Statistical mechanics of collisionless relaxation in a non-interacting system

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 369, Issue 1935, 2011, Pages 439-452

  De Buyl, Pierre ^a   Mukamel, David ^b   Ruffo, Stefano ^c,d,e  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c UNIVERSITY OF FLORENCE   (Italy)

^d INFN SEZIONE DI FIRENZE   (Italy)

^e UNIVERSITÉ DE LYON   (France)

Author keywords

Hamiltonian mean field model; Quasi stationary states; Vlasov equation

Indexed keywords

BELLS; DISTRIBUTION FUNCTIONS; EQUATIONS OF STATE; STATISTICAL MECHANICS; VLASOV EQUATION;

COLLISIONLESS; CONSERVED QUANTITY; DYNAMICAL BEHAVIORS; ENERGY DISTRIBUTION FUNCTIONS; INTEGRABLE MODELS; LONG RANGE INTERACTIONS; MEAN FIELD MODELS; MEAN-FIELD; NON-INTERACTING SYSTEM; NUMERICAL EXPERIMENTS; PENDULA; QUASI-STATIONARY STATE; SINGLE-PARTICLE DISTRIBUTION FUNCTION; ZERO FIELDS;

HAMILTONIANS;

EID: 79251488184     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2010.0251     Document Type: Article

References (39)

1. Dauxois, T., Ruffo, S., Arimondo, E. & Wilkens, M. (eds) 2002 Dynamics and thermodynamics of systems with long range interactions. Lecture Notes in Physics, vol. 602. Berlin, Germany: Springer.
2. Campa, A., Giansanti, A., Morigi, G. & Sylos Labini, F. (eds) 2008 Dynamics and thermodynamics of systems with long range interactions: theory and experiments. AIP Conference Proceedings, vol. 970. College Park, MD: American Institute of Physics.
3. Campa, A., Dauxois, T. & Ruffo, S. 2009 Statistical mechanics and dynamics of solvable models with long-range interactions. Phys. Rep. 480, 57-159. (doi:10.1016/j.physrep.2009.07.001)
4. Dauxois, T., Ruffo, S. & Cugliandolo, L. 2009 Long range interacting systems, Les Houches Summer School 2008. Oxford, UK: Oxford University Press.
5. Manfredi, G. 2001 Self-consistent fluid model for a quantum electron gas. Phys. Rev. B 64, 075316. (doi:10.1103/PhysRevB.64.075316)
6. Balescu, R. 1997 Statistical dynamics: matter out of equilibrium. London, UK: Imperial College Press.
7. Nicholson, D. R. 1992 Introduction to plasma physics. New York, NY: Krieger Publishing.
8. Braun, W. & Hepp, K. 1977 The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles. Commun. Math. Phys. 56, 101-113. (doi:10.1007/BF01611497)
9. Neunzert, H. 1984 An introduction to the nonlinear Boltzmann-Vlasov equation. In Kinetic theories and the Boltzmann equation (ed. C. Cercignani), pp. 60-71. Lecture Notes in Mathematics, no. 1048. Berlin, Germany: Springer.
10. Chavanis, P. H. 2008 Dynamics and thermodynamics of systems with long-range interactions: interpretation of the different functionals. In Dynamics and thermodynamics of systems with long range interactions: theory and experiments (eds A. Campa, A. Giansanti, G. Morigi & F. Sylos Labini). AIP Conference Proceedings, vol. 970. College Park, MD: American Institute of Physics.
11. Hénon, M. 1964 L'évolution initiale d'un amas sphérique. Ann. Astrophys. 27, 83-91.
12. Lynden-Bell, D. 1967 Statistical mechanics of violent relaxation in stellar systems. Mont. Not. R. Astron. Soc. 136, 101-121.
13. Antoni, M. & Ruffo, S. 1995 Clustering and relaxation in Hamiltonian long-range dynamics. Phys. Rev. E 52, 2361-2374. (doi:10.1103/PhysRevE.52.2361)
14. Elskens, Y. & Escande, D. 2002 Microscopic dynamics of plasmas and chaos. Bristol, UK: IOP Publishing.
15. Campa, A., Khomeriki, R., Mukamel, D. & Ruffo, S. 2007 Long-range effects in layered spin structure. Phys. Rev. B 76, 064415. (doi:10.1103/ PhysRevB.76.064415)
16. Dauxois, T., de Buyl, P., Lori, L. & Ruffo, S. 2010 Models with short and longrange interactions: phase diagram and re-entrant phase. J. Stat. Mech. June, P06015. (doi:10.1088/1742-5468/2010/06/P06015)
17. Messer, J. & Spohn, H. 1982 Statistical mechanics of the isothermal Lane-Emden equation. J. Stat. Phys. 29, 561-578. (doi:10.1007/BF01342187)
18. Bouchet, F. 2004 Stochastic process of equilibrium fluctuations of a system with long-range interactions. Phys. Rev. E 70, 036113. (doi:10.1103/PhysRevE.70.036113)
19. Bouchet, F. & Dauxois, T. 2005 Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics. Phys. Rev. E 72, 045103(R). (doi:10.1103/PhysRevE.72. 045103)
20. Yamaguchi, Y. Y., Barré, J., Bouchet, F., Dauxois, T. & Ruffo, S. 2004 Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model. Physica A 337, 36-66. (doi:10.1016/j.physa.2004.01.041)
21. Chavanis, P. H. 2006 Lynden-Bell and Tsallis distributions for the HMF model. Eur. Phys. J. B 53, 487-501. (doi:10.1140/epjb/e2006-00405-5)
22. Antoniazzi, A., Fanelli, D., Ruffo, S. & Yamaguchi, Y. Y. 2007 Nonequilibrium tricritical point in a system with long-range interactions. Phys. Rev. Lett. 99, 040601. (doi:10.1103/PhysRevLett.99.040601)
23. Antoniazzi, A., Fanelli, D., Barré, J., Chavanis, P.-H., Dauxois, T. & Ruffo, S. 2007 Maximum entropy principle explains quasistationary states in systems with long-range interactions: the example of the Hamiltonian mean-field model. Phys. Rev. E 75, 011112. (doi:10.1103/PhysRevE.75.011112)
24. Barré, J., Dauxois, T., De Ninno, G., Fanelli, D. & Ruffo, S. 2004 Statistical theory of high-gain free-electron laser saturation. Phys. Rev. E 69, 045501(R). (doi:10.1103/PhysRevE.69.045501)
25. Curbis, F., Antoniazzi, A., De Ninno, G. & Fanelli, D. 2007 Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser. Eur. Phys. J. B 59, 527-533. (doi:10.1140/epjb/e2007-00306- 1)
26. de Buyl, P., Fanelli, D., Bachelard, R. & De Ninno, G. 2009 Out-of-equilibrium mean-field dynamics of a model for wave-particle interaction. Phys. Rev. ST Accel. Beams 12, 060704.
27. Yamaguchi, Y. Y. 2008 One-dimensional self-gravitating sheet model and Lynden-Bell statistics. Phys. Rev. E 78, 041114. (doi:10.1103/PhysRevE.78. 041114)
28. Levin, Y., Pakter, R. & Rizzato, F. B. 2008 Collisionless relaxation in gravitational systems: from violent relaxation to gravothermal collapse. Phys. Rev. E 78, 021130. (doi:10.1103/PhysRevE.78.021130)
29. Teles, T. N., Levin, Y., Pakter, R. & Rizzato, F. B. 2010 Statistical mechanics of unbound two-dimensional self-gravitating systems. J. Stat. Mech. May, P05007. (doi:10.1088/1742-5468/2010/05/P05007)
30. Levin, Y., Pakter, R. & Teles, T. N. 2008 Collisionless relaxation in non-neutral plasmas. Phys. Rev. Lett. 100, 040604. (doi:10.1103/PhysRevLett. 100.040604)
31. Severne, G. & Luwel, M. 1986 Violent relaxation and mixing in non-uniform one-dimensional gravitational systems. Astrophys. Space Sci. 122, 299-325. (doi:10.1007/BF00650198)
32. Funato, Y., Makino, J. & Ebisuzaki, T. 1992 Violent relaxation is not a relaxation process. Publ. Astron. Soc. Jpn 44, 613-621.
33. Yamashiro, T., Gouda, N. & Sakagami, N. 1992 Origin of core-halo structure in one-dimensional self-gravitating system. Prog. Theor. Phys. 88, 269-282. (doi:10.1143/PTP.88.269)
34. Tsuchiya, T., Konishi, T. & Gouda, N. 1994 Quasiequilibria in one-dimensional self-gravitating many-body systems. Phys. Rev. E 50, 2607-2615. (doi:10.1103/PhysRevE.50.2607)
35. Pomeau, Y. 2008 Statistical mechanics of gravitational plasmas. Second Warsaw School of Statistical Physics. See http://www.fuw.edu.pl/?wssph/Lecture- notes/Pomeau.pdf
36. Sonnendrücker, E., Roche, J., Bertrand, P. & Ghizzo, A. 1999 The semi-Lagrangian method for the numerical resolution of the Vlasov equation. J. Comp. Phys. 149, 201-220. (doi:10.1006/jcph.1998.6148)
37. de Buyl, P. 2010 Numerical resolution of the Vlasov equation for the Hamiltonian mean-field model. Commun. Nonlinear Sci. Numer. Simul. 15, 2133-2139. (doi:10.1016/j.cnsns.2009.08.020)
38. Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1996 Numerical recipes in Fortran 90: the art of scientific computing, 2nd edn. New York, NY: Cambridge University Press.
39. de Buyl, P., Mukamel, D. & Ruffo, S. In preparation. Self-consistent steady states in Hamiltonian mean-field dynamics.