Düsseldorf 2007 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 17: Quantengase (Bosonische Gitter I)
Q 17.6: Vortrag
Dienstag, 20. März 2007, 11:45–12:00, 6J
Quenching, relaxation, and a central limit theorem for quantum lattice systems — Christopher Dawson1,2, Tobias Osborne3, Jens Eisert1,2, and •Marcus Cramer4 — 1QOLS, Blacket Laboratory, Imperial College London, Exhibition Road, London, SW7 2BW, UK — 2Institute for Mathematical Sciences, Imperial College London, Exhibition Road, London, SW7 2BW, UK — 3Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom — 4Institut für Physik, Universität Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany
A folk conjecture in the study of interacting quantum systems says that, independent of initial state, the system will tend to equilibrate. In this work we study a setting where relaxation to a steady state is exact, namely for the Bose-Hubbard model where the system is quenched from a Mott phase to the strong superfluid regime. We find that the evolving state locally relaxes to a steady state with maximum entropy constrained by the initial local energy. Remarkably, this relaxation is true for all large times, and no time average is necessary to obtain relaxation. Our argument makes use of a non-commutative central limit theorem for harmonic systems. Additionally, we show that for large finite blocks the system will also relax, but not to the thermal state of the new Hamiltonian. We outline generalisations to spin systems, sketch implications for the foundations of quantum statistical mechanics, and discuss signatures of relaxation in the experimental context of cold atoms in optical lattices.