Publication: Hybrid classical-quantum formulations ask for hybrid notions
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2012-10-22
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American Physical Society
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Abstract
We reappraise some of the hybrid classical-quantum models proposed in the literature with the goal of retrieving some of their common characteristics. In particular, first, we analyze in detail the Peres-Terno argument regarding the inconsistency of hybrid quantizations of the Sudarshan type. We show that to accept such hybrid formalism entails the necessity of dealing with additional degrees of freedom beyond those in the straight complete quantization of the system. Second, we recover a similar enlargement of degrees of freedom in the so-called statistical hybrid models. Finally, we use Wigner's quantization of a simple model to illustrate how in hybrid systems the subsystems are never purely classical or quantum. A certain degree of quantumness (classicality) is being exchanged between the different sectors of the theory, which in this particular unphysical toy model makes them undistinguishable.
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©2012 American Physical Society.
Special thanks go to Lorenzo Luis Salcedo and an anonymous referee for enlightening comments and bringing important references to our attention. The authors also want to thank Víctor Aldaya, Luis C. Barbado, Julio Guerrero, Gil Jannes, and Francisco López-Ruiz for helpful ciscussions. Financial support was provided by the Spanish MINECO through projects FIS2011-30145-C03-01 and FIS2011-30145- C03-02, by the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042), and by the Junta de Andalucía through project FQM219. R.C. acknowledge support from CSIC through the JAE predoc program, cofunded by FSE.
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[1] G. F. R. Ellis, Ann. Phys. (NY) 327, 1890 (2012).
[2] W. Boucher and J. H. Traschen, Phys. Rev. D 37, 3522 (1988).
[3] A. Anderson, Phys. Rev. Lett. 74, 621 (1995).
[4] B. O. Koopman, Proc. Natl. Acad. Sci. 17, 315 (1931).
[5] J. von Neumann, Ann. Math. 33, 587 (1932).
[6] E. C. G. Sudarshan, Pramana 6, 117 (1976).
[7] T. N. Sherry and E. C. G. Sudarshan, Phys. Rev. D 18, 4580 (1978).
[8] T. N. Sherry and E. C. G. Sudarshan, Phys. Rev. D 20, 857 (1979).
[9] S. R. Gautam, T. N. Sherry, and E. C. G. Sudarshan, Phys. Rev. D 20, 3081 (1979).
[10] A. Peres and D. R. Terno, Phys. Rev. A 63, 022101 (2001).
[11] D. R. Terno, Found. Phys. 36, 102 (2006).
[12] A. Heslot, Phys. Rev. D 31, 1341 (1985).
[13] H.-T. Elze, Phys. Rev. A 85, 052109 (2012).
[14] J. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuchí, P. Echenique, and F. Falceto, arXiv:1010.1494.
[15] J. L. Alonso, A. Castro, J. Clemente-Gallardo, J. C. Cuchí, P. Echenique, and F. Falceto,J. Phys. A: Math. Theor. 44, 395004 (2011).
[16] J. L. Alonso, J. Clemente-Gallardo, J. C. Cuchí, P. Echenique, and F. Falceto, J. Chem. Phys. 137, 054106 (2012).
[17] M. J. W. Hall and M. Reginatto, Phys. Rev. A 72, 062109 (2005).
[18] M. J. W. Hall, Phys. Rev. A 78, 042104 (2008).
[19] A. J. K. Chua, M. J. W. Hall, and C. M. Savage, Phys. Rev. A 85, 022110 (2012).
[20] D. I. Bondar, R. Cabrera, R. R. Lompay, M. Y. Ivanov, and H. A. Rabitz, arXiv:1105.4014.
[21] J. Caro and L. L. Salcedo, Phys. Rev. A 60, 842 (1999).
[22] R. H. Brandenberger, Rev. Mod. Phys. 57, 1 (1985).
[23] D. Sudarsky, in Proceedings of the VIII Mexican School on Gravitation and Mathematical Physics, AIP Conf. Proc. No. 1256 (AIP, New York, 2010), pp. 107–121.
[24] I. V. Aleksandrov, Z. Naturforsch. A 36a, 902 (1981).
[25] L. L. Salcedo, Phys. Rev. A 54, 3657 (1996).
[26] D. Sahoo, J. Phys. A 37, 997 (2004).
[27] T. Dass, arXiv:0909.4606.
[28] L. L. Salcedo, Phys. Rev. A 85, 022127 (2012).
[29] M. Radonjic, S. Prvanoviíic, and N. Buric, Phys. Rev. A 85, 064101 (2012).
[30] D. Mauro, arXiv:quant-ph/0301172.
[31] L. E. Ballentine, Quantum Mechanics: A Modern Development (World Scientific, Singapore, 1998).
[32] M. Reed and B. Simon, Methods of Modern Mathematical Physics: Functional Analysis (Academic Press, Orlando, FL, 1981), Vol. 1.
[33] L. E. Ballentine and S. M. McRae, Phys. Rev. A 58, 1799 (1998).
[34] H. R. Jauslin and D. Sugny, in Mathematical Horizons for Quantum Physics, edited by H. Araki, B.-G. Englert, L.-C. Kwek, and J. Suzuki, Lecture Notes Series (Institute for Mathematical Sciences, National University of Singapore, 2010), pp. 65–96.
[35] W. G. Unruh and R. M. Wald, Phys. Rev. D 40, 2598 (1989).
[36] W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003).
[37] An anonymous referee made us notice that there is an analogy to this behavior in de Broglie–Bohm quantum mechanics. To calculate the trajectory of one particle in a two-particle system it is not enough to know the initial position and velocity of the particle and its reduced density matrix; one has to specify the entire wave function of the two-particle system. Different wave functions having the same reduced density matrix could lead to completely different particle trajectories.
[38] J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).
[39] H. J. Groenewold, Physica 12, 405 (1946).
[40] B. S. DeWitt, J. Math. Phys. 3, 619 (1962).
[41] B. S. DeWitt, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), Chap. 8, pp. 266–381.
[42] W. Unruh, in Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. DeWitt, edited by S. M. Christensen (Hilger, Bristol, 1984), Chap. 8, pp. 234–242.
[43] L. Diosi, ´ Phys. Lett. A 120, 377 (1987).
[44] R. Penrose, Gen. Relativ. Gravitation 28, 581 (1996).
[45] W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, Phys. Rev. Lett. 91, 130401 (2003).
[46] G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986).