Bogoliubov's Vision: Quasiaverages and Broken Symmetry to Quantum Protectorate and Emergence

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 domain of quantum statistical mechanics, quantum field theory and in the 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 a 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.

88 pages, 1 figure, Refs.426

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• Comment on "Space-Time Crystals of Trapped Ions": And Yet it Moves Not !
• Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems
• Updating the phase diagram of the archetypal frustrated magnet Gd3Ga5O12
• Electronic Transport in Metallic Systems and Generalized Kinetic Equations
• Unconventional and Exotic Magnetism in Carbon-Based Structures and Related Materials
• First principles derivation of NLS equation for BEC with cubic and quintic nonlinearities at non zero temperature. Dispersion of linear waves
• Physical limitations of the Hohenberg-Mermin-Wagner theorem
• Decoherence wave in magnetic systems and creation of Néel antiferromagnetic state by measurement
• An operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity (final version)
• Smoothness and monotone decreasingness of the solution to the BCS-Bogoliubov gap equation for superconductivity
• Antiferromagnetic order without recourse to staggered fields
• Fundamental Principles of Theoretical Physics and Concepts of Quasiaverages, Quantum Protectorate and Emergence
• An operator-theoretical study of the specific heat and the critical magnetic field in the BCS-Bogoliubov model of superconductivity
• Irreversible Evolution of Open Systems and the Nonequilibrium Statistical Operator Method
• Another operator-theoretical proof for the second-order phase transition in the BCS-Bogoliubov model of superconductivity
• An operator-theoretical study on the BCS-Bogoliubov model of superconductivity near absolute zero temperature
• Bogoliubov's Quasiaverages, Broken Symmetry and Quantum Statistical Physics
• Lipschitz continuity and monotone decreasingness of the solution to the BCS gap equation for superconductivity
• The BCS-Bogoliubov gap equation with external magnetic field and the first-order phase transition
• Bogoliubov's Vision and Modern Theoretical Physics
• Fundamental Principles of Theoretical Physics and Concepts of Quantum Protectorate and Emergence