Marco Merkli
Positive Commutators in Non-Equilibrium Quantum Statistical Mechanics
(118K, Latex with an epic figure)
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.\\
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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.