Hamburg 2009 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 3: Quantengase: Dynamik in Gittern
Q 3.6: Vortrag
Montag, 2. März 2009, 12:00–12:15, VMP 6 HS-A
Exact local relaxation in a class of quantum lattice systems: Central limit theorems and experimentally accessible signatures — •Marcus Cramer1, Andreas Flesch2, Ulrich Schollwöck2, and Jens Eisert3 — 1Imperial College London, UK — 2RWTH Aachen, Germany — 3Universität Potsdam, Germany
A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial
state, the system will tend to equilibrate. We present a setting in which relaxation to a steady state is provably
exact, namely for the Bose-Hubbard model where the system is quenched from a Mott quantum phase to the
strong superfluid regime. We find that the evolving state locally relaxes to a steady state with maximum entropy
constrained by the constants of motion [1]. Our argument includes a quantum central limit theorem and
exploits the finite speed of information propagation. In addition, we present a setting—atoms in optical super-lattices—in which one can experimentally probe signatures of this local relaxation without the need
of addressing single sites [2]. This opens up a way to explore the convergence of subsystems to maximum entropy
states in quenched quantum many-body systems with present technology. We also outline generalizations to arbitrary
initial states and quasi-free dynamics.
[1] M. Cramer, C.M. Dawson, J. Eisert, T.J. Osborne, Phys. Rev. Lett. 100, 030602 (2008).
[2] M. Cramer, A. Flesch, I.P. McCulloch, U. Schollwoeck, J. Eisert, Phys. Rev. Lett. 101, 063001 (2008).