Positive Commutators in Non-Equilibrium Statistical Mechanics

Details Positive Commutators in Non-Equilibrium Statistical Mechanics Positive Commutators in Non-Equilibrium Statistical Mechanics

2004-10-04

arxiv.org/abs/math-ph/0410014v1

Comm. Math. Phys. 223, 327-362 (2001)

Physics

Mathematical Physics

1 figure

Scientific paper

10.1007/s002200100545

The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a fundamental property of a certain class of large quantum systems, called {\it Return to Equilibrium}. This property says that equilibrium states are (asymptotically) stable: if a system is slightly perturbed from its equilibrium state, then it converges back to that equilibrium state as time goes to infinity.

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