Quantum flows as Markovian limit of emission, absorption and scattering interactions

Communications in Mathematical Physics

Volumn 254, Issue 2, 2005, Pages 489-512

  Gough, John ^a  

^a NOTTINGHAM TRENT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13244259380     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1163-y     Document Type: Article

References (27)

1. Accardi, L., Frigerio, A., Lu, Y.G.: Weak coupling limit as a quantum functional central limit theorem. Commun. Math. Phys. 131, 537-570 (1990)
2. Pulé, J.V.: The Bloch equations. Commun. Math. Phys. 38, 241-256 (1974)
3. Hudson, R.L., Streater R.F.: Itô's formula is the chain rule with Wick ordering. Phys. Lett. 86, 277-279 (1982)
4. Krée, P., Raczka, R.: Kernels and symbols of operators in quantum field theory. Ann. Inst. H. Poincaré, Sect. A. 28, 41-73 (1978)
5. Gough, J.: Asymptotic stochastic transformations for non-linear quantum dynamical systems. Reports Math. Phys. 44(3), 313-338 (1999)
6. Van Hove, L.: Quantum mechanical perturbations giving rise to a statistical transport equation. Physica. 21, 617-640 (1955)
7. Hudson, R.L., Parthasarathy, K.R.: Quantum Itô's formula and stochastic evolutions. Commun. Math. Phys. 93, 301-323 (1984)
8. Wong, E., Zakai, M.: On the relationship between ordinary and stochastic differential equations. Int. J. Eng. Sci. 3, 213-229 (1965)
9. Frigerio, A., Gorini V.: Diffusion processes, quantum dynamical semigroups, and the classical KMS condition. J. Math. Phys. 25(4), 1050-1065 (1984)
10. Bismut, J.M.: Mecanique Aléatoire. Lecture Notes in Mathematics 866, Berlin: Springer-Verlag, 1981
11. Spohn, H.: Kinetic Equations from Hamiltonian dynamics: Markovian limits. Rev. Mod. Phys. 53, 569-615 (1980)
12. Davies, E.B.: Markovian master equations. Commun. Math. Phys. 39, 91-110 (1974)
13. Davies, E.B.: Quantum theory of Open Systems. London, New York: Academic Press, 1976
14. Gorini, V., Kossakowski, A., Sudarshan, E.C.G.: Completely positive dynamical semigroups on N-level systems. J. Math. Phys. 17, 821-825 (1976)
15. Lindblad, G.: On the generators of completely positive semi-groups. Commun. Math. Phys. 48, 119-130 (1976)
16. Von Waldenfels, W.: Itô Solution of the Linear Quantum Stochastic Differential Equation Describing Light Emission and Absorption. Lecture Notes in Mathematics 1055, Berlin Heidelberg-New York: Springer, 1986, pp. 384-411
17. Spohn, H., Lebowitz, J.L.: Irreversible thermodynamics for quantum systems weakly coupled to thermal reservoirs. Adv. Chem. Phys. 38, 109-142 (1978)
18. Chebotarev, A.N.: Symmetric form of the Hudson-Parthasarathy equation. Mat. Zametki 60(5), 725-750 (1996)
19. Gough, J.: Noncommutative Markov approximations. Dokl. Akad. Nauk. 379(6), 112-116 (2001)
20. Parthasarathy, K.R.: An Introduction to Quantum Stochastic Calculus. Basel: Birkhaüser, 1992
21. Riordan, J.: An Introduction to Combinatorial Analysis. New York: Wiley, 1980
22. Rota, G.-C., Wallstrom, T.C.: Stochastic integrals: a combinatorial approach. Ann Probab. 25, 1257-1283 (1997)
23. Abrikosov, A.A., Gorkov, L.P., Dzyaloshinski, I.E.: Methods of Quantum field Theory in Statistical Physics. New York: Dover Publications, 1963
24. Pathria, K.R.: Statistical Mechanics. Oxford: Butterworth-Heinemann, 1972
25. Gough, J.: A new approach to non-commutative white noise analysis. C.R. Acad. Sci. Paris t. 326, série I, 981-985 (1998)
26. Accardi, L., Frigerio, A., Lu, Y.G.: The quantum weak coupling limit (II): Langevin equation and finite temperature case. Publ. RIMS Kyoto 31, 545-599 (1995)
27. Accardi, L., Lu, Y.G., Volovich, I.V.: Quantum Theory and its Stochastic Limit. Berlin Heidelberg: Springer-Verlag, 2002