Fluctuations of composite observables and stability of statistical systems

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

Volumn 72, Issue 6, 2005, Pages

  Yukalov, V I ^a,b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

DISPERSIONS; MAGNETIC SUSCEPTIBILITY; STATISTICAL METHODS; THEOREM PROVING;

GLOBAL DISPERSION; PARTIAL OPERATOR; SELF-ADJOINT TERMS; STATISTICAL SYSTEMS;

THERMODYNAMIC STABILITY;

EID: 33244473224     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.066119     Document Type: Article

References (65)

1. H. B. Callen, Thermodynamics (Wiley, New York, 1960).
2. K. Huang, Statistical Mechanics (Wiley, New York, 1963).
3. R. Kubo, Statistical Mechanics (North-Holland, Amsterdam, 1965).
4. Y. P. Terletsky, Statistical Physics (Higher School, Moscow, 1973).
5. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975).
6. R. Kubo, Thermodynamics (North-Holland, Amsterdam, 1968).
7. V. I. Yukalov and A. S. Shumovsky, Lectures on Phase Transitions (World Scientific, Singapore, 1990).
8. W. Scharlau, Quadratic and Hermitian Forms (Springer, Berlin, 1985).
9. V. I. Yukalov, Laser Phys. Lett. LPLABC 1612-2011 2, 156 (2005).
10. P. W. Courteille, V. S. Bagnato, and V. I. Yukalov, Laser Phys. LAPHEJ 1054-660X 11, 659 (2001).
11. J. O. Andersen, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76. 599 76, 599 (2004).
12. K. Bongs and K. Sengstock, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/67/6/R03 67, 907 (2004).
13. V. I. Yukalov, Laser Phys. Lett. LPLABC 1612-2011 10.1002/lapl.200410097 1, 435 (2004).
14. V. I. Yukalov, E. P. Yukalova, and V. S. Bagnato, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.56.4845 56, 4845 (1997).
15. E. A. Ostrovskaya, Y. S. Kivshar, M. Lisak, B. Hall, F. Cattani, and D. Anderson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.031601 61, 031601 (R) (2000).
16. Y. S. Kivshar, T. J. Alexander, and S. K. Turitsyn, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(00)00774-X 278, 225 (2001).
17. R. D'Agosta, B. A. Malomed, and C. Presilla, Laser Phys. LAPHEJ 1054-660X 12, 37 (2002).
18. R. D'Agosta and C. Presilla, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.043609 65, 043609 (2002).
19. N. P. Proukakis and L. Lambropoulos, Eur. Phys. J. D EPJDF6 1434-6060 10.1007/s10053-002-8885-1 19, 355 (2002).
20. V. I. Yukalov and E. P. Yukalova, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/40/317 35, 8603 (2002).
21. V. I. Yukalov, E. P. Yukalova, and V. S. Bagnato, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.043602 66, 043602 (2002).
22. V. I. Yukalov, K. P. Marzlin, and E. P. Yukalova, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.023620 69, 023620 (2004).
23. L. S. Cederbaum and A. I. Streltsov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.023610 70, 023610 (2004).
24. M. M. Cola and N. Piovella, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.045601 70, 045601 (2004).
25. D. ter Haar, Lectures on Selected Topics in Statistical Mechanics (Pergamon, Oxford, 1977).
26. R. M. Ziff, G. E. Uhlenbeck, and M. Kac, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(77)90052-7 32, 169 (1977).
27. N. N. Bogolubov, J. Phys. (Moscow) JOPYA6 0368-3400 11, 23 (1947).
28. N. N. Bogolubov, Moscow Univ. Phys. Bull. MUPBAC 0027-1349 7, 43 (1947).
29. N. N. Bogolubov, Lectures on Quantum Statistics (Gordon and Breach, New York, 1967), Vol. 1.
30. A. Z. Patashinsky and V. L. Pokrovsky, Fluctuational Theory of Phase Transitions (Nauka, Moscow, 1982).
31. Z. Idziaszek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.053604 71, 053604 (2005).
32. C. W. Gardiner, Handbook of Statistical Methods (Springer, Berlin, 1985).
33. P. Carruthers and M. M. Nieto, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.40.411 40, 411 (1968).
34. R. Lynch, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(94)00095-K 256, 367 (1995).
35. E. A. Kochetov and V. I. Yukalov, Laser Phys. LAPHEJ 1054-660X 5, 186 (1995).
36. D. T. Pegg and S. M. Barnett, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003497154049 44, 225 (1997).
37. V. I. Yukalov, Many-Body Theory (Lectures at Free University of Berlin, Berlin, 2005).
38. P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(65)90280-0 34, 291 (1965).
39. N. N. Bogolubov, Lectures on Quantum Statistics (Gordon and Breach, New York, 1970), Vol. 2.
40. V. I. Yukalov, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(91)90074-V 208, 395 (1991).
41. F. A. Berezin, Method of Second Quantization (Academic, New York, 1966).
42. N. N. Bogolubov and N. N. Bogolubov, Jr., Introduction to Quantum Statistical Mechanics (Gordon and Breach, Lausanne, 1994).
43. J. R. Klauder and B. S. Skagerstam, Coherent States (World Scientific, Singapore, 1985).
44. V. I. Yukalov, Statistical Green's Functions (Queen's University, Kingston, 1998).
45. H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982).
46. J. Ginibre, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01646422 8, 26 (1968).
47. H. D. Politzer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.5048 54, 5048 (1996).
48. M. Wilkens and C. Weiss, J. Mod. Opt. JMOPEW 0950-0340 10.1080/095003497152816 44, 1801 (1997).
49. V. I. Yukalov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.033608 72, 033608 (2005).
50. J. W. Gibbs, Collected Works (Longmans, New York, 1931), Vol. 2.
51. D. ter Haar, Elements of Statistical Mechanics (Reinhart, New York, 1954).
52. D. ter Haar, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/24/1/307 24, 304 (1961).
53. V. I. Yukalov, Int. J. Mod. Phys. B IJPBEV 0217-9792 17, 2333 (2003).
54. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices (Springer, Berlin, 2000).
55. R. S. Ellis, K. Haven, and B. Turkington, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1026446225804 101, 999 (2000).
56. R. S. Ellis, H. Touchette, and B. Turkington, Physica A PHYADX 0378-4371 10.1016/j.physa.2003.11.028 335, 518 (2004).
57. T. Dauxois, P. Holdsworth, and S. Ruffo, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510050009 16, 659 (2000).
58. J. BarrÃ, D. Mukamel, and S. Ruffo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.030601 87, 030601 (2001).
59. M. Kac, G. E. Uhlenbeck, and P. C. Hemmer, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703946 4, 216 (1963).
60. T. Padmanabhan, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(90)90051-3 188, 285 (1990).
61. D. Lynden-Bell, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98)00518-4 263, 293 (1999).
62. D. Ruelle, Statistical Mechanics (Benjamin, New York, 1969).
63. G. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley, New York, 1972).
64. J. T. Lewis and J. V. PulÃ, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01646022 36, 1 (1974).
65. L. Vandevenne, A. Verbeure, and V. A. Zagrebnov, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1649793 45, 1606 (2004).