Quantum-field-theoretical approach to phase-space techniques: Generalizing the positive-P representation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 1, 2003, Pages

  Plimak, L I ^a,b   Fleischhauer, M ^a   Olsen, M K ^c   Collett, M J ^b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

^c FLUMINENSE FEDERAL UNIVERSITY   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CONFORMAL MAPPING; DIFFERENCE EQUATIONS; FOUR WAVE MIXING; GREEN'S FUNCTION; INTEGRAL EQUATIONS; MONTE CARLO METHODS; OPTICAL KERR EFFECT; OPTICAL PARAMETRIC OSCILLATORS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES;

FOKKER-PLANCK EQUATION; KERR OSCILLATOR; PHASE-SPACE TECHNIQUE; QUANTUM FIELD THEORY; STOCHASTIC DIFFERENCE EQUATION; STOCHASTIC DIFFERENTIAL EQUATION;

QUANTUM OPTICS;

EID: 0037241059     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. C.W. Gardiner, Quantum Noise (Springer-Verlag, Berlin, 1991).
2. D.F. Walls and G.J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1995).
3. M.J. Steel, M.K. Olsen, L.I. Plimak, P.D. Drummond, S.M. Tan, M.J. Collett, D.F. Walls, and R. Graham, Phys. Rev. A 58, 4824 (1998).
4. P.D. Drummond and J.F. Corney, Phys. Rev. A 60, R2661 (1999).
5. J.J. Hope and M.K. Olsen, Phys. Rev. Lett. 86, 3220 (2001).
6. J. J. Hope, Phys. Rev. A 64, 053608 (2001).
7. U.V. Poulsen and K. Mølmer, Phys. Rev. A 64, 013616 (2001).
8. H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984).
9. P.D. Drummond and C.W. Gardiner, J. Phys. A 13, 2353 (1980).
10. L.I. Plimak, M.K. Olsen, and M.J. Collett, Phys. Rev. A 64, 025801 (2001).
11. P. Deuar and P.D. Drummond, Comput. Phys. Commun. 142, 442 (2001)
12. Phys. Rev. A 66, 033812 (2002).
13. A. Sinatra, C. Lobo, and Y. Castin, J. Phys. B 35, 3599 (2002).
14. A. Gilchrist, C.W. Gardiner, and P.D. Drummond, Phys. Rev. A 55, 3014 (1997).
15. R. Kubo, Rep. Prog. Phys. 29, 255 (1966).
16. L.I. Plimak, Phys. Rev. A 50, 2120 (1994).
17. M.K. Olsen, L.I. Plimak, M.J. Collett, and D.F. Walls, Phys. Rev. A 62, 023802 (2000).
18. O.V. Konstantinov and V.I. Perel, Zh. Éksp. Teor. Fiz. 39, 197 (1960) [Sov. Phys. JETP 12, 142 (1961)]
19. L.V. Keldysh, ibid. 47, 1515 (1964) [20, 1018 (1964)].
20. R.F. Pawula, Phys. Rev. 162, 186 (1967).
21. L.I. Plimak, M. Fleischhauer, M.J. Collett, and D.F. Walls, e-print cond-mat/9712192.
22. H.W. Wyld, Ann. Phys. (Leipzig) 14, 143 (1961).
23. L.I. Plimak, M. Fleischhauer, and D.F. Walls, Europhys. Lett. 43, 641 (1998).
24. L.I. Plimak and D.F. Walls, Phys. Rev. A 50, 2627 (1994).
25. J.W. Negerle and H. Orland, Quantum Many-Particle Systems (Addison Wesley, Reading, MA, 1978).
26. M.K. Olsen, L.I. Plimak, and M. Fleischhauer, Phys. Rev. A 65, 053806 (2002).
27. M.K. Olsen, L.I. Plimak and M.J. Collett, Phys. Rev. A 64, 063601 (2001).
28. S. S. Schweber, An Introduction to Relativistic Quantum Field Theory, (Row, Peterson, Evanston, IL, 1961).
29. L.I. Plimak, M.J. Collett, D.F. Walls, and M. Fleischhauer, in Proceedings of the Sixth International Conference on Path Integrals from peV to TeV, edited by R. Casalbuoni et al. (World Scientific, London, 1999), p. 241.
30. T. Hori, Prog. Theor. Phys. 7, 378 (1952).
31. L.I. Plimak, M. Fleishhauer, M.K. Olsen, and M.J. Collett, e-print cond-mat/0102483.
32. R.J. Glauber, Phys. Rev. 130, 2529 (1963)
33. P.L. Kelly and W.H. Kleiner, ibid. 136, 316 (1964).
34. L.I. Plimak, Quantum Semiclassic. Opt. 8, 323 (1996).
35. C. W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, 2002).
36. L. I. Plimak (unpublished).
37. L.I. Plimak, M.K. Olsen, M. Fleischhauer, and M.J. Collett, Europhys. Lett. 56, 372 (2001).
38. S.T. Gevorkyan, G. Yu. Kruchkyan, and K.V. Kheruntsyan, Opt. Commun. 134, 440 (1997).
39. S.T. Gevorkyan, Phys. Rev. A 58, 4862 (1998).
40. Causal variables were first introduced in relativistic quantum electrodynamics by one of the present authors in Ref. [15], where one can find a formal discussion of all related causality properties.