Scaling approach to quantum non-equilibrium dynamics of many-body systems

New Journal of Physics

Volumn 12, Issue , 2010, Pages

  Gritsev, Vladimir ^a   Barmettler, Peter ^a,b   Demler, Eugene ^c  

^a UNIVERSITY OF FRIBOURG   (Switzerland)

^b CENTRE DE PHYSIQUE THÉORIQUE   (France)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOSONS; LINEAR TRANSFORMATIONS; MATHEMATICAL TRANSFORMATIONS; QUANTUM THEORY;

INTERACTING BOSONS; INTERACTING SYSTEM; NON-EQUILIBRIUM DYNAMICS; NON-LOCAL INTERACTIONS; PARABOLIC POTENTIAL; SCALING TRANSFORMATION; SELF-CONSISTENCY EQUATIONS; THEORETICAL PHYSICS;

DYNAMICS;

EID: 78149446770     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/12/11/113005     Document Type: Article

References (70)

1. Giamarchi T 2003 Quantum Physics in One Dimension (Oxford: Clarendon)
2. Rigol M, Dunjko V and Olshanii M 2008 Thermalization and its mechanism for generic isolated quantum systems Nature 452 854
3. Barankov R A and Levitov L S 2006 Synchronization in the BCS pairing dynamics as a critical phenomenon Phys. Rev. Lett. 96 230403
4. Yuzbashyan E A, Kuznetsov V B and Altshuler B L 2005 Integrable dynamics of coupled Fermi-Bose condensates Phys. Rev. B 72 144524
5. Yuzbashyan E A, Altshuler B L, Kuznetsov V B and Enolskii V Z 2005 Solution for the dynamics of the BCS and central spin problems J. Phys. A: Math. Gen. 38 7831
6. Yuzbashyan E A, Altshuler B L, Kuznetsov V B and Enolskii V Z 2005 Nonequilibrium Cooper pairing in the nonadiabatic regime Phys. Rev. B 72 220503
7. Faribault A, Calabrese P and Caux J-S 2009 Quantum quenches from integrability: the fermionic pairing model J. Stat. Mech. P03018
8. Faribault A, Calabrese P and Caux J-S 2009 Bethe ansatz approach to quench dynamics in the Richardson model J. Math. Phys. 50 095212
9. Calabrese P and Cardy J 2006 Time-dependence of correlation functions following a quantum quench Phys. Rev. Lett. 96 136801
10. Calabrese P and Cardy J 2007 Quantum quenches in extended systems J. Stat. Mech. P06008
11. Kollath C, Laeuchli A and Altman E 2007 Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model Phys. Rev. Lett. 98 180601
12. Bistritzer R and Altman E 2007 Intrinsic dephasing in one dimensional ultracold atom interferometers Proc. Natl Acad. Sci. USA 104 9955
13. Cazalilla M A 2006 Effect of suddenly turning on interactions in the Luttinger Model Phys. Rev. Lett. 97 156403
14. Iucci A and CazalillaMA 2009 Quantum quench dynamics of some exactly solvable models in one dimension Phys. Rev. A 80 063619
15. Daley A J, Kollath C, Schollwoeck U and Vidal G 2004 Time-dependent density-matrix renormalizationgroup using adaptive effective Hilbert spaces J. Stat. Mech. P04005
16. Kollath C, Iucci A, Giamarchi T, Hofstetter W and Schollwoeck U 2006 Spectroscopy of ultracold atoms by periodic lattice modulations, Phys. Rev. Lett. 97 050402
17. Schollwoeck U 2005 Time-dependent density-matrix renormalization-group methods J. Phys. Soc. Japan 74 (Suppl.) 246
18. Schollwoeck U 2005 The density-matrix renormalization group Rev. Mod. Phys. 77 259
19. Altland A, Gurarie V, Kriecherbauer T and Polkovnikov A 2009 Non-adiabacity and large flucutations in a many particle Landau-Zener problem Phys. Rev. A 79 042703
20. Itin A P and Törmä P 2009 Dynamics of a many-particle Landau-Zener model: inverse sweep Phys. Rev. A 79 055602
21. Barmettler P, Punk M, Gritsev V, Demler E and Altman E 2009 Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench Phys. Rev. Lett. 102 130603
22. Barmettler P, Punk M, Gritsev V, Demler E and Altman E 2010 Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium New J. Phys. 12 055017
23. Heidrich-Meisner F et al 2008 Ground-state reference systems for expanding correlated fermions in one dimension Phys. Rev. A 78 013620
24. Lewis H R 1968 Class of exact invariants for classical and quantum time-dependent harmonic oscillators J. Math. Phys. 9 1976
25. Lewis H R and Riesenfeld W B 1969 An exact quantum theory of the time-dependent harmonic oscillator and of a charged particle in a time-dependent eectromagnetic field J. Math. Phys. 10 1458
26. Popov V S and Perelomov A M 1969 J. Exp. Theor. Phys. 29 738
27. Popov V S and Perelomov A M 1970 J. Exp. Theor. Phys. 30 910
28. Perelomov A M and Popov V S 1969 Group-theoretical aspects of the variable frequency oscillator problem Theor. Math. Phys. 1 275
29. Perelomov A M 1986 Generalized Coherent States and Their Applications (New York: Springer)
30. Malkin I A, Man'ko V I and Trifonov D A 1970 Coherent states and transition probabilities in a timedependent electromagnetic field Phys. Rev. D 2 1371
31. Selezneva A N 1995 Unitary transformations for the time-dependent quantum oscillator Phys. Rev. A 51 950
32. Schuch D 2008 Riccati and Ermakov equations in time-dependent and time-independent quantum systems SIGMA 4 43
33. Cariñena J F, De Lucas J and Rañada M F 2008 Recent applications of the theory of Lie systems in Ermakov systems SIGMA 4 31
34. Berry M G and Klein G 1984 Newtonian trajectories and quantum waves in expanding force fields J. Phys. A: Math. Gen. 17 1805
35. Sutherland B 1998 Exact coherent states of a one-dimensional quantum fluid in a time-dependent trapping potential Phys. Rev. Lett. 80 3678
36. Castin Y and Dum R 1996 Bose-Einstein Condensates in time dependent traps Phys. Rev. Lett. 77 5315
37. Kagan Yu, Surkov E L and Shlyapnikov G V 1996 Evolution of a Bose-condensed gas under variations of the confining potential Phys. Rev. A 54 R1753
38. Werner F and Castin Y 2006 Unitary gas in an isotropic trap: Symmetry properties and applications Phys. Rev. A 74 053604
39. Pitaevskii L P and Rosch A 1997 Breathing modes and hidden symmetry of trapped atoms in two dimensions Phys. Rev. A 55 R853
40. Ghosh P 2001 Conformal symmetry and the nonlinear Schrödinger equation Phys. Rev. A 65 012103
41. Son D T and Wingate M 2006 General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas Ann. Phys. 321 197
42. Garcia-Ripoll J J, Pérez-Garcia V M and Torres P 1999 Extended parametric resonances in nonlinear Schrödinger systems Phys. Rev. Lett. 83 1715
43. Pérez-Garcia V M, Torres P J and Montesinos G D 2007 SIAM J. Appl. Math. 67 990
44. Minguzzi A and Gangardt D M 2005 Exact coherent states of a harmonically confined Tonks-Girardeau gas Phys. Rev. Lett. 94 240404
45. Bloch I, Dalibard J and Zwerger W 2008 Many-body physics with ultracold gases Rev. Mod. Phys. 80 885
46. Fleischhauer M, Imamoglu A and Marangos J P 2005 Electromagnetically induced transparency: optics in coherent media Rev. Mod. Phys. 77 633
47. Hartmann M J, Brandao F G S L and Plenio M B 2006 Strongly interacting polaritons in coupled arrays of cavities Nat. Phys. 2 849
48. Fleischhauer M, Otterbach J and Unanyan R G 2008 Bose-Einstein condensation of stationary-light polaritons Phys. Rev. Lett. 101 163601
49. Shen J-T and Fan S 2007 Strongly correlated multiparticle transport in one dimension through a quantum impurity Phys. Rev. A 76 062709
50. Chang D E, Gritsev V, Morigi G, Vuletic V, Lukin M and Demler E 2008 Crystallization of strongly interacting photons in a nonlinear optical fiber Nat. Phys. 4 884
51. Meystre P and Sargent M 1999 Elements of Quantum Optics (New York: Springer)
52. Lobo C and Gensemer S D 2008 Technique for measuring correlation functions in interacting gases Phys. Rev. A 78 023618
53. Leach P G L and Andriopoulos K 2008 The Ermakov equation: a commentary Appl. Anal. Discrete Math. 2 146
54. Ermakov V P 1880 Transformation of differential equations Univ. Izv. Kiev. 20 1-19
55. Petrov D S, Gangardt D M and Shlyapnikov G V 2004 Low-dimensional trapped gases J. Physique IV 116 3
56. Xia X and Silbey R J 2005 Effective Lagrangian approach to the trapped Bose gases at low temperatures Phys. Rev. A 71 063604
57. Bogoliubov N M, Malyshev C, Bullough R K and Timonen J 2004 Finite-temperature correlations in the one-dimensional trapped and untrapped Bose gases Phys. Rev. A 69 023619
58. Lieb E H and Liniger W 1963 Exact analysis of an interacting Bose gas. I. The general solution and the ground state Phys. Rev. 130 1605
59. Gerbier F et al 2008 Expansion of a quantum gas released from an optical lattice Phys. Rev. Lett. 101 155303
60. Son D T 2008 Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry Phys. Rev. D 78 046003
61. Balasubramanian K and McGreevy J 2008 Gravity duals for nonrelativistic conformal field theories Phys. Rev. Lett. 101 061601
62. Kachru S, Liu X and Mulligan M 2008 Gravity duals of Lifshitz-like fixed points Phys. Rev. D 78 106005
63. Adams A, Balasubramanian K and McGreevy J 2008 Hot spacetimes for cold atoms J. High Energy Phys. JHEP11(2008)059 (arXiv:0807.1111)
64. Goldberger W D 2008 AdS/CFT duality for non-relativistic field theory arXiv:0806.2867
65. Haller E, Gustavsson M, Mark M J, Danzl J G, Hart R, Pupillo G and Nägerl H-C 2009 Realization of an excited, strongly correlated quantum gas phase Science 325 1224
66. Polyanin A D and Zaitsev V F 2003 Handbook of Exact Solutions for Ordinary Differential Equations 2nd edn (Boca Raton, FL: Chapman and Hall/CRC)
67. Kundu A 2008 Integrable inhomogeneous NLS equations are equivalent to the standard NLS arXiv:0809.1924
68. Ramesh Kumar V, Radha R and Panigrahi P K 2008 Dynamics of Bose-Einstein condensates in a timedependent trap Phys. Rev. A 77 023611
69. Kundu A 2007 Integrable inhomogeneous NLS equations are equivalent to the standard NLS Phys. Rev. Lett. 99 154101
70. Calabrese P, Caux J-S and Slavnov N 2007 One-particle dynamical correlations in the one-dimensional Bose gas J. Stat. Mech. P01008