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• W1992032903 abstract "In this paper, as a personal review, we suppose a possible extension of Gibbs ensemble theory so that it can provide a reasonable description of phase transitions and spontaneous symmetry breaking. The extension is founded on three hypotheses, and can be regarded as a microscopic edition of the Landau phenomenological theory of phase transitions. Within its framework, the stable state of a system is determined by the evolution of order parameter with temperature according to such a principle that the entropy of the system will reach its minimum in this state. The evolution of order parameter can cause a change in representation of the system Hamiltonian; different phases will realize different representations, respectively; a phase transition amounts to a representation transformation. Physically, it turns out that phase transitions originate from the automatic interference among matter waves as the temperature is cooled down. Typical quantum many-body systems are studied with this extended ensemble theory. We regain the Bardeen–Cooper–Schrieffer solution for the weak-coupling superconductivity, and prove that it is stable. We find that negative-temperature and laser phases arise from the same mechanism as phase transitions, and that they are unstable. For the ideal Bose gas, we demonstrate that it will produce Bose–Einstein condensation (BEC) in the thermodynamic limit, which confirms exactly Einstein's deep physical insight. In contrast, there is no BEC either within the phonon gas in a black body or within the ideal photon gas in a solid body. We prove that it is not admissible to quantize the Dirac field by using Bose–Einstein statistics. We show that a structural phase transition belongs physically to the BEC happening in configuration space, and that a double-well anharmonic system will undergo a structural phase transition at a finite temperature. For the O(N)-symmetric vector model, we demonstrate that it will yield spontaneous symmetry breaking and produce Goldstone bosons; and if it is coupled with a gauge field, the gauge field will obtain a mass (Higgs mechanism). Also, we show that an interacting Bose gas is stable only if the interaction is repulsive. For the weak interaction case, we find that the BEC is a 'λ-transition' and its transition temperature can be lowered by the repulsive interaction. In connection with liquid 4He, it is found that the specific heat at constant pressure CP will show a T3 law at low temperatures, which is in agreement with the experiment. If the system is further cooled down, the theory predicts that CP will vanish linearly as , which is anticipating experimental verifications." @default.
• W1992032903 created "2016-06-24" @default.
• W1992032903 creator A5063055633 @default.
• W1992032903 date "2006-09-14" @default.
• W1992032903 modified "2023-10-14" @default.
• W1992032903 title "Extended ensemble theory, spontaneous symmetry breaking, and phase transitions" @default.
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