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Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons
Open accessAbstract
In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].
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Cites
Information theory and statistical mechanics
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.106.620 · Cited by 12,931
Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W., & Bloch, I. (2002) · Nature · doi:10.1038/415039a · Cited by 5,935
Boson localization and the superfluid-insulator transition
Fisher, M. P. A., Weichman, P. B., Grinstein, G., & Fisher, D. S. (1989) · Physical Review B · doi:10.1103/physrevb.40.546 · Cited by 3,512
Information Theory and Statistical Mechanics. II
Jaynes, E. T. (1957) · Physical Review · doi:10.1103/physrev.108.171 · Cited by 3,253
Transition from a strongly interacting 1D superfluid to a Mott insulator
Stöferle, T., Moritz, H., Schori, C., Köhl, M., & Esslinger, T. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.130403 · Cited by 1,047
Cited by
Many-body physics with ultracold gases
Bloch, I., Dalibard, J., & Zwerger, W. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.885 · Cited by 8,114
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems
Polkovnikov, A., Sengupta, K., Silva, A., & Vengalattore, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.863 · Cited by 2,562
Many-Body Localization and Thermalization in Quantum Statistical Mechanics
Nandkishore, R., & Huse, D. A. (2015) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031214-014726 · Cited by 2,376
Quantum many-body systems out of equilibrium
Eisert, J., Friesdorf, M., & Gogolin, C. (2015) · Nature Physics · doi:10.1038/nphys3215 · Cited by 1,255
Quasiparticle engineering and entanglement propagation in a quantum many-body system
Jurcevic, P., Lanyon, B. P., Hauke, P., Hempel, C., Zoller, P., Blatt, R., & Roos, C. F. (2014) · Nature · doi:10.1038/nature13461 · Cited by 863
Metadata
- Authors
- Rigol, M., Dunjko, V., Yurovsky, V., & Olshanii, M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-02-01
- Volume
- 98
- Issue
- 5
- Pages
- 050405-050405
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1970087737
- Cited by
- 1,578
- References
- 5
- FWCI
- 20.98
- Type
- journal article
- Language
- en
- Open access
- green
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- Rigol, M., Dunjko, V., Yurovsky, V., & Olshanii, M. (2007). Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons. Physical Review Letters. https://doi.org/10.1103/physrevlett.98.050405
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