Exactly solvable models in atomic and molecular physics

Nuclear Physics B

Volumn 777, Issue 3, 2007, Pages 373-403

  Foerster, A ^a   Ragoucy, E ^b  

^a FEDERAL UNIVERSITY OF RIO GRANDE DO SUL   (Brazil)

^b LABORATOIRE DE PHYSIQUE DES PARTICULES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34447101320     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2007.03.039     Document Type: Article

References (68)

1. Batchelor M.T., Guan X.-W., Oelkers N., and Foerster A. Thermal and magnetic properties of integrable spin-1 and spin-3/2 chains with applications to real compounds. J. Stat. Mech. 0410 (2004) P017
2. Batchelor M.T., Guan X.-W., Oelkers N., Sakai K., Tsuboi Z., and Foerster A. Exact results for thermal and magnetic properties of strong coupling ladder compounds. Phys. Rev. Lett. 91 (2003) 217202
3. Batchelor M.T., Guan X.-W., Oelkers N., and Tsuboi Z. Integrable models and quantum spin ladders: Comparison between theory and experiment for the strong coupling compounds. cond-mat/0512489
4. Black C.T., Ralph D.C., and Tinkham M. Spectroscopy of the superconducting gap in individual nanometer-scale aluminum particles. Phys. Rev. Lett. 76 (1996) 688
5. Black C.T., Ralph D.C., and Tinkham M. Gauge-voltage studies of discrete electronic states in aluminum nanoparticles. Phys. Rev. Lett. 78 (1997) 4087
6. von Delft J., and Ralph D.C. Spectroscopy of discrete energy levels in ultrasmall metallic grains. Phys. Rep. 345 (2001) 61
7. Baxter R.J. Exactly Solved Models in Statistical Mechanics (1982), Academic Press
8. Essler F.H., and Korepin V.E. Exactly Solvable Models of Strongly Correlated Electrons (1994), World Scientific
9. L.D. Faddeev, The Bethe Ansatz, Andrejeroski Lectures, 1993, SFB288 preprint 70
10. Iachello F., and Arimo A. The Interacting Boson Model (1995), Cambridge Univ. Press
11. Leggett A.J. Bose-Einstein condensation in the alkali gases: Some fundamental concepts. Rev. Mod. Phys. 73 (2001) 307
12. Lipatov L. High energy asymptotics of multi-colour QCD and exactly solvable lattice models. JETP Lett. 59 (1994) 596. hep-th/9311037
13. Faddeev L., and Korchemsky G. High energy QCD as a completely integrable model. Phys. Lett. B 342 (1995) 311. hep-th/9404173
14. Ferretti G., Heise R., and Zarembo K. New integrable structures in large-N QCD. hep-th/0404187
15. Belitsky A.V., Braun V.M., Gorsky A.S., and Korchemsky G.P. Integrability in QCD and beyond. Int. J. Mod. Phys. A 19 (2004) 4715. hep-th/0407232
16. Minahan J.A., and Zarembo K. The Bethe-Ansatz for N = 4 super-Yang-Mills. JHEP 0303 (2003) 013. hep-th/0212208
17. Beisert N., and Staudacher M. The N = 4 SYM integrable super spin chain. Nucl. Phys. B 670 (2003) 439
18. Beisert N., and Staudacher M. Long-Range PSU(2, 2|4) Bethe Ansaetze for Gauge Theory and Strings. Nucl. Phys. B 727 (2005) 1. hep-th/0504190
19. Bose S.N. Plancks Gesetz und Lichtquantenhypothese. Z. Phys. 26 (1924) 178
20. Einstein A. Quantentheorie des einatomigen idealen Gases. Sitzungsber. Preussichen Akad. Wiss. Phys.-Math. Kl. (1924) 261
21. Cornell E.A., and Wieman C.E. Nobel lecture: Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments. Rev. Mod. Phys. 74 (2002) 875
22. Anglin J.R., and Ketterle W. Bose-Einstein condensation of atomic gases. Nature 416 (2002) 211
23. Zoller P. Bose-Einstein condensation: Making it with molecules. Nature 417 (2002) 493
24. Hutson J., and Soldán P. Molecule formation in ultracold atomic gases. physics/0607234
25. Héritier M. In search of exact solutions. Nature 414 (2001) 31
26. Batchelor M.T. The Bethe ansatz after 75 years. Phys. Today 60 (2007) 36
27. Stickney J., Zozulya A., and Anderson D. Transistor-like behaviour of a Bose-Einstein condensate in a triple well potential. cond-mat/0607706
28. Sklyanin E.K., and Faddeev L.D. Quantum mechanical approach to completely integrable models of field theory. Dokl. Acad. Nauk SSSR 243 (1978) 1430
29. Sklyanin E.K., and Faddeev L.D. Method of the inverse scattering problem and quantum nonlinear Schrödinger equation. Dokl. Acad. Nauk SSSR 244 (1978) 1337
30. Sklyanin E.K. Quantum version of the method of inverse scattering problem. Zap. Nauchn. Sem. LOMI 95 (1980) 55
31. Kulish P.P., Reshetikhin N.Yu., and Sklyanin E.K. Yang-Baxter equation and representation theory: I. Lett. Math. Phys. 5 (1981) 393
32. Kulish P.P., and Sklyanin E.K. Quantum inverse scattering method and the Heisenberg ferromagnet. Phys. Lett. A 70 (1979) 461
33. Faddeev L.D., Reshetikhin N.Yu., and Takhtajan L.A. Quantization of Lie groups and Lie algebras. Leningrad Math. J. 1 (1990) 193
34. Korepin V.E. New effects in the massive Thirring model: Repulsive case. Commun. Math. Phys. 76 (1980) 165
35. Korepin V.E., Izergin G., and Bogoliubov N.M. Quantum Inverse Scattering Method, Correlation Functions and Algebraic Bethe Ansatz (1993), Cambridge Univ. Press
36. Faddeev L.D., and Takhtajan L.A. Spectrum and scattering of excitations in the one-dimensional isotropic Heisenberg model. J. Sov. Math. 24 (1984) 241
37. Faddeev L.D., and Takhtajan L.A. What is the spin of a spin wave?. Phys. Lett. A 85 (1981) 375
38. Kulish P., and Reshetikhin N.Yu. Diagonalisation of GL (N) invariant transfer matrices and quantum N-wave system (Lee model). J. Phys. A 16 (1983) L591
39. Ogievetsky E., and Wiegmann P. Factorized S-matrix and the Bethe ansatz for simple Lie groups. Phys. Lett. B 168 (1986) 360
40. Drinfel'd V.G. Hopf algebras and the quantum Yang-Baxter equation. Sov. Math. Dokl. 32 (1985) 254
41. Drinfel'd V.G. A new realization of Yangians and quantized affine algebras. Sov. Math. Dokl. 36 (1988) 212
42. Baxter R.J. Partition function of the eight-vertex lattice model. Ann. Phys. 70 (1972) 193
43. Baxter R.J. J. Stat. Phys. 8 (1973) 25
44. Yang C.N. Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Rev. Lett. 19 (1967) 1312
45. Ge M.-L., Xue K., and Wang Y. An Introduction to Yangian in Physics (1995), Second Pacific Winter School in Theoretical Physics, Korea. cond-mat/9509090
46. Kundu A. Yang-Baxter algebra and generation of quantum integrable models. nlin.SI/0609001
47. Ortiz G., Somma R., Dukelsky J., and Rombouts S. Exactly-solvable models derived from a generalized Gaudin algebra. Nucl. Phys. B 707 (2005) 421
48. Jaynes E.T., and Cummings F.W. Proc. IEEE 51 (1963) 89
49. Jonathan D., Furuya K., and Vidiella-Barranco A. Dressed-state approach to population trapping in the Jaynes-Cummings model. quant-ph/9904067 and references therein
50. Haken H., Wolf H., and Brewer W.D. The Physics of Atoms and Quanta: Introduction to Experiments and Theory (2004), Springer
51. Links J., Zhou H.-Q., McKenzie R.H., and Gould M.D. Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: Applications to models of Bose-Einstein condensates in metallic nanograins. J. Phys. A 36 (2003) R63
52. Foerster A., Links J., and Zhou H.-Q. Exact Solvability in Contemporary Physics, Classical and Quantum Nonlinear Integrable Systems (2003), IOP Publ.
53. Zhou H.-Q., Links J., Gould M.D., and McKenzie R.H. Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme. J. Math. Phys. 44 (2003) 4690. cond-mat/0211249
54. Duncan M., Foerster A., Links J., Mattei E., Oelkers N., and Tonel A. Emergent quantum phases in a heteronuclear molecular Bose-Einstein condensate model. Nucl. Phys. B 767 (2007) 227. quant-ph/0610244
55. Zhou L., Zhang W., Ling H.Y., and Pu H. Quantum correlation in the photoassociation of a heteronuclear Bose-Einstein condensate. quant-ph/0611005
56. Zhou H.-Q., Links J., McKenzie R.H., and Guan X.-W. Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates. J. Phys. A 36 (2003) L113. cond-mat/0203009
57. Milburn G.J., Corney J., Wright E.M., and Walls D.F. Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential. Phys. Rev. A 55 (1997) 4318
58. Tonel A.P., Links J., and Foerster A. Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates. J. Phys. A 38 (2005) 1235
59. Albiez M., Gati R., Fölling J., Hunsmann S., Cristiani M., and Oberthaler M.K. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. Phys. Rev. Lett. 95 (2005) 010402
60. Nemoto K., Holmes C., Milburn G., and Munro W. Quantum dynamics of three coupled atomic Bose-Einstein condensates. Phys. Rev. A 63 (2001) 013604-1
61. Liu B., Fu L.-B., Yang S.-P., and Liu J. Josephson oscillation and transition to self-trapping for Bose-Einstein-condensates in a triple-well trap. cond-mat/0610200
62. Ott H., et al. Bose-Einstein condensation in a surface microtrap. Phys. Rev. Lett. 87 (2001) 230401
63. Hänsel W., et al. Bose-Einstein condensation on a microelectronic chip. Nature 413 (2001) 498
64. Reichel J. Microchip traps and Bose-Einstein condensation. Appl. Phys. B 75 (2002) 469
65. Buonsante P., Franzosi R., and Pena V. Dynamical instability in a trimeric chain of interacting Bose-Einstein condensates. Phys. Rev. Lett. 90 (2003) 050404
66. Dounas-Frazer D.R., Hermundstad A.M., and Carr L.D. Ultracold bosons and entanglement in the tilted double-well. quant-ph/0609119
67. Arnaudon D., Crampé N., Doikou A., Frappat L., and Ragoucy E. Analytical Bethe Ansatz for closed and open gl (n)-spin chains in any representation. J. Stat. Mech. 02 (2005) P007. math-ph/0411021
68. Molev A., Nazarov M., and Olshanski G. Yangians and classical Lie algebras. Russ. Math. Survey 51 (1996) 205. hep-th/9409025