Convergence to equilibrium under a random Hamiltonian
Abstract
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.
Cite
@article{arxiv.1108.2985,
title = {Convergence to equilibrium under a random Hamiltonian},
author = {Fernando G. S. L. Brandão and Piotr Ćwikliński and Michał Horodecki and Paweł Horodecki and Jarosław Korbicz and Marek Mozrzymas},
journal= {arXiv preprint arXiv:1108.2985},
year = {2012}
}
Comments
11 pages, 1 figure, v1-v3: some minor errors and typos corrected and new references added; v4: results for the degenerated spectrum added; v5: reorganized and rewritten version; to appear in PRE