PAPER: Quantum statistical physics, condensed matter, integrable systems Derivation of Bose–Einstein and Fermi–Dirac statistics from quantum mechanics: gauge-theoretical structure

摘要

A possible quantum-mechanical origin of statistical mechanics is discussed, and microcanonical and canonical ensembles of bosons and fermions are derived from the stationary Schr?dinger equation in a unified manner. The interaction Hamiltonians are constructed using discrete phase operators and the gauge-theoretical structure associated with them. It is shown how interaction Hamiltonians, stipulated by the gauge symmetry, generate the specific patterns of entanglement desired for establishing microcanonical ensembles. A discussion is also made about the interrelation between random phases and perfect decoherence in the vanishing-interaction limit.