title: 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.
authors.affiliation: Departamento de Física, Universidade Federal de Minas Gerais, Belo Horizonte, Caixa Postal 702, 30123-970, MG, Brazil.
authors.forename: Fernando G S L
authors.initials: FG
authors.lastname: Brandão
authors.forename: Piotr
authors.initials: P
authors.lastname: Ćwikliński
authors.forename: Michał
authors.initials: M
authors.lastname: Horodecki
authors.forename: Paweł
authors.initials: P
authors.lastname: Horodecki
authors.forename: Jarosław K
authors.initials: JK
authors.lastname: Korbicz
authors.forename: Marek
authors.initials: M
authors.lastname: Mozrzymas