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DY: Fachverband Dynamik und Statistische Physik

DY 6: Quantum Dynamics, Decoherence, and Quantum Information I

DY 6.9: Talk

Monday, March 14, 2011, 16:15–16:30, ZEU 255

Gibbs states, exact thermalization of quantum systems, and a certifiable quantum algorithm for preparing thermal states — •Arnau Riera, Christian Gogolin, and Jens Eisert — Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany

We present three results related to the emergence of thermal states in quantum physics: a) It is known that if a system and its suitable environment are in a microcanonical ensemble, the system is found in a canonical or Gibbs state. Here we introduce precise conditions for the stronger statement of canonical ensembles to emerge for almost all pure states in the subspace corresponding to the energy interval defined by the microcanonical ensemble: This argument makes an idea due to Goldstein et al.\ fully rigorous, including error bounds when employing counting arguments and introducing a precise weak coupling limit, completing an idea going back to Schr{\"o}dinger in 1952.\ b) We establish conditions when subsystems of quenched quantum systems equilibrate to Gibbs states, addressing thermalization -- in contrast to equilibration -- in non-equilibrium many-body dynamics. c) We finally present a first quantum algorithm for preparing Gibbs states with a certified runtime, including full error estimates, complementing quantum Metropolis algorithms which are expected to be efficient but have no known runtime estimate.