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arXiv:1110.1189 · International Journal of Modern Physics B

BOGOLIUBOV'S VISION: QUASIAVERAGES AND BROKEN SYMMETRY TO QUANTUM PROTECTORATE AND EMERGENCE

A. L. Kuzemsky

Published Mar 29, 2010• 40 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1142/s0217979210055378

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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.
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.
The development and applications of the method of quasiaverages developed by N. N. Bogoliubov to quantum statistical physics and to quantum solid state theory and, in particular, to quantum theory of magnetism, were analyzed. The problem of finding the ferromagnetic, antiferromagnetic and superconducting symmetry broken solutions of the correlated lattice fermion models was discussed within the irreducible Green functions method. A unified scheme for the construction of generalized mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation was generalized in order to include the source fields. The interrelation of the Bogoliubov's idea of quasiaverages and the concepts of symmetry breaking and quantum protectorate was discussed briefly in the context of quantum statistical physics. The idea of quantum protectorate reveals the essential difference in the behaviour of the complex many-body systems at the low-energy and high-energy scales. It was shown that the role of symmetry (and the breaking of symmetries) in combination with the degeneracy of the system was reanalyzed and essentially clarified within the framework of the method of quasiaverages. The complementary notion of quantum protectorate might provide distinctive signatures and good criteria for a hierarchy of energy scales and the appropriate emergent behavior.
In the present paper we discuss the interrelation of the advanced interdisciplinary concepts of modern physics such as symmetry breaking, quantum protectorate, emergence and the Bogoliubov's concept of quasiaverages in the context of modern theoretical physics, and, in particular, quantum and statistical physics. The main aim of this analysis was to demonstrate the connection and interrelation of these conceptual advances of the many-particle physics and to try to show explicitly that those concepts, though different in details, have certain common features. Some problems in the field of statistical physics of complex materials and systems e.g. foundation of the microscopic theory of magnetism and superconductivity were pointed in relation to these ideas. The main suggestion is that the emphasis of symmetry breaking concept is on the symmetry itself, whereas the method of quasiaverages emphasizes the degeneracy of a system. The concept of quantum protectorate reveals essential difference in the behavior of the complex many-body systems at the low-energy and high-energy scales. Thus the notion of quantum protectorate might provide distinctive signatures and good criteria for a hierarchy of energy scales and the appropriate emergent behavior.
A concise survey of the advanced unifying ideas of modern physics, namely, spontaneous symmetry breaking, quasiaverages, quantum protectorate and emergence was presented. The interrelation of the concepts of symmetry breaking, quasiaverages and quantum protectorate was analyzed in the context of quantum theory and statistical physics. The main aim of this analysis was 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 a certain common features. Some problems in the field of statistical physics of complex materials and systems e.g. foundation of the microscopic theory of magnetism and superconductivity were pointed 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.
Strong-to-weak spontaneous symmetry breaking (SW-SSB) has recently emerged as a useful framework for studying phases of matter in open systems, quantum or classical. Beginning with the simple idea of extending symmetry breaking to general mixed states, and the familiar equivalence between canonical and grand-canonical ensembles in statistical mechanics, the concept has grown into a unifying perspective connecting many different ideas in physics, including topological orders, emergent hydrodynamics, and information-theoretic characterization of phases of matter. This review provides a bird's-eye view of some of these recent developments.