Exact relaxation in a class of non-equilibrium quantum lattice systems
arXiv:cond-mat/0703314 · doi:10.1103/PhysRevLett.100.030602
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 study a setting where relaxation to a steady state is 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 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. Additionally, we show that for all periodic initial configurations, reminiscent of charge density waves, the system relaxes locally. We sketch experimentally accessible signatures in optical lattices as well as implications for the foundations of quantum statistical mechanics.
8 pages, 3 figures, replaced with final version
References in corpus (10)
- Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
- Evenly distributed unitaries: on the structure of unitary designs
- Quench dynamics across quantum critical points
- Strongly correlated fermions after a quantum quench
- General entanglement scaling laws from time evolution
- Evolution of entanglement after a local quench
- Teleportation fidelities of squeezed states from thermodynamical state space measures
- Unitarity, ergodicity, and quantum thermodynamics
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