Built on

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2011

Convergence to equilibrium under a random Hamiltonian

Brandão, Fernando G. S. L., Ćwikliński, Piotr, Horodecki, Michał et al.

Understand

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.

Built on

E. Bannai and T. Ito, Algebraic combinatorics I. (Benjamin/Cumming Publishing Company, 1984)
Original
1984
Earlier work this paper cites.
R. A. Horn and C. R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985)
1985
Earlier work this paper cites.
R. F. Werner, Phys. Rev. A 40
1989
Earlier work this paper cites.
W. Fulton and J.Harris, Representation Theory - A first Course (Springer-Verlag, New York, 1991)
1991
Earlier work this paper cites.
H. Tasaki, Phys. Rev. Lett. 80
1998
Earlier work this paper cites.
J. Gemmer, M. Michel, and G. Mahler, Quantum Thermodynamics , vol. 657 of Lecture Notes in Physics (Springer, Berlin, 2004)
2004
Earlier work this paper cites.
T. Kinoshita, T. Wenger, and D. S. Weiss, Nature (London) 440
2006
Earlier work this paper cites.
S. Popescu, A. J. Short, and A. Winter, Nat. Phys. 2
2006
Earlier work this paper cites.
S. Hofferberth, I. Lesanovsky, B. Fischer, T. Schumm, and J. Schmiedmayer, Nature 449
Original
2007
Earlier work this paper cites.
S. Chatterjee, J. Funct. Anal. 245
2007
Earlier work this paper cites.