seminar: Quenching, relaxation, and a central limit theorem for quantum lattice systems
speaker: Marcus Cramer (Imperial College London)abstract: A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce a setting where relaxation to a steady state can be shown to be exact, namely for the Bose-Hubbard model where the system is quenched from a Mott quantum phase to the strong superfluid regime, accessible in experiments with ultracold atoms in optical lattices. We prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments, maximizing the entanglement, to a state which is different from the thermal state of the new Hamiltonian. Remarkably, in the infinite system limit this relaxation is true for all large times, and no time average is necessary. For large but finite system size we give a time interval for which the system locally "looks relaxed" up to a prescribed error. Our argument includes a central limit theorem for harmonic systems and exploits the finite speed of sound. We also show that for all periodic initial configurations, reminiscent of charge density waves, the system relaxes locally. We sketch implications for the foundations of quantum statistical mechanics.
timetable:
Mon 26 Mar, 10:50 - 11:20, Aula Dini
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