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Collective Phenomena

Lillian Hartmann Hoddeson, Helmut Schubert, Steve P. Heims, Gordon Baym

Published Oct 1, 1992• 35 citations
Publisher

Abstract

Abstract In the 1930s and 1940s, the quantum theory of solids dealt primarily with singleelectron phenomena. Although surprisingly many problems were solvable within this framework, some were not-for example, the explanation from first principles of superconductivity and the calculation of the cohesive energy of metals. A related problem, whose connection to superconductivity was recognized almost immediately, was the superfluidity of4He, discovered experimentally in 1937. More generally, phase transitions-ordinary liquid-gas and melting, as well as those to the superconducting, superfluid, and ferromagnetic states-lacked adequate theory. These various phenomena, unexplainable within a single-particle framework, depend strongly on the interactions between particles in the systems; today they are recognized as “collective” or “cooperative” phenomena.

DOI
10.1093/oso/9780195053296.003.0008

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Abstract In the 1930s and 1940s, the quantum theory of solids dealt primarily with singleelectron phenomena. Although surprisingly many problems were solvable within this framework, some were not-for example, the explanation from first principles of superconductivity and the calculation of the cohesive energy of metals. A related problem, whose connection to superconductivity was recognized almost immediately, was the superfluidity of4He, discovered experimentally in 1937. More generally, phase transitions-ordinary liquid-gas and melting, as well as those to the superconducting, superfluid, and ferromagnetic states-lacked adequate theory. These various phenomena, unexplainable within a single-particle framework, depend strongly on the interactions between particles in the systems; today they are recognized as “collective” or “cooperative” phenomena.
Abstract Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way. Their consequences in condensed matter systems are also explored. Eschewing advanced formal methods, the book uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-paired systems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity. The physical systems discussed include liquid 4-He, the BEC alkali gases, “classical” superconductors, superfluid 3-He, “exotic” superconductors, and the recently stabilized Fermi alkali gases.
Starting from first principles, this book introduces the closely related phenomena of Bose condensation and Cooper pairing, in which a very large number of single particles or pairs of particles are forced to behave in exactly the same way, and explores their consequences in condensed matter systems. Eschewing advanced formal methods, the author uses simple concepts and arguments to account for the various qualitatively new phenomena which occur in Bose-condensed and Cooper-pairedsystems, including but not limited to the spectacular macroscopic phenomena of superconductivity and superfluidity.
Superfluidity is one of the most striking manifestations of quantum mechanics at macroscopic scales, characterized by frictionless flow and the emergence of collective quantum phenomena. The theoretical foundation of superfluidity in fermionic systems was revolutionized by the Bardeen-Cooper-Schrieffer (BCS) theory, developed in 1957 to explain superconductivity in metals. This groundbreaking work provided a microscopic description of how attractive interactions between electrons near the Fermi surface can lead to the formation of Cooper pairs-correlated pairs of fermions that condense into a coherent quantum state. The BCS theory not only explained superconductivity but also laid the groundwork for understanding superfluidity in systems like liquid helium-3 and ultracold fermionic gases, becoming a cornerstone of condensed matter physics.
Quantum matter is everywhere, from the interiors of neutron stars to the electrons in everyday metals. Like ordinary, classical matter, it is made up of many interacting particles. In classical matter, however, it is possible to think of each particle as an individual entity, whereas in quantum matter Heisenberg's uncertainty principle prevents us from telling individual particles apart: their behaviour can only be described collectively. In spite of this, many types of quantum matter are well understood from a theoretical point of view. For example, the “electron liquid” that is responsible for the flow of electricity through ordinary metals, the magnetic properties of many insulating materials and the normal and superfluid phases of helium at very low temperatures have all succumbed to the probing of theorists.
Surprisingly, it was 30 years after the first liquefaction of (4)He in 1908 that the discovery that liquid (4)He is not just a 'cold' liquid was made. Below T = 2.18 K, it is a 'quantum' liquid which exhibits spectacular macroscopic quantum behaviour that can be seen with the naked eye. Since the observation of superfluidity in liquid (4)He is one of the greatest discoveries in modern physics, we present a day-to-day chronology of the tangled events which preceded the seminal discovery of zero viscosity in 1938 by Kapitza in Moscow and by Allen and Misener in Cambridge. On the theory side, London argued in 1938 that the microscopic basis for this new superfluid phase was the forgotten phenomenon of Bose-Einstein condensation (BEC) first suggested by Einstein in 1925. In 1941, Landau developed a very successful theory of superfluid (4)He, but it was not anchored in a microscopic theory of interacting atoms. It took another 20 years for theorists to unify the two seemingly different theories of Landau and London. Experiments on trapped superfluid atomic gases since 1995 have shone new light on superfluid (4)He. In the mid-1930s, London had emphasized that superconductivity in metals and superfluidity in liquid (4)He were similar. Experiments on trapped two-component Fermi gases in the last five years have shown that a Bose condensate is indeed the basis of both of these superfluid phases. This confirms the now famous Bardeen-Cooper-Schrieffer-BEC crossover scenario developed for superfluidity by Leggett and Nozières in the early 1980s but largely ignored until a few years ago. The study of superfluid (4)He will increasingly overlap with strongly interacting dilute quantum gases, perhaps opening up a new era of research on this most amazing liquid.
Liquids and solids, atoms and molecules, nuclei—all these clearly are interacting many-body systems. Even a nucleon may be regarded as a manyparticle system, not just because it is now known to consist of three quarks interacting via gluons, but because of the possibility in quantum field theory of virtual excitation of many particles from the vacuum. in the table page 56 we list some of the many-particle systems we encounter in the physical world at length scales that range from a few centimeters to a few fermis. Many of these systems exhibit phenomena—superconductivity in solids and fission in nuclei, for example—whose understanding does not follow immediately from knowledge of the constituents of the system and the interactions among the constituents, but requires new concepts and ideas. Many-body physics is the branch of theoretical physics that studies the new phenomena or “emergent properties” that arise from interactions among “elementary” constituents of a many-particle system and provides means and methods for carrying out precise calculations of such characteristic properties of these systems as may be compared with experimental results to verify hypotheses about the nature of the constituents and their interactions.