00-503 Marco Merkli

Positive Commutators in Non-Equilibrium Quantum Statistical Mechanics (118K, Latex with an epic figure) Dec 19, 00

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Abstract. The method of positive commutators, developed for zero temperature problems over the last twenty years, has been powering progress in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics.\\ \indent We use the positive commutator technique to give an alternative proof of a fundamental property 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.

Files: 00-503.tex