Decoherent histories and hydrodynamic equations

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 58, Issue 10, 1998, Pages

  Halliwell, J J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1542629794     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.58.105015     Document Type: Article

References (54)

1. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984);
2. R. B. GriffithsPhys. Rev. Lett. 70, 2201 (1993).
3. M. Gell-Mann and J. B. Hartle, in Complexity, Entropy and the Physics of Information, edited by W. Zurek, SFI Studies in the Sciences of Complexity, Vol. VIII (Addison Wesley, Reading, MA, 1990);
4. in Proceedings of the Third International Symposium on the Foundations of Quantum Mechanics in the Light of New Technology, edited by S. Kobayashi, H. Ezawa, Y. Murayama, and S. Nomura (Physical Society of Japan, Tokyo, 1990).
5. M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47, 3345 (1993).
6. R. Omnès, J. Stat. Phys. 53, 893 (1988);
7. J. Stat. Phys.R. Omnès53, 933 (1988);
8. J. Stat. Phys.R. Omnès53, 957 (1988);
9. J. Stat. Phys.R. Omnès57, 357 (1989);
10. R. OmnèsAnn. Phys. (N.Y.) 201, 354 (1990);
11. R. OmnèsRev. Mod. Phys. 64, 339 (1992).
12. H. F. Dowker and J. J. Halliwell, Phys. Rev. D 46, 1580 (1992).
13. R. P. Feynman and F. L. Vernon, Ann. Phys. (N.Y.) 24, 118 (1963).
14. A. Caldeira and A. Leggett, Physica A 121, 587 (1983).
15. E. Joos and H. D. Zeh, Z. Phys. B 59, 223 (1985).
16. See, for example, J. P. Paz and W. H. Zurek, Phys. Rev. D 48, 2728 (1993);
17. W. Zurek, in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Perez-Mercader, and W. Zurek (Cambridge University Press, Cambridge, England, 1994);
18. W. Zurek, “Decoherence, Einselection, and the Existential Interpretation (The Rough Guide),” quant-ph/9805065.
19. J. J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995);
20. Phys. Rev. DJ. J. HalliwellA. Zoupas55, 4697 (1997).
21. J. B. Hartle, R. Laflamme, and D. Marolf, Phys. Rev. D 51, 7007 (1995).
22. The standard derivation of the hydrodynamic equations from their underlying microscopic origins is described in many places. An interesting discussion of the general issues is by G. E. Uhlenbeck, in M. Kac, Lectures in Applied Mathematics: Probability and Related Topics in the Physics Sciences (Interscience, New York, 1957), Appendix.A useful basic discussion may be found in K. Huang, Statistical Mechanics, 2nd ed. (Wiley, New York, 1987).See also, for example, R. Balescu, Statistical Dynamics: Matter out of Equilibrium (Imperial College Press, London, 1997);
23. D. Forster, Hydrodynamic Fluctuations, Broken Symmetry and Correlation Functions (Benjamin, Reading, MA, 1975);
24. H. J. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundations (Clarendon, Oxford, 1981);
25. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974);
26. D. Zubarev, V. Morozov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes (Akademie-Verlag, Berlin, 1996), Vol. 1.
27. J. B. Hartle, in Proceedings of the Cornelius Lanczos International Centenary Conference, edited by J. D. Brown, M. T. Chu, D. C. Ellison, and R. J. Plemmons (SIAM, Philadelphia, 1994).
28. J. J. Halliwell, in Fundamental Problems in Quantum Theory, edited by D. Greenberger and A. Zeilinger [Ann. (N.Y.) Acad. Sci. 775, 726 (1994)].
29. T. Brun and J. J. Halliwell, Phys. Rev. 54, 2899 (1996).
30. T. Brun and J. B. Hartle, “Hydrodynamic Equations from Decoherent Histories, ” Santa Barbara report (in preparation).
31. E. Calzetta and B. L. Hu, in Directions in General Relativity, edited by B. L. Hu and T. A. Jacobson (Cambridge University Press, Cambridge, England, 1993).
32. B. Carazza, Found. Phys. Lett. 10, 581 (1997).
33. J. C. Flores, “Decoherence from internal degrees of freedom for clusters of mesoparticles: a hierarchy of master equations,” quant-ph/9803032, 1998.
34. C. Anastopoulos, “Hydrodynamic equations from quantum field theory,” gr-qc/9805074, 1998.
35. R. Omnès, comment after talk by W. Zurek, in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Perez-Mercader, and W. Zurek (Cambridge University Press, Cambridge, England, 1994), p. 209.
36. C. L. Feffermann, Bull. Am. Math. Soc. 9, 129 (1983).
37. H. F. Dowker and A. Kent, J. Stat. Phys. 82, 1575 (1996);
38. H. F. DowkerA. KentPhys. Rev. Lett. 75, 3038 (1995).
39. I. Giardina and A. Rimini, Found. Phys. 26, 973 (1996).
40. R. B. Griffiths, Phys. Rev. A 54, 2759 (1996);
41. Phys. Rev. AR. B. Griffiths57, 1604 (1998).
42. J. B. Hartle, “Quantum Pasts and the Utility of Histories,” gr-qc/9712001.
43. H. Risken, The Fokker-Planck Equations: Methods of Solution and Applications, 2nd ed. (Springer-Verlag, Berlin, 1989).
44. R. Omnès, Phys. Rev. A 56, 3383 (1997).
45. L. Diósi, gr-qc/9403046.
46. C. Anastopoulos and J. J. Halliwell, Phys. Rev. D 51, 6870 (1995).
47. D. Finkelstein, Trans. NY Acad. Sci. 25, 621 (1963);
48. N. Graham, in The Many Worlds Interpretation of Quantum Mechanics, edited by B. S. DeWitt and N. Graham (Princeton University Press, Princeton, 1973);
49. J. B. Hartle, Am. J. Phys. 36, 704 (1968).
50. See also E. Farhi, J. Goldstone, and S. Gutmann, Ann. Phys. (N.Y.) 192, 368 (1989).
51. The approach to equilibrium (or local equilibrium) is discussed in many places. Some examples are G. S. Agarwal, Phys. Rev. A 3, 838 (1971);
52. M. A. Huerta and H. S. Robertson, J. Stat. Phys. 1, 393 (1969);
53. M. Tegmark and H. S. Shapiro, Phys. Rev. E 50, 2538 (1994).
54. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974).