Abstract
We show that the ambiguity in choosing the tomographic propagator for an evolving linear quantum system is related to the homogeneity properties of the system symplectic tomogram. We study in detail an example of the driven harmonic oscillator. We prove that two formally different propagators of the quantum kinetic equation for the oscillator are identical on the domain of homogeneous tomographic probability distributions.
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A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).
E. Schrödinger, Ann. Phys., 79, 361 (1926).
E. Schrödinger, Ann. Phys., 81, 109 (1926).
J. von Neumann, Göttingen. Nachr., (245) (1927).
L. D. Landau, Z. Phys., 45, 430 (1927).
S. Mancini, V. I. Manko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).
R. P. Feynmann, Rev. Mod. Phys., 20, 367 (1948).
J. E. Moyal, Proc. Cambridge Philos. Soc., 45, 99 (1949).
E. P. Wigner, Phys. Rev., 40, 749 (1932).
O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 18, 407 (1997).
O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 20, 67 (1999).
V. I. Man’ko and R. Vilela Mendes, Physica D, 145, 330 (2000).
D. B. Lemeshevskiy and V. I. Man’ko, J. Russ. Laser Res., 33, 110 (2012).
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Lemeshevskiy, D.B., Man’ko, V.I. Calculations of the propagator within the tomographic-probability framework. J Russ Laser Res 33, 503–508 (2012). https://doi.org/10.1007/s10946-012-9308-5
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DOI: https://doi.org/10.1007/s10946-012-9308-5