Out-of-equilibrium phase re-entrance(s) in long-range interacting systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 2, 2009, Pages

  Staniscia, F ^a,b   Chavanis, P H ^c,d   De Ninno, G ^b,e   Fanelli, D ^f  

^a UNIVERSITY OF TRIESTE   (Italy)

^b SINCROTRONE TRIESTE   (Italy)

^c UNIVERSITÉ PAUL SABATIER   (France)

^d CNRS   (France)

^e UNIVERSITY OF NOVA GORICA   (Slovenia)

^f UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EQUILIBRIUM PHASE; HAMILTONIAN MEAN FIELD MODELS; INTERACTING SYSTEM; LONG RANGE INTERACTIONS; MAGNETIZED STATE; NUMERICAL SIMULATION; PARAMETER RANGE; QUASI-STATIONARY STATE; SECOND-ORDER PHASE TRANSITION; SYSTEM SIZE; THEORETICAL PREDICTION; VIOLENT RELAXATION;

BELLS; COMPUTER SIMULATION; MAGNETS; MEAN FIELD THEORY; VEHICULAR TUNNELS;

PHASE TRANSITIONS;

EID: 70349513810     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.021138     Document Type: Article

References (39)

1. C. Timm and C. J. Pye, Phys. Rev. B 77, 214437 (2008). 10.1103/PhysRevB.77.214437
2. C. Güven, Phys. Rev. E 77, 061110 (2008). 10.1103/PhysRevE.77.061110
3. S. Han, S. Park, and B. Kim, Phys. Rev. E 79, 066114 (2009). 10.1103/PhysRevE.79.066114
4. M. Sellitto and J. Kurchan, Phys. Rev. Lett. 95, 236001 (2005). 10.1103/PhysRevLett.95.236001
5. C. Ekiz, Phys. Lett. A 332, 121 (2004). 10.1016/j.physleta.2004.09.057
6. L. Radzihovsky, EPL 36, 595 (1996). 10.1209/epl/i1996-00274-6
7. P. H. Chavanis, Astrophys. J. 471, 385 (1996). 10.1086/177977
8. T. Dauxois, Dynamics and Thermodynamics of Systems with Long Range Interactions, Lecture Notes in Physics Vol. 602, (Springer, Berlin, 2002).
9. M. Hénon, Ann. Astrophys. 27, 83 (1964).
10. F. Hohl and J. W. Campbell, Astron. J. 73, 611 (1968). 10.1086/110667
11. A. Taruya and M. Sakagami, Mon. Not. R. Astron. Soc. 364, 990 (2005). 10.1111/j.1365-2966.2005.09635.x
12. J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991). 10.1017/S0022112091000642
13. R. Kawahara and H. Nakanishi, J. Phys. Soc. Jpn. 76, 074001 (2007). 10.1143/JPSJ.76.074001
14. V. Latora, Phys. Rev. Lett. 80, 692 (1998). 10.1103/PhysRevLett.80.692
15. Y. Y. Yamaguchi, Physica A 337, 36 (2004). 10.1016/j.physa.2004.01.041
16. A. Campa, P. H. Chavanis, A. Giansanti, and G. Morelli, Phys. Rev. E 78, 040102 (R) (2008). 10.1103/PhysRevE.78.040102
17. X. P. Huang and C. F. Driscoll, Phys. Rev. Lett. 72, 2187 (1994). 10.1103/PhysRevLett.72.2187
18. H. Brands, P. H. Chavanis, R. Pasmanter, and J. Sommeria, Phys. Fluids 11, 3465 (1999). 10.1063/1.870204
19. J. Barré, T. Dauxois, G. De Ninno, D. Fanelli, and S. Ruffo, Phys. Rev. E 69, 045501 (R) (2004). 10.1103/PhysRevE.69.045501
20. C. Benedetti, Physica A 364, 197 (2006). 10.1016/j.physa.2005.08.054
21. A. Campa, Dynamics and Thermodynamics of Systems with Long Range Interactions: Theory and Experiments, AIP Conf. Proc. No. 970 (AIP, New York, 2008).
22. P. H. Chavanis, Eur. Phys. J. B 53, 487 (2006). 10.1140/epjb/e2006-00405- 5
23. A. Antoniazzi, D. Fanelli, J. Barre, P. H. Chavanis, T. Dauxois, and S. Ruffo, Phys. Rev. E 75, 011112 (2007). 10.1103/PhysRevE.75.011112
24. A. Antoniazzi, F. Califano, D. Fanelli, and S. Ruffo, Phys. Rev. Lett. 98, 150602 (2007). 10.1103/PhysRevLett.98.150602
25. A. Antoniazzi, D. Fanelli, S. Ruffo, and Y. Y. Yamaguchi, Phys. Rev. Lett. 99, 040601 (2007). 10.1103/PhysRevLett.99.040601
26. P. Chavanis, G. De Ninno, D. Fanelli, and S. Ruffo, in Chaos, Complexity and Transport, edited by, C. Chandre, X. Leoncini, and, G. Zaslavsky, (World Scientific, Singapore, 2008), p. 3.
27. D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967).
28. P. H. Chavanis, Ph.D. thesis, ENS Lyon, 1996.
29. M. Antoni and S. Ruffo, Phys. Rev. E 52, 2361 (1995). 10.1103/PhysRevE.52.2361
30. P. H. Chavanis, Physica A 359, 177 (2006). 10.1016/j.physa.2005.06.043
31. P. H. Chavanis, Statistical Mechanics of Violent Relaxation in Stellar Systems, edited by, N. Antonic, C. J. van Duijn, W. Jager, and, A. Mikelic, Proceedings of the Conference on Multiscale Problems in Science and Technology, (Springer, Berlin, 2002).
32. P. H. Chavanis, Eur. Phys. J. B 46, 61 (2005). 10.1140/epjb/e2005-00234-0
33. M. Antoni, EPL 66, 645 (2004). 10.1209/epl/i2004-10028-6
34. P. H. Chavanis, Astron. Astrophys. 432, 117 (2005). 10.1051/0004-6361: 20041114
35. P. H. Chavanis, Physica A 387, 787 (2008). 10.1016/j.physa.2007.10.026
36. R. Bachelard, C. Chandre, D. Fanelli, X. Leoncini, and S. Ruffo, Phys. Rev. Lett. 101, 260603 (2008). 10.1103/PhysRevLett.101.260603
37. L. P. Kadanoff, Statistical Physics Statics, Dynamics, and Renormalization (World Scientific, Singapore, 2000).
38. These parameters are related to those introduced in Ref. by U=∈/4+1/2, β=2η, f0 = η0 /N=μ/ (2π), k=2π/N, x=Δθ, y= (2/π) Δp, and the functions F in Ref. are related to the Fermi integrals by Fk (1/y) = 2 (k+1) /2 y I (k-1) /2 (y).
39. Here, the term "unstable" means that the homogeneous Lynden-Bell distribution is not a maximum entropy state, i.e. (i) it is not the most mixed state, and (ii) it is dynamically unstable with respect to the Vlasov equation. Hence, it should not be reached as a result of violent relaxation. One possibility is that the system converges to the spatially inhomogeneous Lynden-Bell distribution 8 with MQSS 0 which is the maximum entropy state (most mixed) in that case. Another possibility, always to consider, is that the system does not converge towards the maximum entropy state, i.e., the relaxation is incomplete (see Ref.).