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Q: Fachverband Quantenoptik und Photonik
Q 30: Quantum Information: Concepts and Methods V
Q 30.1: Vortrag
Mittwoch, 2. März 2016, 11:00–11:15, e214
Approaching equilibrium: Fermionic Gaussification — Marek Gluza1, •Christian Krumnow1, Mathis Friesdorf1, Christian Gogolin2,3, and Jens Eisert1 — 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany — 2ICFO-The Institute of Photonic Sciences, Mediterranean Technology Park, Barcelona, Spain — 3Max-Planck-Institut für Quantenoptik, Garching, Germany
When and by which mechanism do closed quantum many-body systems equilibrate? This fundamental question has been in the focus of attention for many years. It lies at the very basis of the connection between thermodynamics, quantum mechanics of many constituents and condensed matter theory. In the setting of free fermionic evolutions, we rigorously capture the time evolution in abstract terms and by basing our proof on intuitive mathematical concepts like Lieb-Robinson bounds, notions of particle transport and an algebraic expansion of operators, we uncover the underlying mechanism how local memory of the initial conditions is forgotten. Specifically, starting from an initially short range correlated fermionic states which can be very far from Gaussian, we show that if the Hamiltonian provides sufficient transport, the system approaches a state that cannot be distinguished from a corresponding Gaussian state by local measurements. For experimentally relevant instances of ultra-cold fermions in optical lattices, our result implies equilibration on realistic physical time scales. Moreover, we characterise the equilibrium state, finding an instance of a rigorous convergence to a fermionic Generalized Gibbs ensemble.