Phase space representation of quantum dynamics

Annals of Physics

Volumn 325, Issue 8, 2010, Pages 1790-1852

  Polkovnikov, Anatoli ^a  

^a Boston University   (United States)

Author keywords

Cold atoms; Phase space methods; Quantum dynamics; Weyl quantization

Indexed keywords

EID: 77954386273     PISSN: 00034916     EISSN: 1096035X     Source Type: Journal    
DOI: 10.1016/j.aop.2010.02.006     Document Type: Review

References (99)

1. Moyal J. Proc. Camb. Philos. Soc. 1949, 45:99.
2. Wigner E. Phys. Rev. 1932, 40:749.
3. Hillery M.A., O'Connell R.F., Scully M.O., Wigner E.P. Phys. Rep. 1984, 106:121.
4. Weyl H. Z. Phys. 1927, 46:1.
5. Gardiner C., Zoller P. Quantum Noise 2004, Springer-Verlag, Berlin Heidelberg. third edition.
6. Walls D., Milburn G. Quantum Optics 1994, Springer-Verlag, Berlin.
7. Schrödinger E. Naturwissenschaften 1926, 14:664.
8. Glauber R.J. Phys. Rev. Lett. 1963, 10:84.
9. Sinatra A., Lobo C., Castin Y. J. Phys. B: At. Mol. Opt. Phys. 2002, 35:3599.
10. Steel M.J., Olsen M.K., Plimak L., Drummond P.D., Tan S.M., Collett M.J., Walls D.F., Graham R. Phys. Rev. A 1998, 58:4824.
11. Blakie P.B., Bradley A.S., Davis M.J., Ballagh R.J., Gardiner C.W. Adv. Phys. 2008, 57:363.
12. Drummond P.D., Deuar P., Vaughan T.G., Corney J.F. J. Mod. Opt. 2007, 54:2499.
13. Carusotto I., Castin Y. New J. Phys. 2003, 5:91.
14. Deuar P. Phys. Rev. Lett. 2009, 103:130402.
15. Polkovnikov A. Phys. Rev. A 2003, 68:053604.
16. Polkovnikov A. Phys. Rev. A 2003, 68:033609.
17. Altland A., Gurarie V., Kriecherbauer T., Polkovnikov A. Phys. Rev. A 2009, 79:042703.
18. J.D. Sau, S.R. Leslie, D.M. Stamper-Kurn, and M.L. Cohen, 2009, preprint:arXiv:0904.1199.
19. Berg B., Plimak L.I., Polkovnikov A., Olsen M.K., Fleischhauer M., Schleich W.P. Phys. Rev. A 2009, 80:033624.
20. Mathey L., Polkovnikov A. Phys. Rev. A 2009, 80:041601(R).
21. Zurek W.H. Rev. Mod. Phys. 2003, 75:715.
22. Habib S., Shizume K., Zurek W.H. Phys. Rev. Lett. 1998, 80:4361.
23. Karkuszewski Z.P., Zakrzewski J., Zurek W.H. Phys. Rev. A 2002, 65:042113.
24. Lee H.-W., Scully M. Found. Phys. 1983, 13:61.
25. Kamenev A. Strongly Correlated Fermions and Bosons in Low-Dimensional Disordered Systems 2002, 313. Kluwer Academic Publishers, Dordrecht. I.V. Lerner, B.L. Althsuler, V.I. Fal'Ko, T. Giamarchi (Eds.).
26. Kamenev A., Levchenko A. Adv. Phys. 2009, 58:197.
27. Keldysh L. Sov. Phys. JETP 1965, 20:1018.
28. E.G. Dalla Torre, E. Demler, T. Giamarchi, and E. Altman, 2009, arXiv:0908.0868.
29. Mitra A., Takei S., Kim Y.B., Millis A.J. Phys. Rev. Lett. 2006, 97:236808.
30. Takei S., Kim Y.B. Phys. Rev. B 2008, 78:165401.
31. Altland A., Gurarie V. Phys. Rev. Lett. 2008, 100:063602.
32. L. I.Plimak, M. Fleischhauer, M.K. Olsen, and M.J. Collett, 2001a, arXiv:cond-mat/0102483.
33. L. I.Plimak, M.K. Olsen, M. Fleischhauer, and M.J. Collett, 2001b, arXiv:quant-ph/0108128.
34. Plimak L.I., Olsen M.K., Fleischhauer M., Collett M.J. Europhys. Lett. 2001, 56:372.
35. Gasenzer T. Eur. Phys. J. Spec. Top. 2009, 168:89.
36. Rey A.M., Hu B.L., Calzetta E., Clark C.W. Phys. Rev. A 2005, 72:023604.
37. Kamenev A. Nanophysics: Coherence and Transport: Les Houches 2004 Session LXXXI 2005, Elsevier, Amsterdam, Boston, cond-mat/0412296.
38. Bopp F. Werner Heisenberg und die Physik unserer Zeit 1961, 128. Vieweg, Braunschweig.
39. A.A. Clerk, M.H. Devoret, S.M. Girvin, F. Marquardt, and R.J. Schoelkopf, 2008, to appear in Rev. Mod. Phys., arXiv:0810.4729.
40. Nazarov Y.V., Kindermann M. Eur. Phys. J. B 2003, 35:413.
41. Deuar P., Drummond P.D. Phys. Rev. Lett. 2007, 98:120402.
42. Fetter A., Walecka J. Quantum Theory of Many-Particle Systems 1971, McGraw-Hill Book Co., New York.
43. Wang L., Connell R.F. Found. Phys. 1988, 18:1023.
44. Landau L., Lifshitz E. Mechanics: Course of Theoretical Physics 1982, vol. 1. Butterworth-Heinemann.
45. Landau L., Lifshitz E. Quantum Mechanics: Non-Relativistic Theory 1981, vol. 3. Butterworth-Heinemann.
46. Kubo R. J. Phys. Soc. Jpn. 1964, 19:2127.
47. Osborn T.A., Molzahn F.H. Annals Phys. 2002, 241:79.
48. Negele J.W., Orland H. Quantum Many-Particle Systems 1988, Perseus Books.
49. Gevorkyan S.T. Phys. Rev. A 1998, 58:4862.
50. Gevorkyan S.T., Kryuchkyan G.Y., Kheruntsyan K.V. Opt. Commun. 1997, 134:440.
51. Pethick C.J., Smith H. Bose-Einstein Condensation in Dilute Gases 2001, Cambridge University Press, Cambridge, UK.
52. Polkovnikov A., Sachdev S., Girvin S.M. Phys. Rev. A 2002, 66:053607.
53. Trombettoni A., Smerzi A. Phys. Rev. Lett. 2001, 86:2353.
54. Bloch I., Dalibard J., Zwerger W. Rev. Mod. Phys. 2008, 80:885.
55. Auerbach A. Interacting Electrons and Quantum Magnetism (Graduate Texts in Contemporary Physics) 1998, Springer-Verlag, Berlin Heidelberg. second edition.
56. Takahashi Y., Shibata F. J. Phys. Soc. Jpn. 1975, 38:656.
57. Arovas D.P., Auerbach A. Phys. Rev. B 2009, 38:316.
58. Cohen L., Scully M. Found. Phys. 1986, 16:295.
59. Polkovnikov A., Wang D.-W. Phys. Rev. Lett. 2004, 93:070401.
60. Das A., Chakrabarti B. Quantum Annealing and Other Optimization Methods 2005, Springer-Verlag, New York.
61. Farhi E., Goldstone J., Gutmann S., Lapan J., Lundgren A., Preda D. Science 2001, 292:472.
62. Kadowaki T., Nishimori H. Phys. Rev. E 1998, 58:5355.
63. Santoro G.E., Martonak R., Tosatti E., Car R. Science 2002, 295:2427.
64. Bistritzer R., Altman E. PNAS 2007, 104:9955.
65. Polkovnikov A., Gritsev V. Nature Phys. 2008, 4:477.
66. Shankar R. Principles of Quantum Mechanics 1994, Springer, New York.
67. Giamarchi T. Quantum Physics in One Dimension 2004, Clarendon Press, Oxford.
68. Lukyanov S., Zamolodchikov A. Nucl. Phys. B 1997, 493:571.
69. Chaikin P.M., Lubensky T.C. Principles of Condensed Matter Physics 1995, Cambridge Univesrity Press, Cambridge.
70. Büchler H.P., Blatter G., Zwerger W. Phys. Rev. Lett. 2003, 90:130401.
71. Cazalilla M. J. Phys. B 2004, 37:S1.
72. De Grandi C., Barankov R.A., Polkovnikov A. Phys. Rev. Lett. 2008, 101:230402.
73. Donohue P., Giamarchi T. Phys. Rev. B 2001, 63:180508.
74. Mathey L., Polkovnikov A., Neto A.H.C. Europhys. Lett. 2008, 81:10008.
75. Gritsev V., Demler E., Lukin M., Polkovnikov A. Phys. Rev. Lett. 2007, 99:200404.
76. Gritsev V., Polkovnikov A., Demler E. Phys. Rev. B 2007, 75:174511.
77. Abrikosov A., Gor'kov L., Dzyaloshinsky I. Quantum Field Theoretical Methods in Statistical Physics 1965, Pergamon, Oxford.
78. S. Fang, R.-K. Lee, and D.-W. Wang, 2009, arXiv:0910.1518.
79. Hipolito R., Polkovnikov A. Phys. Rev. A 2010, 81.
80. A.D. Martin, and J. Ruostekoski, 2009, arXiv:0909.2621.
81. Greiner M., Mandel O., Hänsch T.W., Bloch I. Nature 2002, 419:51.
82. Trotzky S., Cheinet P., Fölling S., Feld M., Schnorrberger U., Rey A.M., Polkovnikov A., Demler E.A., Lukin M.D., Bloch I. Science 2008, 319:295.
83. E. Fermi, J. Pasta, and S. Ulam, May 1955, Document LA-1940.
84. Kollath C., Läuchli A.M., Altman E. Phys. Rev. Lett. 2007, 98:180601.
85. Reimann P. Phys. Rev. Lett. 2008, 101:190403.
86. Rigol M. Phys. Rev. Lett. 2009, 103:100403.
87. Rigol M., Dunjko V., Olshanii M. Nature 2008, 452:854.
88. Wright T.M., Ballagh R.J., Bradley A.S., Blakie P.B., Gardiner C.W. Phys. Rev. A 2008, 78:063601.
89. Keeling J., Gurarie V. Phys. Rev. Lett. 2008, 101:033001.
90. Zener C. Proc. R. Soc. A 1932, 137:696.
91. Anderson P.W. Phys. Rev. 1958, 112:1900.
92. S. Regal, 2006, experimental realization of BCS-BEC crossover physics with a Fermi gas of atoms, PhD. Thesis, University of Colorado, Boulder, 2006; C. Regal, D. S. Jin, arXiv:cond-mat/0601054.
93. Andreev A.V., Gurarie V., Radzihovsky L. Phys. Rev. Lett. 2004, 93:130402.
94. Barankov R.A., Levitov L.S., Spivak B.Z. Phys. Rev. Lett. 2004, 93:160401.
95. A. Itin, and P. Törmä, 2009, preprint: arXiv:0901.4778.
96. C. Kiegel, 2009, semiclassical approach to driven many-particle systems, Diploma Thesis, Institute for Theoretical Physics, Univesrity of Cologne, Germany.
97. N.C. Dias, A. Mikovic, J.N. Prata, J. Math. Phys. 47 (2006) 082101.
98. Nuno Costa Dias, Joao Nuno Prata, J. Math. Phys. 48 (2007) 012109.
99. G. Braunss, J. Phys. A: Math. Theor. 43 (2010) 025302.