Atomic theory of liquid helium near absolute zero. Offprint from Physical Review, Vol. 91, No. 6, September 15, 1953.

[Lancaster, PA and New York, NY: American Institute of Physics, 1953].

First edition, extremely rare offprint, of the first of Feynman’s important papers which provided a quantum mechanical explanation of the superfluidity of liquid helium at temperatures below the ‘lambda-point’ of 2.18K. “The dramatic announcement of superfluidity of liquid He4 in 1938 is one of the defining moments in modern physics” (Griffin, p. 1). In 1938, Pyotr Kapitza in Moscow and John Allen and Donald Misener in Cambridge (UK) discovered independently that, at sufficiently low temperatures, liquid He4 has zero viscosity. Phenomenological theories of this property of superfluidity were developed by Fritz London and Laszlo Tisza before World War II, and by Lev Landau in the 1940s. Successful as these theories were, they lacked an atomistic foundation. “Between 1953 and 1958, Feynman published a seminal series of papers on the atomic theory of superfluid helium … A significant part of Feynman’s central contribution was the demonstration that these phenomenological concepts arose directly from the fundamental quantum mechanics of interacting bosonic atoms with strong repulsive cores. One of his earliest helium papers [offered here] showed in detail how the symmetric character of the many-body wave function severely restricts the allowed class of low-lying excited states” (Selected Papers of Richard Feynman (2000), p. 313). Widely regarded as the most brilliant, influential, and iconoclastic figure in theoretical physics in the post-World War II era, Feynman shared the Nobel Prize in Physics 1965 with Sin-Itiro Tomonaga and Julian Schwinger “for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles.” No copies in auction records, or on OCLC.

Helium was first liquefied by the Dutch physicist Heike Kamerlingh Onnes (1853–1926) in 1908, who is best known for his discovery three years later of superconductivity in mercury at very low temperatures. “Kamerlingh Onnes also observed the transition to the related phenomenon of superfluidity in liquid helium in an experiment performed in 1908, without recognizing it. The nominal discovery of superfluidity came in 1937 when Pyotr Kapitza in the Soviet Union and John Allen and Donald Misener at Cambridge independently discovered it. Three papers were published, one after the other, in Nature on January 8, 1938. Appallingly, when Kapitsa was awarded the Nobel Prize in 1978, no mention was made of Allen’s simultaneous discovery, probably because of the dominance of Kapitsa’s group after the war” (Purrington, p. 337). (See Griffin for a detailed analysis of the relation between the work of Kapitsa and Allen & Misener.)

The most spectacular signature of the transition of liquid 4He into the superfluid phase is the sudden onset of the ability to flow without apparent friction through capillaries so small that any ordinary liquid (including 4He itself above the lambda transition) would be clamped by its viscosity; thus, a vessel that was ‘helium-tight’ in the so-called normal phase (i.e., above the lambda temperature) might suddenly spring leaks below it. Related phenomena observed in the superfluid phase include the ability to sustain persistent currents in a ring-shaped container; the phenomenon of film creep, in which the liquid flows without apparent friction up and over the side of a bucket containing it; and a thermal conductivity that is millions of times its value in the normal phase and greater than that of the best metallic conductors. Another property is less spectacular but is extremely significant for an understanding of the superfluid phase: if the liquid is cooled through the lambda transition in a bucket that is slowly rotating, then, as the temperature decreases toward absolute zero, the liquid appears gradually to come to rest with respect to the laboratory even though the bucket continues to rotate. This non-rotation effect is completely reversible; the apparent velocity of rotation depends only on the temperature and not on the history of the system” (Britannica).

The papers of Kapitsa and Allen & Misener “stimulated feverish activity in the period leading up to World War II, and in the 1950s developed into a major research area called ‘quantum fluids.’ The phenomenon of flow without any measurable viscosity suggested that liquid He4 below the transition temperature of 2.18K was some strange new phase of matter. Within a few weeks after the discovery, Fritz London [and Laszlo Tisza] suggested that this new phase might have some connection with the phenomenon of Bose-Einstein condensation (BEC). This was originally predicted by Einstein to occur in an ideal gas of atoms in a 1925 paper, but this had been largely discounted as wrong over the next decade” (Griffin, p. 1). Landau rejected the description of He4 below the lambda-point as an ideal Bose-Einstein gas, and proposed instead to derive the properties of the superfluid from a consistent quantum-mechanical approach to a fluid. His phenomenological ‘two-fluid’ model of superfluidity, published in 1941, led to his award of the Nobel Prize for Physics in 1962.

Then, in the spring of 1953, “Richard Feynman entered the scene. He set himself the task of providing a theoretical understanding of the problem of liquid helium on an atomic basis, which could only be done if one approached the problem from first principles. While he greatly admired Landau’s contributions to and successes in the field, Feynman pointed out several weaknesses in Landau’s theory. Notably, Landau’s quantum hydrodynamical approach treated Helium II [i.e., He4 below the lambda-point] as a continuous medium which right from the beginning sacrificed the atomic structure of the liquid and thus forestalled the possibility of calculating the various characteristics of the system, such as the various parameters, on an atomic basis … By writing ‘the exact partition function as an integral over trajectories, using the space-time approach to quantum mechanics’, Feynman could indeed derive a Landau-type energy spectrum [in the present paper]” (Mehra & Rechenberg, The Historical Development of Quantum Theory, Vol. 6, p. 1160).

In the abstract of the present paper, Feynman writes: “The properties of liquid helium at very low temperatures (below 0.5°K) are discussed from the atomic point of view. It is argued that the lowest states are compressional waves (phonons). Long-range motions which leave density unaltered (stirrings) are impossible for Bose statistics since they simply permute the atoms. Motions on an atomic scale are possible, but require a minimum energy of excitation. Therefore at low temperature the specific heat varies as T3 and the flow resistance of the fluid is small.”

Feynman’s only earlier paper on superfluid helium [‘Atomic theory of the lambda transition in liquid helium,’ Physical Review 91, pp. 1291-1301] dealt with the transition at the lambda-point “which signals the formation of a new phase Helium II (and the onset of superfluidity); this paper is necessarily quite different from those focussing on the low temperature behaviour” (Selected Papers, p. 314). Thus, this earlier paper was devoted to an explanation of the transition itself, rather than of the superfluid behaviour below the lambda-point.

“Today, it is generally accepted that the phenomenon of Bose-condensation underlies all the unusual properties of superfluid He4, superconductivity in metals, and superfluidity of liquid He3. More recently, the achievement of BEC in an ultra-cold

trapped gas of Bose atoms has opened up a whole new field of research into the superfluid properties and the coherent matter waves which arise in atomic gases. All this work, lying at the core of modern condensed matter and atomic physics, has put renewed emphasis on the historical importance of the dramatic and unexpected discovery of the superfluid behaviour in liquid He4 in the last months of 1937” (Griffin, p. 1).

The only other offprints of Feynman’s Physical Review papers we have ever seen on the market are two (on a different subject) we ourselves handled a few years ago. The present offprint derives from the estate of an officer of the Press Office of the Physics Department at Caltech, where Feynman spent most of his career.

Griffin, The discovery of superfluidity: a chronology of events in 1935-1938 (http://www.pi5.uni-stuttgart.de/lectures/89/Superfluidity%20article%202.pdf).



4to (266 x 200 mm), pp. 1301-1308. Self-wrappers, stapled as issued (punch holes in inner margin filled, not affecting text).

Item #4594

Price: $6,500.00

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