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TMF, 2005, Volume 142, Number 2, Pages 371–387 (Mi tmf1789)  

This article is cited in 9 scientific papers (total in 9 papers)

Center-of-mass tomography and probability representation of quantum states for tunneling

A. S. Arkhipova, Yu. E. Lozovikb, V. I. Man'koc, V. A. Sharapova

a Moscow Institute of Physics and Technology
b Institute of Spectroscopy, Russian Academy of Sciences
c P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: We develop a representation of quantum states in which the states are described by fair probability distribution functions instead of wave functions and density operators. We present a one-random-variable tomography map of density operators onto the probability distributions, the random variable being analogous to the center-of-mass coordinate considered in reference frames rotated and scaled in the phase space. We derive the evolution equation for the quantum state probability distribution and analyze the properties of the map. To illustrate the advantages of the new tomography representations, we describe a new method for simulating nonstationary quantum processes based on the tomography representation. The problem of the nonstationary tunneling of a wave packet of a composite particle, an exciton, is considered in detail.

Keywords: quantum tomography, state reconstruction, tunneling, quantum dynamics, computer simulation

DOI: https://doi.org/10.4213/tmf1789

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English version:
Theoretical and Mathematical Physics, 2005, 142:2, 311–323

Bibliographic databases:


Citation: A. S. Arkhipov, Yu. E. Lozovik, V. I. Man'ko, V. A. Sharapov, “Center-of-mass tomography and probability representation of quantum states for tunneling”, TMF, 142:2 (2005), 371–387; Theoret. and Math. Phys., 142:2 (2005), 311–323

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Filinov, VS, “Center-of-mass tomographic approach to quantum dynamics”, Physics Letters A, 372:30 (2008), 5064  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    2. Amosov, GG, “A classical limit for the center-of-mass tomogram in view of the central limit theorem”, Physica Scripta, 80:2 (2009), 025006  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    3. Amosov G.G., Goranskaya D., Traskunov I., “Quantum tomography and Kohn density functional theory”, Journal of Russian Laser Research, 31:3 (2010), 232–238  crossref  mathscinet  isi  scopus  scopus
    4. Dvornikov M., “Pairing of Charged Particles in a Quantum Plasmoid”, J. Phys. A-Math. Theor., 46:4 (2013), 045501  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    5. Fedorov A., “Feynman Integral and Perturbation Theory in Quantum Tomography”, Phys. Lett. A, 377:37 (2013), 2320–2323  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Fedorov A.K., Kiktenko E.O., “Quaternion Representation and Symplectic Spin Tomography”, J. Russ. Laser Res., 34:5 (2013), 477–487  crossref  isi  scopus  scopus
    7. Thapliyal K. Banerjee S. Pathak A., “Tomograms For Open Quantum Systems: in(Finite) Dimensional Optical and Spin Systems”, Ann. Phys., 366 (2016), 148–167  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Trushechkin A., “Semiclassical Evolution of Quantum Wave Packets on the Torus Beyond the Ehrenfest Time in Terms of Husimi Distributions”, J. Math. Phys., 58:6 (2017), 062102  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Aliyeva N.Sh., Bayramova G.A., Chobanova A.A., Jafarov R.G., “Investigation of the Quantum Spherically Symmetric Object and Some Inconsistencies of Familiar Quantum Mechanical Relations in Case of Singular Potentials and Operators”, Proceedings of the 6Th International Conference on Control and Optimization With Industrial Applications, Vol II, eds. Fikret A., Tamer B., Baku State Univ, Inst Applied Mathematics, 2018, 68–70  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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