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arXiv · 1108.2985

Convergence to equilibrium under a random Hamiltonian

Fernando G. S. L. Brandão·Piotr Ćwikliński·Michał Horodecki·Paweł Horodecki·Jarosław Korbicz·Marek Mozrzymas
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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.

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Fernando G. S. L. Brandão, Piotr Ćwikliński, Michał Horodecki, Paweł Horodecki, Jarosław Korbicz, Marek Mozrzymas. 2012-08-30. Convergence to equilibrium under a random Hamiltonian. https://doi.org/10.1103/physreve.86.031101

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