Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure

Omar Morandi; Luigi Barletti; Giovanni Frosali

Bollettino dell'Unione Matematica Italiana (2011)

  • Volume: 4, Issue: 1, page 1-18
  • ISSN: 0392-4041

Abstract

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A new approach to perturbation theory in the quantum phase-space formalism is proposed, in order to devise some approximated description of the quantum phase-space dynamics, which is not directly related to the usual semi-classical approximation. A general class of equivalent quasi-distribution functions based on the Wigner-Moyal formalism is considered and a first-order invariant formulation of the dynamics is obtained. The relationship between the various phase-space representations is expressed in term of a pseudo-differential operator defined by the Moyal product. In particular, our theory is applied to the sub-class of representations obtained by a first order perturbation of the Wigner representation. Finally the connection of our approach with some well established gauge-invariant formulations of the Wigner dynamics in the presence of an external magnetic field is investigated.

How to cite

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Morandi, Omar, Barletti, Luigi, and Frosali, Giovanni. "Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure." Bollettino dell'Unione Matematica Italiana 4.1 (2011): 1-18. <http://eudml.org/doc/290734>.

@article{Morandi2011,
abstract = {A new approach to perturbation theory in the quantum phase-space formalism is proposed, in order to devise some approximated description of the quantum phase-space dynamics, which is not directly related to the usual semi-classical approximation. A general class of equivalent quasi-distribution functions based on the Wigner-Moyal formalism is considered and a first-order invariant formulation of the dynamics is obtained. The relationship between the various phase-space representations is expressed in term of a pseudo-differential operator defined by the Moyal product. In particular, our theory is applied to the sub-class of representations obtained by a first order perturbation of the Wigner representation. Finally the connection of our approach with some well established gauge-invariant formulations of the Wigner dynamics in the presence of an external magnetic field is investigated.},
author = {Morandi, Omar, Barletti, Luigi, Frosali, Giovanni},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {1-18},
publisher = {Unione Matematica Italiana},
title = {Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure},
url = {http://eudml.org/doc/290734},
volume = {4},
year = {2011},
}

TY - JOUR
AU - Morandi, Omar
AU - Barletti, Luigi
AU - Frosali, Giovanni
TI - Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure
JO - Bollettino dell'Unione Matematica Italiana
DA - 2011/2//
PB - Unione Matematica Italiana
VL - 4
IS - 1
SP - 1
EP - 18
AB - A new approach to perturbation theory in the quantum phase-space formalism is proposed, in order to devise some approximated description of the quantum phase-space dynamics, which is not directly related to the usual semi-classical approximation. A general class of equivalent quasi-distribution functions based on the Wigner-Moyal formalism is considered and a first-order invariant formulation of the dynamics is obtained. The relationship between the various phase-space representations is expressed in term of a pseudo-differential operator defined by the Moyal product. In particular, our theory is applied to the sub-class of representations obtained by a first order perturbation of the Wigner representation. Finally the connection of our approach with some well established gauge-invariant formulations of the Wigner dynamics in the presence of an external magnetic field is investigated.
LA - eng
UR - http://eudml.org/doc/290734
ER -

References

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  9. MORANDI, O., Multiband Wigner-function formalism applied to the Zener band transition in a semiconductor, Phys. Rev. B, 80 (2009), 024301. 
  10. BARLETTI, L. - DEMEIO, L. - FROSALI, G., Multiband quantum transport models for semiconductor devices. In: C. Cercignani, E. Gabetta (Eds.) Transport Phenomena and Kinetic Theory, Birkhauser, Basel (2007), 55-89. Zbl1121.82036MR2334306DOI10.1007/978-0-8176-4554-0_4
  11. VON NEUMANN, J., Mathematische Grundlagen der Quantomechanik, Springer Verlag, Berlin (1932). 
  12. COHEN, L., Generalized phase-space distribution functions, J. Math. Phys., 7 (1966), 781. MR194105DOI10.1063/1.1931206
  13. FOLLAND, G. B., Harmonic Analysis in Phase Space, Princeton University Press, Princeton (1989). Zbl0682.43001MR983366DOI10.1515/9781400882427
  14. HAUG, H. - JAUHO, A.-P., Quantum Kinetics in Transport and Optic of Semiconductor, Springer Series in Solid-State, Berlin (1996). 
  15. VARRO, S. - JAVANAINEN, J., Gauge-invariant relativistic Wigner functions, J. Opt. B: Quantum Semiclass. Opt., 5 (2003), 402. Zbl1016.81038MR1992721DOI10.1088/1464-4266/5/3/377

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