Phase transitions in self-gravitating systems

International Journal of Modern Physics B

Volumn 20, Issue 22, 2006, Pages 3113-3198

  Chavanis, P H ^a  

^a UNIVERSITÉ PAUL SABATIER   (France)

Author keywords

Ensembles inequivalence; Gravity; Long range interactions; Negative specific heats; Phase transitions

Indexed keywords

EID: 33749256260     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979206035400     Document Type: Article

References (182)

1. T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens (eds.), Dynamics and Thermodynamics of Systems with Long Range Interactions, Lecture Notes Phys., Vol. 602 (Springer-Verlag, Berlin, 2002).
2. E. Abdalla and M. R. Tabar, Phys. Lett. B 440, 339 (1998).
3. J. J. Aly, Phys. Rev. E 49, 3771 (1994).
4. J. J. Aly and J. Perez, Phys. Rev. E 60, 5185 (1999).
5. V. A. Antonov, Vest. Leningr. Gos. Univ. 7, 135 (1962).
6. V. A. Antonov, Translation in IAU Symposium 113, 525 (1985).
7. E. B. Aronson, C. J. Hansen, Astrophys. J. 177, 145 (1972).
8. A. I. Artemiev, I. E. Mazets, G. Kurizki and D. O'Dell, Int. J. Mod. Phys. B 18, 2027 (2004).
9. J. Barré, F. Bouchet, T. Dauxois, S. Ruffo and Y. Yamaguchi, Physica A 365, 177 (2006).
10. J. Barré, T. Dauxois, G. de Ninno, D. Fanelli and S. Ruffo, Phys. Rev. E 69, 5501 (2004).
11. J. Barré, D. Mukamel and S. Ruffo, Phys. Rev. Lett. 87, 030601 (2001).
12. J. D. Barrow, Phil. Trans. R. Soc. Lond. A 310, 337 (1983).
13. B. Baumgartner, Commun. Math. Phys. 48, 207 (1976).
14. J. D. Beckenstein, Phys. Rev. D 9, 3292 (1974).
15. N. Bilic and R. Viollier, Phys. Lett. B 408, 75 (1997).
16. J. Binney and S. Tremaine Galactic Dynamics, Princeton Series in Astrophysics (1987).
17. W. B. Bonnor, Mon. Not. R. Astron. Soc. 116, 351 (1956).
18. F. Bouchet and J. Barré, J. Stat. Phys. 118, 1073 (2005).
19. A. Bracco, P. H. Chavanis, A. Provenzale and E. Spiegel, Phys. Fluids 11, 2280 (1999).
20. W. Braun and K. Hepp, Commun. Math. Phys. 56, 101 (1977).
21. P. Cally and J. J. Monaghan, J. Math. Phys. 22, 348 (1981).
22. G. L. Camm, Mon. Not. R. Astron. Soc. 110, 305 (1950).
23. R. D. Carlitz, Phys. Rev. D 5, 3231 (1972).
24. M. L. Chabanol, F. Corson and Y. Pomeau, Europhys. Lett. 50, 148 (2000).
25. S. Chandrasekhar, Astrophys. J. 74, 81 (1931).
26. S. Chandrasekhar, An Introduction to the Theory of Stellar Structure (Dover Publications, New York, 1942).
27. S. Chandrasekhar, Principles of Stellar Dynamics (University of Chicago Press, Chicago, 1942).
28. S. Chandrasekhar, Astrophys. J. 97, 263 (1943).
29. S. Chandrasekhar, Ellipsoidal Figures of Equilibrium (Yale University Press, New Haven, 1969).
30. P. H. Chavanis, Contribution à la Mécanique Statistique des Tourbillons Bidimensionnels. Analogie avec la Relaxation Violente des Systèmes Stellaires, PhD thesis (ENS, Lyon, 1996).
31. P. H. Chavanis, Mon. Not. R. Astron. Soc. 300, 981 (1998).
32. P. H. Chavanis, Astron. Astrophys. 356, 1089 (2000).
33. P. H. Chavanis, Statistical mechanics of two-dimensional vortices and stellar systems, in Dynamics and Thermodynamics of Systems with Long Range Interactions, eds. T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens, Lecture Notes Phys., Vol. 602 (Springer-Verlag, Berlin, 2002) [cond-mat/0212223].
34. P. H. Chavanis, Phys. Rev. E 65, 056123 (2002).
35. P. H. Chavanis, Astron. Astrophys. 381, 340 (2002).
36. P. H. Chavanis, Astron. Astrophys. 381, 709 (2002).
37. P. H. Chavanis, Astron. Astrophys. 386, 732 (2002).
38. P. H. Chavanis, Astron. Astrophys. 396, 315 (2002).
39. P. H. Chavanis, Astron. Astrophys. 401, 15 (2003).
40. P. H. Chavanis, Phys. Rev. E 69, 066126 (2004).
41. P. H. Chavanis, Physica A 332, 89 (2004).
42. P. H. Chavanis, Astron. Astrophys. 432, 117 (2005).
43. P. H. Chavanis, Physica A 361, 55 (2006).
44. P. H. Chavanis, Physica A 361, 81 (2006).
45. P. H. Chavanis, Physica A 365, 102 (2006).
46. P. H. Chavanis, Astron. Astrophys. 451, 109 (2006).
47. P. H. Chavanis, Eur. Phys. J. B 52, 61 (2006).
48. P. H. Chavanis, astro-ph/0604012.
49. P. H. Chavanis, C. R. Physique 7, 331 (2006).
50. P. H. Chavanis and F. Bouchet, Astron. Astrophys. 430, 771 (2005).
51. P. H. Chavanis and I. Ispolatov, Phys. Rev. E 66, 036109 (2002).
52. P. H. Chavanis and M. Rieutord, Astron. Astrophys. 412, 1 (2003).
53. P. H. Chavanis and C. Sire, Phys. Rev. E 69, 016116 (2004).
54. P. H. Chavanis and C. Sire, Phys. Rev. E 70, 026115 (2004).
55. P. H. Chavanis and C. Sire, Phys. Rev. E 73, 066103 (2006).
56. P. H. Chavanis and C. Sire, Phys. Rev. E 73, 066104 (2006).
57. P. H. Chavanis and C. Sire, Physica A 356, 419 (2005).
58. P. H. Chavanis and J. Sommeria, Mon. Not. R. Astron. Soc. 296, 569 (1998).
59. P. H. Chavanis, P. Laurençot and M. Lemou, Physica A 341, 145 (2004).
60. P. H. Chavanis, C. Rosier and C. Sire, Phys. Rev. E 66, 036105 (2002).
61. P. H. Chavanis, J. Vatteville and F. Bouchet, Eur. Phys. J. B 46, 61 (2005).
62. P. H. Chavanis, M. Ribot, C. Rosier and C. Sire, Banach Center Publ. 66, 103 (2004).
63. P. H. Chavanis, J. Sommeria and R. Robert, Astrophys. J. 471, 385 (1996).
64. H. Cohn, Astrophys. J. 242, 765 (1980).
65. M. Costeniuc, R. Ellis, H. Touchette and B. Turkington, Phys. Rev. E 73, 026105 (2006).
66. T. Dauxois, V. Latora, A. Rapisarda, S. Ruffo and A. Torcini, The Hamiltonian mean field model: from dynamics to statistical mechanics and back, in Dynamics and Thermodynamics of Systems with Long Range Interactions, eds. T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens, Lecture Notes Phys. Vol. 602 (Springer-Verlag, Berlin, 2002), [cond-mat/0208456].
67. H. J. de Vega, N. Sanchez and F. Combes, Nature 383, 56 (1996).
68. H. J. de Vega, N. Sanchez and F. Combes, Astrophys. J. 500, 8 (1998).
69. H. J. de Vega and N. Sanchez, Nucl. Phys. B 625, 409 (2002).
70. H. J. de Vega and N. Sanchez, Nucl. Phys. B 625, 460 (2002).
71. H. J. de Vega and J. A. Siebert, Phys. Rev. E 66, 016112 (2002).
72. H. J. de Vega and J. A. Siebert, Nucl. Phys. B 707, 529 (2005).
73. H. J. de Vega and J. A. Siebert, Nucl. Phys. B 726, 464 (2005).
74. R. Ebert, Z. Astrophys. 37, 217 (1955).
75. A. S. Eddington, The Internal Constitution of the Stars (Cambridge University Press, Cambridge, 1926).
76. P. Ehrenfest, Proc. Am. Acad. Arts Sci. 20, 200 (1917).
77. R. Ellis, K. Haven and B. Turkington, J. Stat. Phys. 101, 999 (2000).
78. R. Ellis, K. Haven and B. Turkington, Nonlinearity 15, 239 (2002).
79. R. Emden, Gaskugeln (Teubner Verlag, Leipzig, 1907).
80. O. Fliegans and D. H. E. Gross, Phys. Rev. E 65, 046143 (2002).
81. E. Follana and V. Laliena, Phys. Rev. E 61, 6270 (2000).
82. R. H. Fowler, Mon. Not. R. Astron. Soc. 87, 114 (1926).
83. I. H. Gilbert, Astrophys. J. 152, 1043 (1968).
84. I. H. Gilbert, Astrophys. Space Sci. 14, 3 (1971).
85. D. H. E. Gross, Microcanonical thermodynamics: phase transitions in "small" systems, Lecture Notes Phys. Vol. 66 (World Scientific, Singapore, 2001).
86. D. H. E. Gross, cond-mat/0307535/0403582.
87. I. Hachisu and Y. Eriguchi, PASJ 36, 239 (1984).
88. S. W. Hawking, Nature 248, 30 (1974).
89. D. C. Heggie, Mon. Not. R. Astron. Soc. 173, 729 (1975).
90. M. Hénon, Ann. Astrophys. 24, 369 (1961).
91. P. Hertel, Acta Physica Austriaca Suppl. 17, 209 (1977).
92. P. Hertel and W. Thirring, in Quanten und Felder, ed. H. P. Dürr (Vieweg, Braunschweig, 1971).
93. P. Hertel and W. Thirring, Commun. Math. Phys. 24, 22 (1971).
94. P. Hertel and W. Thirring, Annals of Phys. 63, 520 (1971).
95. P. Hertel, H. Narnhofer and W. Thirring, Commun. Math. Phys. 28, 159 (1972).
96. J. Hjorth and J. Madsen, Mon. Not. R. Astron. Soc. 265, 237 (1993).
97. G. Horwitz and J. Katz, Astrophys. J. 211, 226 (1977).
98. G. Horwitz and J. Katz, Astrophys. J. 222, 941 (1978).
99. O. Iguchi, Phys. Rev. E 66, 051112 (2002).
100. S. Inagaki and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 205, 913 (1983).
101. G. Ingrosso, M. Merafina, R. Ruffini and F. Strafella, Astron. Astrophys. 258, 223 (1992).
102. I. Ispolatov and E. G. Cohen, Phys. Rev. Lett. 87, 210601 (2001).
103. I. Ispolatov and E. G. Cohen, Phys. Rev. E 64, 056103 (2001).
104. I. Ispolatov, Phys. Rev. E 72, 026115 (2005).
105. I. Ispolatov and M. Karttunen, Phys. Rev. E 68, 036117 (2003).
106. I. Ispolatov and M. Karttunen, Phys. Rev. E 70, 026102 (2004).
107. R. A. James, Astrophys. J. 140, 552 (1964).
108. J. H. Jeans, Astronomy and Cosmogony (Cambridge University Press, Cambridge, 1929).
109. H. Kandrup, Phys. Rep. 63, 1 (1980).
110. H. Kandrup, Astrophys. J. 244, 316 (1981).
111. J. Katz, Mon. Not. R. Astron. Soc. 183, 765 (1978).
112. J. Katz, Mon. Not. R. Astron. Soc. 190, 497 (1980).
113. J. Katz, Found. Phys. 33, 223 (2003).
114. J. Katz and M. Lecar, Astrophys. Space Sci. 68, 495 (1980).
115. J. Katz and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 184, 709 (1978).
116. J. Katz and I. Okamoto, Mon. Not. R. Astron. Soc. 371, 163 (2000).
117. M. Kiessling, J. Stat. Phys. 55, 203 (1989).
118. I. R. King, Astron. J. 70, 376 (1965).
119. S. Kothandaraman, Etude des transitions de phase dans les systèmes auto-gravitants par une méthode numérique basée sur un algorithme Monté Carlo (Metropolis). Stage de DEA "Physique de la Matière" de Toulouse, 2003 (supervisors: M. Belkacem and P. H. Chavanis).
120. C. Lagoute and P. Y. Longaretti, Astron. Astrophys. 308, 441 (1996).
121. V. Laliena, Phys. Rev. E 59, 4786 (1999).
122. R. Larson, Mon. Not. R. Astron. Soc. 147, 323 (1970).
123. M. Lecar and J. Katz, Astrophys. J. 243, 983 (1981).
124. M. P. Leubner, Astrophys. J. 632, L1 (2005).
125. J. M. Lévy-Leblond, J. Math. Phys. 10, 806 (1969).
126. D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136, 101 (1967).
127. D. Lynden-Bell, Extrait du Bulletin Astronomique 3, 305 (1968).
128. D. Lynden-Bell, Physica A 263, 293 (1999).
129. D. Lynden-Bell, astro-ph/0007116.
130. D. Lynden-Bell and P. P. Eggleton, Mon. Not. R. Astron. Soc. 191, 483 (1980).
131. D. Lynden-Bell and R. M. Lynden-Bell, Mon. Not. R. Astron. Soc. 181, 405 (1977).
132. D. Lynden-Bell and R. Wood, Mon. Not. R. Astron. Soc. 138, 495 (1968).
133. W. H. McCrea, Mon. Not. R. Astron. Soc. 117, 562 (1957).
134. J. Messer, Z. Physik B 33, 313 (1979).
135. J. Messer, J. Math. Phys. 22, 2910 (1981).
136. J. Messer and H. Spohn, J. Stat. Phys. 29, 561 (1982).
137. R. W. Michie, Mon. Not. R. Astron. Soc. 125, 127 (1963).
138. B. Miller and P. Youngkins, Phys. Rev. Lett. 81, 4794 (1998).
139. H. Narnhofer and G. L. Sewell, Commun. Math. Phys. 79, 9 (1981).
140. K. F. Ogorodnikov, Dynamics of Stellar Systems (Pergamon, Edinburg, 1965).
141. J. R. Oppenheimer and G. M. Volkoff, Phys. Rev. 55, 374 (1939).
142. J. Ostriker, Astrophys. J. 140, 1056 (1964).
143. T. Padmanabhan, Astrophys. J. Supp. 71, 651 (1989).
144. T. Padmanabhan, Astrophys. J. 344, 848 (1989).
145. T. Padmanabhan, Phys. Rep. 188, 285 (1990).
146. T. Padmanabhan, Mon. Not. R. Astron. Soc. 253, 445 (1991).
147. T. Padmanabhan, Statistical mechanics of gravitating systems in static and cosmological backgrounds, in Dynamics and Thermodynamics of Systems with Long Range Interactions, eds. T. Dauxois, S. Ruffo, E. Arimondo and M. Wilkens, Lecture Notes Phys., Vol. 602 (Springer-Verlag, Berlin, 2002) [astro-ph/0206131].
148. C. Pichon, Dynamics of self-gravitating disks. Ph.D. thesis (University of Cambridge, 1994).
149. A. R. Plastino and A. Plastino, Phys. Lett. A 174, 384 (1993).
150. M. V. Penston, Mon. Not. R. Astron. Soc. 144, 425 (1969).
151. M. J. Rees, Mon. Not. R. Astron. Soc. 176, 483 (1976).
152. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1989).
153. R. Robert, Class. Quantum Grav. 15, 3827 (1998).
154. G. B. Rybicki, Astrophys. Space Sci. 14, 56 (1971).
155. A. M. Salzberg, J. Math. Phys. 6, 158 (1965).
156. W. C. Saslaw, Gravitational Physics of Stellar and Galactic Systems (Cambridge University Press, Cambridge, 1985).
157. W. Saslaw, The Distribution of the Galaxies: Gravitational Clustering in Cosmology (Cambridge University Press, Cambridge, 2000).
158. B. Semelin, N. Sanchez, H. J. de Vega and F. Combes, Phys. Rev. D 59, 125021 (1999).
159. B. Semelin, N. Sanchez and H. J. de Vega, Phys. Rev. D 63, 084005 (2001).
160. C. Sire and P. H. Chavanis, Phys. Rev. E 66, 046133 (2002).
161. C. Sire and P. H. Chavanis, Phys. Rev. E 69, 066109 (2004).
162. J. Sopik, C. Sire and P. H. Chavanis, Phys. Rev. E 72, 026105 (2005).
163. J. Sopik, C. Sire and P. H. Chavanis, Phys. Rev. E 74, 011112 (2006).
164. L. Spitzer, Dynamical Evolution of Globular Clusters (Princeton University Press, New Jersey, 1987).
165. L. Spitzer, Astrophys. J. 95, 329 (1942).
166. B. Stahl, M. K. H. Kiessling and K. Schindler, Planet Space Sci. 43, 271 (1994).
167. R. Stanczy, Methods Appl. Sci. 28, 975 (2005).
168. M. Stiavelli and G. Bertin, Mon. Not. R. Astron. Soc. 229, 61 (1987).
169. J. S. Stodolkiewicz, Acta Astr. 13, 30 (1963).
170. D. Sugimoto and E. Bettwieser, Mon. Not. R. Astron. Soc. 204, 19 (1983).
171. L. G. Taff, H. M. Van Horn and C. J. Hansen, Astrophys. J. 197, 651 (1975).
172. A. Taruya and M. Sakagami, Physica A 322, 285 (2003).
173. T. Tatekawa, F. Bouchet, T. Dauxois and S. Ruffo, Phys. Rev. E 71, 6111 (2005).
174. W. Thirring, Z. Phys. 235, 339 (1970).
175. H. Touchette, R. S. Ellis and B. Turkington, Physica A 340, 138 (2004).
176. S. Tremaine, M. Hénon and D. Lynden-Bell, Mon. Not. R. Astron. Soc. 219, 285 (1986).
177. M. Trenti, G. Bertin and T. S. van Albada, Astron. Astrophys. 433, 57 (2005).
178. C. Tsallis, J. Stat. Phys. 52, 479 (1988).
179. P. Valageas, Astron. Astrophys. 450, 445 (2006).
180. E. V. Votyakov, H. Hidmi, A. De Martino and D. H. E. Gross, Phys. Rev. Lett. 89, 031101 (2002).
181. E. V. Votyakov, A. De Martino and D. H. E. Gross, Eur. Phys. J. B 29, 593 (2002).
182. V. Youngkins and B. Miller, Phys. Rev. E 62, 4583 (2000).