The quantum measurement process: Lessons from an exactly solvable model

Beyond the Quantum

Volumn , Issue , 2007, Pages 53-65

  ALlahverdyan, A E ^a   Balian, R ^b   Nieuwenhuizen, Th M ^c  

^a YEREVAN PHYSICS INSTITUTE   (Armenia)

^b CEA SACLAY   (France)

^c UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Apparatus; Collapse; Decoherence; Quantum measurement model; Registration; Schr dinger cats; Spin

Indexed keywords

EID: 84968779691     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812771186_0004     Document Type: Chapter

References (31)

1. J. A. Wheeler and W. H. Zurek, Quantum Theory and Measurements (Princeton University Press, 1983)
2. P. Busch, P. J. Lahti and P. Mittelstaedt, The Quantum Theory of Measurements (Springer, Berlin, 1996).
3. M. Schlosshauer, Rev. Mod. Phys. 76 1267 (2004).
4. K. Hepp, Helvetica Physica Acta 45, 237 (1972).
5. M. Cini, Nuovo Cimento B 73, 27 (1983).
6. B. Gaveau and L.S. Schulman, J. Stat. Phys. 58, 1209 (1990).
7. L. S. Schulman, Ann. Phys. 212, 315 (1991).
8. F. Haake and M. Zukowski, Phys. Rev. A 47, 2506 (1993).
9. A. Venugopalan, Phys. Rev. A 61, 012102 (2000).
10. D. Mozyrsky and V. Privman, cond-mat/9903403.
11. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Phys. Rev. A 64, 032108 (2001).
12. D. Braun, F. Haake, and W. T. Strunz, Phys. Rev. Lett. 86, 2913 (2001).
13. G. Sewell, math-ph/0505032.
14. R. Merlin, Europhys. Lett. 76, 541 (2006); quant-ph/05072508.
15. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Europhys. Lett. 61, 452 (2003).
16. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, The quantum measurement process: an exactly solvable model, Atti d. Fond. G. Ronchi, An. LVIII, N. 6, 719 (2003); cond-mat/0309188.
17. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, The quantum measurement process in an exactly solvable model, in AIP Conf. Proc. 750, ed. A. Khrennikov (Am. Inst. Phys., Melville, NY, 2005), pp. 26-34.
18. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Physica E 29, 261 (2005).
19. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Phase Transitions and Quantum Measurements, quant-ph/0508162. In AIP Conf. Proc. 810: Quantum Theory:Reconsideration of Foundations-3, G. Adenier, A. Yu Khrennikov and Th. M. Nieuwenhuizen, eds, (Am. Inst. Phys., Melville, NY, 2006), pp 47-58.
20. For our quadratic interaction the paramagnet is unstable at low temperatures, and this is a drawback for our purposes, since the state will decay without coupling with the tested spin. More precisely, for p = 2 and g = 0 the instability time for the paramagnetic state can be estimated to be or order lnN; if N is so large that this time is larger than the measurement time α 1/γ, then the model with p = 2 is still reasonable as an apparatus.
21. R. T. Cox, Am. J. Phys. 14, 1 (1946).
22. B. de Finetti, Theory of Probability (Wiley, New York, 1990).
23. C. M. Caves, C. A. Fuchs, R. Schack, J. Math. Phys. 43 (2002) 4537.
24. R. Balian, From Microphysics to Macrophysics, in two volumes (Springer, Berlin, 1992).
25. J. E. Mayer and M. G. Mayer, Statistical Mechanics, second ed. (Wiley, New York, 1977), pp. 145-154
26. R. Balian, Am. J. Phys. 67, 1078 (1999).
27. D. Giulini, E. Joos and C. Kiefer, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996); and references therein.
28. R. Balian and M. Vénéroni, Ann. Phys. 174, 229 (1987).
29. W. M. de Muynck, Foundations of Quantum Mechanics, an Empiricist Approach, (Kluwer, Dordrecht, 2002).
30. N. G. van Kampen, Physica A 153, 97 (1988).
31. R. Balian, Am. J. Phys. 57, 1019 (1989).