricted their travel on the paranoid notion that they would not return. It was then, by the invitation of renowned physicist Piotr Kapista, Landau took over the theoretical section of the Moscow Institute for Physical Problems. Kapista, like Landau, had virtually become a prisoner in his own country, no longer being allowed to travel abroad. Although Landau always professed to be a firm Marxist, believing it would be the salvation of humanity, he hated the current regime, especially Stalin. He remained vocal about it to the extent his students would plead with him to be less candid. Finally, in the winter of 1938, government officials dressed in civilian cloths picked up Landau at his home and brought him to the infamous Butyrskaya prison in central Moscow. There he was told he had been found guilty of spying for the Germans and sentenced to ten years in prison. (He was actually quite fortunate. Many political prisoners and "traitors" were sent into exile in Siberia.) After a year, his friend and colleague Kapista was allowed to visit Landau. After seeing the abysmal state that Lev was in and fully realizing that a man of his weaker constitution would not survive much longer in such conditions, Kapista took it upon himself to get Landau released. Risking certain prison or execution Piotr Kapista demanded that Landau be freed or his contribution to the Soviet scientific effort was over. The government finally relented, releasing Landau, but not after one of the more trying and frightening chapters of Lev Landau's life.

The Catharsis on the Physical States of Helium

The forties brought about a renewed scientific power in Landau. This was also the time when his first and only child was born. His son, Igor Landau, went on to become a experimental physicist. Still working in Moscow, he produced a number of theories on near liquids near absolute zero and superfluidity. It was soon after the terrifying experience that Landau published his quantum mechanical analysis of Helium II.

The area of study that was of most interest in the years following world war II were the theories of liquid helium, which was eventually the source of Landau's Nobel Prize. Helium 4 is a "Bose" type liquid. The defining charecteristic of a Bose liquid lies in the fact that when a system of bosons is cooled to near absolute zero, a large fraction of those particles can occupy the same quantum state of lowest energy. Drawing on the experimental findings of his good friend and brilliant colleague, Kapista, Landau attempted to express a theory for the odd nature of Helium II liquid state at low temperatures. When cooled sufficiently, liquid helium undergoes a further phase change to what is known as Helium II. Also, helium does not under go a phase change to a solid without pressure towards absolute zero. The real oddity of the Helium II as opposed to normal liquid helium was that Kapista reported "superfluidity" properties. This means that it seams to lack viscosity when passing through a slit or a capillary. Neither of these phenomena can be explained by classical mechanics and therefore, must be explained as quantum properties. The approach used by Landau was the basic idea that the equilibrium properties of helium II could be expressed on the basis of the energy spectrum of the elementary excitations possible in helium.

He begins his discussion on the subject by a rather in depth treatment of the quantisation of the motion of liquids. He starts with the classical equations for describing liquid motion by means of density, flow of mass, and the radius vector of the particle with its mass. He converts the theory to quantum by making the density and flow of mass quantities into operators. Using a combination of the classical representation of these equations and assumption about their quantum relationships (such as commutation and solving Hamiltonians).

The second area of investigation involves the exploration of the energy spectrum of a quantum liquid. In classical mechanics, the velocity is potential (curl of v = 0). However, in quantum mechanics would have a state in which v could equal a non-zero number, but arbitrarily small. Between the potential (curl of v = 0) and the "vortex" (v dose not equal zero), there can be no continuity. Therefore, there must be a finite, measurable gap between the lowest forms of these two types of motion. Although the gap or energy between these two states could not be calculated exactly, its order of magnitude was estimated in terms of the density and the mass by a factor of Planck constant. The potential part of the spectrum, referred to as phonons, correspond to longitudinal, or sound waves. In order for a liquid to take on superfluidity characteristics, the vortex motion must be higher then the potential motion because, as helium passes through a slit or capillary it cannot be slowed down by exciting an elementary excitation. The change in energy, which is equal to the energy function of the density and the density dot velocity) required for the excitation of a phonon or a roton (the vortex quasi-particle) must be negative. However, it is impossible to find a velocity sufficiently small to get a negative change in total energy, the excitation of the particles in the liquid cannot happen and the liquid cannot be slowed down. This is the proof of the superfluidity of helium II.

In the nineteen fifties, Landau turned his attention to another type of extremely cooled substance, Fermi liquids. Rather than bosons, Fermi liquids, such as the He 3 isotope, depend on the interaction of fermions. It is predicted that there would be some obvious anomalies between a "Bose" and a "Fermi" liquid based on this fact. Much the way he went about mathematically expressing the superfluid characteristics of Helium 4, Landau published a number of papers expressing his reasoning on the basis of the aforementioned Fermi liquids. He also did extensive work on the theory of superconductivity and nuclear theory.

However, the fifties were also a time of great political unrest die to the cold war between the Untied States and the Soviet Union. By this time, Landau was one of the most distinguished physicists in the world. He, like many of his colleagues, was recruited to head research towards the nuclear arms race. Although much of the progress on the first Russian atomic weapons were due to espionage, when considering the development of the thermonuclear bomb, also known as the hydrogen bomb, due credit must be given to its physicists. This is one area of the nuclear arms race in which the Soviet Union maintained a notable lead when they detonated their first thermonuclear weapon on a small island in Siberia in 1953.

An Icy Road in January

In January of 1962, Landau was in a severe traffic accident. Both his lungs had been punctured, his rib cage crushed, and his forehead was cracked open. What followed was one the most extensive efforts to save one man's life in the history of the Soviet Union. Four times he was pronounced dead and four times doctors brought him back to life. He was unconscious a period of 4 weeks, and he was only allowed to return home from the hospital two years later. Although he lived for another six years after the accident, Landau's career was over. His name appears on a few co-authored books after the accident, but his contribution to these was minimal. He never recaptured the genius and mathematical insight that had punctuated his life up to that point.

Final Thoughts and Reflections

Despite his impressive math skills, Landau's greatest asset was that he could always apply it to the physical. He saw the places that classical mechanics and contemporary theories failed and quickly applied the relatively new concept of quantum theory to explain the discrepancies. This can be seen in almost all of his papers from superconductivity and low temperature liquids to solid state physics. His greatest contribution is the wide application of quantum mechanics and physics to actual, physical systems.

The scientific achievements of Lev Davidovich Landau are notable. In his lifetime he authored or co-authored some 67 journal articles, books on relativity, nuclear theory and an eight-volume course in theoretical physics that, despite being written in 1938, continued to be published until 1980. However, his achievements become truly marvelous when one examines the turmoil that existed around him. Historians have conjectured about the possible state of Russian physics, and sciences in general, had the country not gone through so many chaotic changes. Truly, the same can be wondered about Landau. Despite his sometimes imposing, condescending nature, he was a man that was described by his friends and colleges as a deeply moral and kind hearted individual. Although the criteria to get into his physics programs was extremely high, he lavished attention on his students while the legend of his teaching ability grew to mythic proportions in the Soviet Empire. Despite his frailty, he always spoke his mind, regardless of the consequences. Although his genius was immortalized in the form of a long deserved Nobel Prize in Physics in 1962, his horrific accident in January of the same year serves as a somber reminder of his humanity and mortality.

Bibliography

1. Dorozynski, Alexander. The Man They Wouldn't Let Die. The MacMillan Company, New York, New York 1965.

2. Haar, D. ter Men of Physics: L. D. Landau. Pergamon Press, London, England 1965.

3. Landau, Lev D.; Smorodinsky, Ya. A. Lectures on Nuclear Theory. Consultants Bureau, New York, NY 1958.

4. Landau, Lev D. Encyclepedia Britanica Entry http://www.britannica.com/eb/article?eu=48133 (Accessed 5/03)

5. Lev Davidovich Landau. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Landau_Lev.html (Accessed 4/19)

6. Lev Davidovich Landau - Biography. http://www.nobel.se/physics/laureates/1962/landau-bio.html (Accessed 4/03)

7. Lifshitz, E. M., Lev Davidovich Landau. Biographical Memoirs or Fellows of the Royal Society, v. 15 1969 P. 141-58

(Left) Lev Davidovich Landau

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