• DOI:10.1103/PhysRevE.86.031101
• Corpus ID: 22204325

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
        }
}

• F. Brandão, Piotr Ćwikliński, +3 authors M. Mozrzymas
• Published 15 August 2011
• Mathematics
• Physical review. E, Statistical, nonlinear, and soft matter physics

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.