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.

Decoherence wave in magnetic systems and creation of Néel antiferromagnetic state by measurement

“…The textbook procedure is to introduce an infinitesimal staggered magnetization h st , which breaks time reversal symmetry [5,[17][18][19]. The conjugate field h st points in a particular direction, e.g., the z direction, and alternates in sign when going from one sublattice to another.…”

Comment on “Space-Time Crystals of Trapped Ions”

“…1 before taking the limit v ! 0 [6]. TL effectively take limits in the wrong order and thus obtain a state with unbroken symmetries.…”

Smoothness and Monotone Decreasingness of the Solution to the BCS-Bogoliubov Gap Equation for Superconductivity

“…In [1] the gap equation in the Hubbard model for a constant potential was studied, and its solution was shown to be strictly decreasing with respect to the temperature. In this connection, for interdisciplinary reviews of the BCS-Bogoliubov model of superconductivity, see [8,9].…”