Simple theoretical tools for low dimension Bose gases

Journal De Physique. IV : JP

Volumn 116, Issue , 2004, Pages 89-132

  Castin, Y ^a  

^a LABORATOIRE KASTLER BROSSEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COHERENT LIGHT; DENSITY (OPTICAL); EIGENVALUES AND EIGENFUNCTIONS; ELECTRON TRAPS; FERMI LEVEL; HAMILTONIANS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS;

CHEMICAL POTENTIALS; QUANTUM GASES; THERMAL EQUILIBRIUMS; WAVEFUNCTIONS;

QUANTUM THEORY;

EID: 7044235687     PISSN: 11554339     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1051/jp4:2004116004     Document Type: Conference Paper

References (46)

1. Castin Y., in Coherent atomic matter waves, Lecture notes of Les Houches summer school, edited by R. Kaiser, C. Westbrook and F. David, EDP Sciences and Springer-Verlag (2001), p. 1-136.
2. Diu B., Guthman C., Lederer D. and Roulet B., Physique Statistique (Hermann, Paris, France, 1989).
3. Holthaus M. and Kalinowski E., "The saddle-point method for condensed Bose gases", Ann. Phys. (N.Y.) 276 (1999) 321.
4. Sinatra A., Lobo C. and Castin Y., "The truncated Wigner method: limits of validity and applications", J. Phys. B 35 (2002) 3599-3631.
5. Lieb E.H. and Liniger W., "Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State", Phys. Rev. 130 (1963) 1605.
6. Yang C.N. and Yang C.P., "Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction", J. Math. Phys. 10 (1969) 1115.
7. Gaudin M., La fonction d'onde de Bethe, Masson (Paris, 1983).
8. Castin Y. and Herzog C., "Bose-Einstein condensates in symmetry breaking states", Comptes Rendus de l'Académie des Sciences de Paris, tome 2, série IV (2001) p.419-443.
9. Kheruntsyan K.V., Gangardt D.M., Drummond P.D. and Shlyapnikov G.V., "Pair Correlations in a Finite-Temperature 1D Bose Gas", Phys. Rev. Lett. 91 (2003) 040403.
10. Scalapino D.J., Sears M. and Ferrell R.A., "Statistical Mechanics of One-Dimensional Ginzburg-Landau Fields", Phys. Rev. B 6 (1972) 3409.
11. Castin Y., Dum R., Mandonnet E., Minguzzi A. and Carusotto I., "Coherence properties of a continuous atom laser", Journal of Modern Optics 47 (2000) 2671-2695.
12. Gardiner C., Quantum Noise, Springer-Verlag Berlin Heidelberg (1991), chapter 4 "Phase space methods".
13. Kagan Yu. and Svistunov B., 'Evolution of Correlation Properties and Appearance of Broken Symmetry in the Process of Bose-Einstein Condensation', Phys. Rev. Lett. 79 (1997) 3331 and references therein.
14. Kashurnikov V.A., Prokof'ev N.V. and Svistunov B.V., "Critical Temperature Shift in Weakly Interacting Bose Gas", Phys. Rev. Lett. 87 (2001) 120402.
15. Arnold P. and Moore G., "BEC Transition Temperature of a Dilute Homogeneous Imperfect Bose Gas", Phys. Rev. Lett. 87 (2001) 120401.
16. Popov V.N., Functional Integrals in Quantum Field Theory and Statistical Physics, (Reidel, Dordrecht, 1983).
17. Prokof'ev N.V. and Svistunov B.V., "Two Definitions of Superfluid Density", Phys. Rev. B 61 (2000) 11282.
18. Carusotto I. and Castin Y., "Superfluidity of the 1D Bose gas", C. R. Physique 5 (2004) 107-127.
19. We have discovered a posteriori that such a proof of non-existence for continuous bosonic fields was available in the literature, see H. Fröhlich, Physica 34 (1967) 47.
20. Girardeau M. and Arnowitt R., "Theory of Many-Boson Systems: Pair Theory", Phys. Rev. 113 (1959) 755.
21. Castin Y. and Dum R., "Low temperature Bose-Einstein condensates in time dependent traps: beyond the U(1)-symmetry breaking approach", Phys. Rev. A 57 (1998) 3008-3021.
22. Barnett S.M. and Pegg D.C., "The Hermitian Optical Phase Operator", in S. Reynaud, E. Giacobino and J. Zinn-Justin, editors, Fluctuations Quantiques, école d'été des Houches 1995, p. 563 (Elsevier, 1997).
23. Newton R., Scattering Theory of Waves and Particles, Dover (2003).
24. Mora C. and Castin Y., "Extension of Bogoliubov theory to quasicondensates", Phys. Rev. A 67 (2003) 053615.
25. Combescot R., "Feshbach Resonance in Dense Ultracold Fermi Gases", Phys. Rev. Lett. 91 (2003) 120401.
26. Olshanii M., "Atomic Scattering in the Presence of an External Confinement and a Gas of Impenetrable Bosons", Phys. Rev. Lett. 81 (1998) 938-941.
27. Bergeman T., Moore M. G. and Olshanii M., "Atom-Atom Scattering under Cylindrical Harmonic Confinement: Numerical and Analytic Studies of the Confinement Induced Resonance", Phys. Rev. Lett. 91(2003) 163201.
28. Blaizot J.P. and Ripka G., Quantum Theory of Finite Systems (The MIT Press, 1985).
29. Lewenstein M. and You Li, "Quantum Phase Diffusion of a Bose-Einstein Condensate", Phys. Rev. Lett. 77 (1996) 3489.
30. Popov V.N., "Long-wave asymptotic form of the many-body Green's functions of a one-dimensional Bose gas", JETP Lett. 31 (1980) 526.
31. Schwartz M., "Off-diagonal long-range behaviour of interacting Bose systems", Phys. Rev. B 15 (1977) 1399.
32. Mora C., thèse de doctorat de l'Université Paris 6 (2003), published on http://ccsd.cnrs.fr
33. Olshanii M. and Dunjko V., "Short distance correlation properties of the Lieb-Liniger system and momentum distributions of trapped one-dimensional atomic gases", Phys. Rev. Lett. 91 (2003) 090401.
34. Efetov K.B. and Larkin A.I., "Correlation functions in one-dimensional systems with a strong interaction", Sov. Phys. JETP 42 (1976) 390.
35. Haldane F.D.M., "Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids", Phys. Rev. Lett. 47 (1981) 1840.
36. Girardeau M., "Relationship between Systems of Imepenetrable Bosons and Fermions in One Dimension", J. Math. Phys. 1 (1960) 516.
37. Schultz T.D., "Note on the One-Dimensional Gas of Impenetrable Point-Particle Bosons", J. Math. Phys. 4 (1963) 666.
38. Cazalilla M.A., "One-dimensional optical lattices and impenetrable bosons", Phys. Rev. A 67 (2003) 053606.
39. Carusotto I. and Castin Y., "An exact reformulation of the Bose-Hubbard model in terms of a stochastic Gutzwiller ansatz", New Journal of Physics 5 (2003) 91.1-91.13.
40. Korepin V.E., Bogoliubov N.M. and Izergin A.G., "Quantum Inverse Scattering Method and Correlation Functions", (Cambridge University Press 1993).
41. Lenard A., "Momentum distribution in ground state of 1-dimensional system of impenetrable bosons", J. Math. Phys. 5 (1964) 930; "One-dimensional impenetrable bosons in thermal equilibrium", J. Math. Phys. 7 (1966) 1268.
42. Lenard A., "Momentum distribution in ground state of 1-dimensional system of impenetrable bosons", J. Math. Phys. 5 (1964) 930; "One-dimensional impenetrable bosons in thermal equilibrium", J. Math. Phys. 7 (1966) 1268.
43. Vaidya H.G. and Tracy C.A., "One-Particle Reduced Density Matrix of Impenetrable Bosons in One Dimension at Zero Temperature", Phys. Rev. Lett. 42 (1979) 3 and J. Math. Phys. 20 (1979) 2291.
44. Vaidya H.G. and Tracy C.A., "One-Particle Reduced Density Matrix of Impenetrable Bosons in One Dimension at Zero Temperature", Phys. Rev. Lett. 42 (1979) 3 and J. Math. Phys. 20 (1979) 2291.
45. Gangardt D., "Universal correlations of trapped one-dimensional impenetrable bosons", cond-mat/0404104.
46. FX limit: see the paragraph below Eq.(31) in the paper by L.S. Levitov, H.-W. Lee and G.B. Lesovik, J. Math. Phys. 37 4845 (1996).