|
|
|
References
|
|
|
1. |
Agarwal G. S., “Entropy, the wigner distribution function, and the approach to equilibrium of a system of coupled harmonic oscillators”, Phys. Rev. A, 3 (1971), 828–831 |
2. |
Arnold V. I., Kozlov V. V., Neishtadt A. I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, VINITI, M., 1985 |
3. |
Berezin F. A., Shubin M. A., Uravneniya Shrëdingera, MGU, M., 1983 |
4. |
Bhatia R., Matrix analysis, Grad. Texts in Math., 169, Springer, New York, 1997 |
5. |
Breuer H. P., Petruccione F., The theory of open quantum systems, Oxford Univ. Press, New York, 2002 |
6. |
Blume-Kohout R., Zurek W. H., “Decoherence form chaotic environment: an upside down “oscillator” as a model”, Phys. Rev. A, 68 (2003), 032104 |
7. |
Caldeira A. O., Leggett A. J., “Influence of damping on quantum interference: An exactly soluble model”, Phys. Rev. A, 31 (1985), 1059–1066 |
8. |
Combescure M., Robert D., Coherent states and applications in mathematical physics, Springer-Verlag, Dordreht, 2012 |
9. |
Davies E. B., Quantum theory of open systems, Acad. Press, London, 1976 |
10. |
Dodonov V. V., Man'ko O. V., Man'ko V. I., “Quantum non-stationary oscillators: models and applications”, J. Russian Laser Research, 16:1 (1995), 1–56 |
11. |
Dodonov V. V., “Parametric excitation and generation of nonclassical states in linear media”, Theory of Non classical States of Light, Taylor & Francis, London, 2003, 153–218 |
12. |
Eisert J., Plenio M. B., “Quantum and classical correlations in quantum brownian motion”, Phys. Rev. Lett., 89:13 (2002), 137902 |
13. |
Feynman R. P., Vernon F. L., “The theory of a general quantum system interacting with a linear dissipative system”, Ann. Phys., 24 (1963), 118–173 |
14. |
Fleming C. H., Hu B. L., Roura A., “Exact analytical solutions to the master equation of Brownian motion for a general environment”, Ann. Phys., 326:5 (2011), 1207–1258 |
15. |
Folland G., Harmonic analysis in phase space, Ann. Math. Stud., 122, Princeton Univ. Press, Princeton, 1989 |
16. |
Ford G. W., Kac M., “On the quantum Langevin equation”, J. Statist. Phys., 46:5–6 (1987), 803–810 |
17. |
Ford G. W., Kac M., Mazur P., “Statistical mechanics of assemblies of coupled oscillators”, J. Math. Phys., 6 (1965), 504–515 |
18. |
Ford G. W., O'Connell R. F., “Exact solution of the Hu–Paz–Zhang master equation”, Phys. Rev. D, 64 (2001), 105020 |
19. |
Gokhberg I., Krein M. G.,, Vvedenie v teoriyu nesamosopryazhennykh operatorov v gilbertovom prostranstve, Nauka, M., 1965 |
20. |
Halliwell J. J., Yu T., “Alternative derivation of the Hu–Paz–Zhang master equation of quantum Brownian motion”, Phys. Rev. D, 53:4 (1966), 2012–2019 |
21. |
Gerschgorin S., “Über die Abgrenzung der Eigenwerte einer Matrix”, Izv. AN SSSR. Ser. mat., 1931, no. 6, 749–754 |
22. |
Hörmander L., “Symplectic classification of quadratic forms, and general Mehler formulas”, Math. Z., 219:3 (1995), 413–449 |
23. |
Horodecki M., Horodecki P., Horodecki R., “Separability of mixed states: necessary and sufficient conditions”, Phys. Lett. A, 223:1–2 (1966), 1–8 |
24. |
Hu B. L., Paz J. P., Zhang Y., “Quantum Brownian motion in a general environment: exact master equation with nonlocal dissipation and colored noise”, Phys. Rev. D, 45:8 (1992), 2843–2861 |
25. |
Joos E., Zeh H. D., “The emergence of classical properties through interaction with the environment”, Z. Phys. B Condensed Matter, 59 (1985), 223–243 |
26. |
Hornberger K., “Introduction to decoherence, entangement and decoherence”, Lecture Notes in Phys., 768, Springer, Berlin, 2009, 221–276 |
27. |
Maspero A., Robert D., “On time dependent Schrödinger eqiations: global well-posedness and growth of Sobolev norms”, J. Funct. Anal., 273:2 (2017), 721–781 |
28. |
Nielsen M. A., Chuang I. L., Quantum computation and quantum information, Cambridge Univ. Press, Cambridge, 2000 |
29. |
Robert D., Time evolution of states for open quantum systems. The quadratic case, 2012, arXiv: 1208.1598v2[math-ph] |
30. |
Schlosshauer M., Decoherence and the quantum-to-classical transition, Springer-Verlag, Heidelberg, 2007 |
31. |
Simon R., Chaturvedi S., Srinivasan V., “Congruences and canonical forms for a positive matrix: application to Schweinler–Wigner extremum principle”, J. Math. Phys., 40:7 (1999), 3632–3643 |
32. |
Simon R., Susarshan E. C. G., Mukada N., “Gaussian–Wigner distributions: a complete characterization”, Phys. Lett. A, 124:4–5 (1987), 223–228 |
33. |
Simon R., “Peres–Horodecki separability criterion for continuous variable systems”, Phys. Rev. Lett., 84:12 (2000), 2726–2729 |
34. |
Schrödinger E., “Discussion of probability Relations between Separated Systems”, Proc. Cambridge Philos. Soc., 31 (1935), 555–563 |
35. |
Werner R. F., Wolf M. M., “Bound entangled Gaussian states”, Phys. Rev. Lett., 86:16 (2001), 3658–3661 |
36. |
Williamson J., “On algebraic problem concerning the normal forms of linear dynamical systems”, Amer. J. Math., 58:1 (1936), 141–163 |
37. |
Zurek W. H., “Pointer basis of quantum apparatus: into what mixture does the wave packet collapse”, Phys. Rev. D, 24:6 (1981), 1516–1525 |