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Low Temperature Physics

On self-consistent determination of the quasi-average in statistical physics

Yu. M. Poluéktov

Published Sep 1, 1997• 4 citations
Publisher

Abstract

The concept of quasi-average introduced by N. N. Bogoliubov for describing the states of many-particle systems with spontaneously broken symmetry (superfluid liquids, superconductors, crystals, etc.) is generalized so that the fields introduced into the initial Hamiltonian for breaking its symmetry are not presumed to be given from outside, but are determined by the properties of the physical object itself and can be found by solving the system of equations in the self-consistent field approximation.

DOI
10.1063/1.593364

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The concept of quasi-average introduced by N. N. Bogoliubov for describing the states of many-particle systems with spontaneously broken symmetry (superfluid liquids, superconductors, crystals, etc.) is generalized so that the fields introduced into the initial Hamiltonian for breaking its symmetry are not presumed to be given from outside, but are determined by the properties of the physical object itself and can be found by solving the system of equations in the self-consistent field approximation.
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In the present interdisciplinary review, we focus on the applications of the symmetry principles to quantum and statistical physics in connection with some other branches of science. The profound and innovative idea of quasiaverages formulated by N. N. Bogoliubov, gives the so-called macro-objectivation of the degeneracy in the domain of quantum statistical mechanics, quantum field theory and quantum physics in general. We discuss the complementary unifying ideas of modern physics, namely: spontaneous symmetry breaking, quantum protectorate and emergence. The interrelation of the concepts of symmetry breaking, quasiaverages and quantum protectorate was analyzed in the context of quantum theory and statistical physics. The chief purposes of this paper were to demonstrate the connection and interrelation of these conceptual advances of the many-body physics and to try to show explicitly that those concepts, though different in details, have certain common features. Several problems in the field of statistical physics of complex materials and systems (e.g., the chirality of molecules) and the foundations of the microscopic theory of magnetism and superconductivity were discussed in relation to these ideas.
Abstract: A brief survey of the author’s works on the fundamental conceptual ideas of quantum statistical physics developed by N. N. Bogoliubov and his school was given. The development and applications of the method of quasiaverages to quantum statistical physics and condensed matter physics were analyzed. The relationship with the concepts of broken symmetry, quantum protectorate and emergence was examined, and the progress to date towards unified understanding of complex many-particle systems was summarized. Current trends for extending and using these ideas in quantum field theory and condensed matter physics were discussed, including microscopic theory of superfluidity and superconductivity, quantum theory of magnetism of complex materials, Bose-Einstein condensation, chirality of molecules, etc.
A brief survey of the author's works on the fundamental conceptual ideas of quantum statistical physics developed by N. N. Bogoliubov and his school was given. The development and applications of the method of quasiaverages to quantum statistical physics and condensed matter physics were analyzed. The relationship with the concepts of broken symmetry, quantum protectorate and emergence was examined, and the progress to date towards unified understanding of complex many-particle systems was summarized. Current trends for extending and using these ideas in quantum field theory and condensed matter physics were discussed, including microscopic theory of superfluidity and superconductivity, quantum theory of magnetism of complex materials, Bose-Einstein condensation, chirality of molecules, etc.