Convergence to equilibrium under a random Hamiltonian.

@article{Brando2012ConvergenceTE,
  title={Convergence to equilibrium under a random Hamiltonian.},
  author={Fernando G. S. L. Brand{\~a}o and Piotr {\'C}wikliński and Michal Horodecki and Paweł Horodecki and Jarek K. Korbicz and Marek Mozrzymas},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={86 3 Pt 1},
  pages={
          031101
        }
}
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… 

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