A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states

By M. Cramer, Jens Eisert. 2009

149 citations recorded by the source corpus.

We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states—pure or mixed—which have to satisfy merely weak conditions concerning the decay of correlations. The considered setting is a proven instance of a situation where dynamically evolving closed quantum systems locally appear as if they had truly relaxed, to maximum entropy states for fixed second moments. This furthers the understanding of relaxation in suddenly quenched quantum many-body systems. The proof features a non-commutative central limit theorem for non-i.i.d. random variables, showing convergence to Gaussian characteristic functions, giving rise to trace-norm closeness. We briefly link our findings to the ideas of typicality and concentration of measure.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b371485930b0e3d041d769deaba622b3852203ca

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Local random quantum circuits are approximate polynomial-designs: numerical results (2012, background): “[24] M.”
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems (2010, background): “This does not imply though that it can not reach a well defined asymptotic state in the long time limit (Barthel and Schollwöck, 2008; Cramer and Eisert, 2010).”