Brandão, Fernando G. S. L. and Ćwikliński, Piotr and Horodecki, Michał and Horodecki, Paweł and Korbicz, Jarosław K. and Mozrzymas, Marek (2012) Convergence to equilibrium under a random Hamiltonian. Physical Review E, 86 (3). Art. No. 031101. ISSN 1539-3755. https://resolver.caltech.edu/CaltechAUTHORS:20160526-082007335
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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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| Additional Information: | © 2012 American Physical Society. Received 21 November 2011; revised manuscript received 25 July 2012; published 4 September 2012. We would like to thank Robert Alicki for stimulating discussions. P.Ć., M.H., P.H., and J.K. are supported by Polish Ministry of Science and Higher Education Grant No. N N202 231937. F.B. is supported by a “Conhecimento Novo” fellowship from the Brazilian agency Fundacão de Amparo a Pesquisa do Estado de Minas Gerais (FAPEMIG). J.K. acknowledges the financial support of the QCS and TOQUATA projects. Part of this work was done at the National Quantum Information Centre of Gdańsk. F.B. and M.H. acknowledge the hospitality of Mittag Leffler Institute within the program “Quantum Information Science,” where part of the work was done. F.B. and J.K. acknowledge the kind hospitality of the National Quantum Information Centre in Gdansk, where part of the work was completed. | ||||||||||
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| Issue or Number: | 3 | ||||||||||
| Classification Code: | PACS: 05.30.−d, 05.20.−y, 03.65.Ud, 03.67.−a | ||||||||||
| Record Number: | CaltechAUTHORS:20160526-082007335 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160526-082007335 | ||||||||||
| Official Citation: | Convergence to equilibrium under a random Hamiltonian Fernando G. S. L. Brandão, Piotr Ćwikliński, Michał Horodecki, Paweł Horodecki, Jarosław K. Korbicz, and Marek Mozrzymas Phys. Rev. E 86, 031101 | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 67376 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | Tony Diaz | ||||||||||
| Deposited On: | 26 May 2016 19:19 | ||||||||||
| Last Modified: | 03 Oct 2019 10:05 |
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