Lévy distribution in many-particle quantum systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 4, 2010, Pages

  Ponomarev, A V ^a   Denisov, S ^a   Hanggi P ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL SYSTEMS; COMPLEX BEHAVIOR; FINITE TEMPERATURES; GRAND-CANONICAL FORMALISM; MANY-BODY; QUANTUM MANY-BODY SYSTEMS; QUANTUM STATE; QUANTUM SYSTEM; SCALING EXPONENT; TONKS-GIRARDEAU GAS;

QUANTUM OPTICS;

QUANTUM ELECTRONICS;

EID: 77951110079     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.043615     Document Type: Article

References (31)

1. D. J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic Press, New York, 1961);
2. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover, New York, 2003).
3. H. J. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer, New York, 1999).
4. O. Morsch and M. Oberthaler, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.78.179 78, 179 (2006).
5. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.80.885 80, 885 (2008).
6. M. Girardeau, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1703687 1, 516 (1960).
7. B. Paredes, Nature (London) NATUAS 0028-0836 10.1038/nature02530 429, 277 (2004). (Pubitemid 38684809)
8. T. Kinoshita, T. Wenger, and D. S. Weiss, Science SCIEAS 0036-8075 10.1126/science.1100700 305, 1125 (2004). (Pubitemid 39100318)
9. M. Olshanii and V. Dunjko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.090401 91, 090401 (2003).
10. T. Papenbrock, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.041601 67, 041601 (R) (2003).
11. A. Minguzzi, P. Vignolo, and M. P. Tosi, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(02)00042-7 294, 222 (2002).
12. L. Pollet, S. M. A. Rombouts, and P. J. H. Denteneer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.210401 93, 210401 (2004). (Pubitemid 40015697)
13. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1991), Vol. 2.
14. M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, Nature (London) NATUAS 0028-0836 10.1038/363031a0 363, 31 (1993);
15. A. Blumen, G. Zumofen, and J. Klafter, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.3964 40, 3964 (1989).
16. F. Bardou, J.-P. Bouchaud, A. Aspect, and C. Cohen-Tannoudji, Levy Statistics and Laser Cooling (Cambridge University Press, Cambridge, 2002).
17. R. N. Mantegna and H. E. Stanley, Nature (London) NATUAS 0028-0836 10.1038/376046a0 376, 46 (1995).
18. E. Barkai, R. Silbey, and G. Zumofen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5339 84, 5339 (2000).
19. R. Segev, M. Benveniste, E. Hulata, N. Cohen, A. Palevski, E. Kapon, Y. Shapira, and E. Ben-Jacob, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.118102 88, 118102 (2002).
20. C.-K. Peng, J. Mietus, J. M. Hausdorff, S. Havlin, H. E. Stanley, and A. L. Goldberger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1343 70, 1343 (1993).
21. M. Rigol, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.063607 72, 063607 (2005). (Pubitemid 41776045)
22. M. Rigol and A. Muramatsu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.031603 70, 031603 (R) (2004);
23. M. Rigol and A. Muramatsu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.013604 72, 013604 (2005). (Pubitemid 41492536)
24. D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3108 81, 3108 (1998).
25. The critical density n s is found via mapping the single-particle version of (1) onto the quantum pendulum [23].
26. A. V. Ponomarev and A. R. Kolovsky, Laser Phys. LAPHEJ 1054-660X 10.1134/S1054660X06020289 16, 367 (2006). (Pubitemid 44726264)
27. C. Beck and E. G. D. Cohen, Physica A PHYADX 0378-4371 10.1016/S0378-4371(03)00019-0 322, 267 (2003).
28. R. Pezer and H. Buljan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.240403 98, 240403 (2007). (Pubitemid 47139860)
29. R. L. Liboff, Introductory Quantum Mechanics (Addison-Wesley, San Francisco, 2003).
30. G. Barton, Elements of Green's Functions and Propagation (Oxford University Press, Oxford, 1989).
31. P. Jordan and E. Wigner, Z. Phys. EPJAFV 1434-6001 10.1007/BF01331938 47, 631 (1928).