1208.1121 (Lorenzo Campos Venuti et al.)

Gaussian Equilibration    [PDF]

Lorenzo Campos Venuti, Paolo Zanardi

A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here quasi-free Fermi systems where the Hamiltonian and observables are quadratic in the Fermi operators. We first prove a novel bound on the temporal fluctuations 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 \Delta\mathcal{A}/\bar{\mathcal{A}}=O(L^{-1/2}) where L is the dimension of the single particle space. We prove the conjecture analytically for the magnetization in the quantum XY model, and numerically for a class of observables in a tight-binding model.

View original: http://arxiv.org/abs/1208.1121