Pure State Quantum Statistical Mechanics

Abstract

The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement and uncertainty relations. No additional randomness is added by hand and no assumptions about a priori probabilities are made, instead measure concentration results are used to justify the methods of Statistical Physics. The approach explains the applicability of the microcanonical and canonical ensemble and the tendency to equilibrate in a natural way. This work contains a pedagogical review of the existing literature and some new results. The most important of which are: i) A measure theoretic justification for the microcanonical ensemble. ii) Bounds on the subsystem equilibration time. iii) A proof that a generic weak interaction causes decoherence in the energy eigenbasis. iv) A proof of a quantum H-Theorem. v) New estimates of the average effective dimension for initial product states and states from the mean energy ensemble. vi) A proof that time and ensemble averages of observables are typically close to each other. vii) A bound on the fluctuations of the purity of a system coupled to a bath.

72 pages, 4 figures, thesis, comments highly welcome

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Cited by in corpus (9)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Dependence of decoherence-assisted classicality on the ways a system is partitioned into subsystems
• Einselection without pointer states
• A necessary condition for the thermalization of a quantum system coupled to a quantum bath
• Equilibration on average in quantum processes with finite temporal resolution
• Relative purity, speed of fluctuations, and bounds on equilibration times
• Interference in a two-mode Bose system with $N$ particles is typical
• The Copenhagen Interpretation Born Again
• Pure states statistical mechanics: On its foundations and applications to quantum gravity