Erlangen 2018 – scientific programme
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Q: Fachverband Quantenoptik und Photonik
Q 10: Quantum Gases (Bosons) I
Q 10.2: Talk
Monday, March 5, 2018, 10:45–11:00, K 2.020
Quantum thermalization in isolated ultracold gases — •Marvin Lenk1, Anna Posazhennikova2, Tim Lappe1, and Johann Kroha1 — 1Physikalisches Institut, Universität Bonn, Germany — 2Department of Physics, Royal Holloway University of London, UK
Quantum thermalization, i.e., how an isolated quantum system with unitary time evolution can ever reach thermal equilibrium behavior, is a long-standing problem of quantum statistics. It has moved in the focus of attention due to realizations in ultracold gas systems. The eigenstate thermalization hypothesis (ETH) poses that, under certain restrictive conditions, a microcanonical average is indistinguishable from the expectation value w.r.t. a typical eigenstate. By contrast, thermal behavior is reached quite generally in a non-integrable quantum many-body system alone due to the vast size of the Hilbert space dimension D. In any realistic experiment, only a small subset of the quantum numbers defining a pure state can be measured, if D is sufficiently large. The Hilbert space spanned by the undetermined quantum numbers is traced over and, thus, forms a grand canonical bath [Ann. Phys. 1700124 (2017)]. We show that this mechanism is valid for a generic system of N interacting bosons in M single-particle levels by computing numerically exactly the time evolution of the reduced densitiy matrix, the entanglement entropy as well as expectation values and fluctuations for the observed subsystem. The thermalizing quantities are, thus, defined by the measurement itself and not restricted to local observables. For N≈ 25 and M≈ 5, D is already large enough for thermalization to occur. We also analyze the validity of ETH.