Long-time asymptotics of the long-range Emch-Radin model

• Authors: Michael Kastner
• Languages of publication: EN

Abstracts

EN

The long-time asymptotic behaviour is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behaviour. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.

Keywords

EN

lattice spin models; approach to equilibrium; quasi-stationary states

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2012
• Volume: 10
• Issue: 3
• Pages: 637-644

Dates

published

1 - 6 - 2012

online

17 - 6 - 2012

Contributors

author

Michael Kastner

References

• [1] D. Lynden-Bell, R. Wood, Mon. Not. R. Astron. Soc. 138, 495 (1968)
• [2] W. Thirring, Z. Phys. 235, 339 (1970) http://dx.doi.org/10.1007/BF01403177[Crossref]
• [3] M. Kastner, Phys. Rev. Lett. 104, 240403 (2010a) http://dx.doi.org/10.1103/PhysRevLett.104.240403[Crossref]
• [4] M. Kastner, J. Stat. Mech.-Theory E 2010, P07006 (2010b) http://dx.doi.org/10.1088/1742-5468/2010/07/P07006[Crossref]
• [5] A. Campa, T. Dauxois, S. Ruffo, Phys. Rep. 480, 57 (2009) http://dx.doi.org/10.1016/j.physrep.2009.07.001[Crossref]
• [6] M. Antoni, S. Ruffo, Phys. Rev. E 52, 2361 (1995) http://dx.doi.org/10.1103/PhysRevE.52.2361[Crossref]
• [7] M. Joyce, T. Worrakitpoonpon, J. Stat. Mech.-Theory E 2010, P10012 (2010) http://dx.doi.org/10.1088/1742-5468/2010/10/P10012[Crossref]
• [8] A. Gabrielli, M. Joyce, B. Marcos, Phys. Rev. Lett. 105, 210602 (2010) http://dx.doi.org/10.1103/PhysRevLett.105.210602[Crossref]
• [9] J. Barré, F. Bouchet, T. Dauxois, S. Ruffo, Y. Y. Yamaguchi, Physica A 365, 177 (2006) http://dx.doi.org/10.1016/j.physa.2006.01.005[Crossref]
• [10] A. Antoniazzi, D. Fanelli, J. Barré, P.-H. Chavanis, T. Dauxois, S. Ruffo, Phys. Rev. E 75, 011112 (2007) http://dx.doi.org/10.1103/PhysRevE.75.011112[Crossref]
• [11] F. Bouchet, S. Gupta, D. Mukamel, Physica A 389, 4389 (2010) http://dx.doi.org/10.1016/j.physa.2010.02.024[Crossref]
• [12] P.-H. Chavanis, F. Baldovin, E. Orlandini, Phys. Rev. E 83, 040101 (2011) http://dx.doi.org/10.1103/PhysRevE.83.040101[Crossref]
• [13] M. Kastner, Phys. Rev. Lett. 106, 130601 (2011) http://dx.doi.org/10.1103/PhysRevLett.106.130601[Crossref]
• [14] G. G. Emch, J. Math. Phys. 7, 1198 (1966) http://dx.doi.org/10.1063/1.1705023[Crossref]
• [15] C. Radin, J. Math. Phys. 11, 2945 (1970) http://dx.doi.org/10.1063/1.1665079[Crossref]
• [16] F. J. Dyson, Commun. Math. Phys. 12, 91 (1969) http://dx.doi.org/10.1007/BF01645907[Crossref]
• [17] W. F. Wreszinski, J. Stat. Phys. 138, 567 (2010) http://dx.doi.org/10.1007/s10955-009-9889-8[Crossref]
• [18] G. A. Baker, Phys. Rev. 122, 1477 (1961) http://dx.doi.org/10.1103/PhysRev.122.1477[Crossref]
• [19] I. J. Lowe, R. E. Norberg, Phys. Rev. 107, 46 (1957) http://dx.doi.org/10.1103/PhysRev.107.46[Crossref]
• [20] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, C. W. Clark (Eds.), NIST handbook of mathematical functions (Cambridge University Press, Cambridge, 2010)
• [21] T. Kinoshita, T. Wenger, D. S. Weiss, Nature 440, 900 (2006) http://dx.doi.org/10.1038/nature04693[Crossref]
• [22] M. Rigol, Phys. Rev. Lett. 103, 100403 (2009) http://dx.doi.org/10.1103/PhysRevLett.103.100403[Crossref]
• [23] A. Relaño, J. Stat. Mech.-Theory E 2010, P07016 (2010) http://dx.doi.org/10.1088/1742-5468/2010/07/P07016[Crossref]
• [24] M. Cramer, C. M. Dawson, J. Eisert, T. J. Osborne, Phys. Rev. Lett. 100, 030602 (2008) http://dx.doi.org/10.1103/PhysRevLett.100.030602[Crossref]
• [25] A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011) http://dx.doi.org/10.1103/RevModPhys.83.863[Crossref]

Identifiers

DOI

10.2478/s11534-011-0122-4