TY  - JOUR
A1  - Cramer, Marcus
A1  - Eisert, Jens
T1  - A quantum central limit theorem for non-equilibrium systems : exact local relaxation of correlated states
N2  - 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.
Y1  - 2010
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/32113
UR  - http://iopscience.iop.org/1367-2630
SN  - 1367-2630
ER  -