Bopp operators and phase-space spin dynamics: Application to rotational quantum Brownian motion

Journal of Physics A: Mathematical and Theoretical

Volumn 40, Issue 17, 2007, Pages 4635-4648

  Zueco, D ^a   Calvo, I ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b LABORATORIO NACIONAL DE FUSIÓN   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36048947078     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/40/17/015     Document Type: Article

References (39)

1. Wigner E 1932 On the quantum correction for thermodynamic equilibrium Phys. Rev. 40 749-59
2. Groenewold H J 1946 On the principles of elementary quantum mechanics Physica 12 405
3. Moyal J E 1949 Quantum Mechanics as a statistical theory Proc. Camb. Phil. Soc. 45 99
4. Bayen F, Flato M, Frondsal C, Lichnerowicz A and Sternheimer D 1978 Deformation theory and quantization Ann. Phys. 111 61-151
5. Kontsevich M 2003 Deformation quantization of Poisson manifolds: I Lett. Math. Phys. 66 157-216
6. Cattaneo A S, Felder G and Tomassini L 2002 From local to global deformation quantization of Poisson manifolds Duke Math. J. 115 329-52
7. Hillery M, O'Connell R F, Scully M O and Wigner E P 1984 Distribution functions in physics: fundamentals Phys. Rep. 106 121-67
8. Lee H-W 1995 Theory and application of the quantum phase-space distribution functions Phys. Rep. 259 147-211
9. Arecchi F T, Courtens E, Gilmore R and Thomas H 1972 Atomic coherent states in quantum optics Phys. Rev. A 6 2211
10. Takahashi Y and Shibata F 1975 Spin coherent state representation in non-equilibrium statistical mechanics J. Phys. Soc. Japan 38 656
11. Takahashi Y and Shibata F 1976 Generalized phase space method in spin systems-spin coherent state representation J. Stat. Phys. 14 49
12. Agarwal G S 1981 Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions Phys. Rev. A 24 2889
13. Cahill K E and Glauber R J 1969 Density operators and quasiprobability distributions Phys. Rev. 177 1882
14. Várilly J C and Gracia-Bond{í}a J 1989 The Moyal representation for spin Ann. Phys., NY 190 107-48
15. Figueroa H, Gracia-Bondía J M and Várilly C 1990 Moyal quantization with compact symmetry groups and noncommutative harmonic analysis J. Math. Phys. 31 2664-71
16. Stratonovich R L 1956 On distributions in representation space Zh. Eksp. Teor. Fiz. 31 1012
17. Stratonovich R L 1957 Sov. Phys. - JETP 4 891
18. Brif C and Mann A 1999 Phase-space formulation of quantum mechanics and quantum-state reconstruction for physical systems with Lie-group symmetries Phys. Rev. A 59 971-987
19. Brif C and Mann A 1998 Letter to the Editor: a general theory of phase-space quasiprobability distributions J. Phys. A: Math. Gen. 31 L9-L17
20. Klimov A B and Espinoza P 2002 Moyal-like form of the star product for generalized SU(2) Stratonovich-Weyl symbols J. Phys. A: Math. Gen. 35 8435-47
21. Bopp F 1956 La mécanique quantique est-elle une mécanique statistique classique particulière? Ann. Inst. H. Poincaré 15 81
22. Weiss U 1993 Quantum Dissipative Systems (Singapore: World Scientific)
23. Zwanzig R 2001 Nonequilibrium Statistical Mechanics (Oxford: Oxford University Press)
24. Breuer H-P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
25. Caldeira A O and Leggett A J 1983 Path integral approach to quantum Brownian motion Physica A 121 587-616
26. Caldeira A O and Leggett A J 1983 Dissipation and quantum tunnelling Ann. Phys. 149 374-456
27. Garc{í}a-Palacios J L 2000 On the statics and dynamics of magneto-anisotropic nanoparticles Adv. Chem. Phys. 112 1-210
28. Zhang W M, Feng D H and Gilmore R 1990 Coherent states: theory and some applications Rev. Mod. Phys. 62 867
29. Klimov A B 2002 Exact evolution equations for SU(2) quasidistribution functions J. Math. Phys. 43 2202-13
30. Klimov A B and Espinoza P 2005 Classical evolution of quantum fluctuations in spin-like systems: squeezing and entanglement J. Opt. B: Quantum Semiclass. Opt. 7 183-8
31. Stone M, Park K-S and Garg A 2000 The semiclassical propagator for spin coherent states J. Math. Phys. 41 8025-49
32. Garg A, Kochetov E, Park K-S and Stone M 2003 Spin coherent-state path integrals and the instanton calculus J. Math. Phys. 44 48-70
33. White R M 1983 Quantum Theory of Magnetism 2nd edn (Berlin: Springer)
34. Agarwal G S, Puri R R and Singh R P 1997 Atomic Schrödinger cat states Phys. Rev. A 56 2249-54
35. Mølmer K and Sørensen A 1999 Multiparticle entanglement of hot trapped ions Phys. Rev. Lett. 82 1835-8
36. M{ö}hring K and Smilansky U 1980 A semi-classical treatment of dissipative processes based on Feynman's influence functional method Nucl. Phys. A 338 227-68
37. Risken H 1989 The Fokker-Planck Equation 2nd edn (Berlin: Springer)
38. Garanin D A, Ishchenko V V and Panina L V 1990 Dynamics of an ensemble of single-domain magnetic particles Theor. Math. Phys. (USSR) 82 169-79
39. Zurek W H 1991 Decoherence and the transition from quantum to classical Phys. Today 44 36-44