title: Gaussian equilibration.
abstract: A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time fluctuations of an observable A are typically exponentially small in the system size. We consider here quasifree Fermi systems where the Hamiltonian and observables are quadratic in the Fermi operators. We first prove a bound on the temporal fluctuations ΔA(2) and then map the equilibration dynamics to a generalized classical XY model in the infinite temperature limit. Using this insight, we conjecture that, in most cases, a central limit theorem can be formulated, leading to what we call Gaussian equilibration: observables display a Gaussian distribution with relative error ΔA/A[over ¯]=O(L(-1/2)), where L is the dimension of the single-particle space. The conjecture, corroborated by numerical evidence, is proven analytically under mild assumptions for the magnetization in the quantum XY model and for a class of observables in a tight-binding model. We also show that the variance is discontinuous at the transition between a quasifree model and a nonintegrable one.
authors: Department of Physics and Astronomy and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089-0484, USA.
authors: Lorenzo Campos
authors: LC
authors: Venuti
authors: Paolo
authors: P
authors: Zanardi
mesh_terms: D003198:Computer Simulation; D015233:Models, Statistical; D016011:Normal Distribution; D011789:Quantum Theory; D013816:Thermodynamics