Regensburg 2016 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 4: Dynamics in many-body systems: Equilibriation and localization
(Joint session of DY and TT organized by DY)
TT 4.7: Vortrag
Montag, 7. März 2016, 11:15–11:30, H47
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 lies at the very basis of the connection between thermodynamics, many-body quantum mechanics and condensed matter theory. In the setting of free fermionic evolutions, we rigorously capture the time evolution in abstract terms and 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 locally cannot be distinguished from a corresponding Gaussian state. In this way, strongly correlated states, as encountered in the Fermi-Hubbard model, will become locally Gaussian during the evolution under a hopping Hamiltonian, leading to density-density correlations that factor according to Wick's theorem. 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 Generalized Gibbs ensemble.