Geodesic
Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 1, pp. 1-18.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
@article{BUMI_2011_9_4_1_a0,
     author = {Morandi, Omar and Barletti, Luigi and Frosali, Giovanni},
     title = {Perturbation {Theory} in {Terms} of a {Generalized} {Phase-Space} {Quantization} {Procedure}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {1--18},
     publisher = {mathdoc},
     volume = {Ser. 9, 4},
     number = {1},
     year = {2011},
     zbl = {1234.81078},
     mrnumber = {2797463},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a0/}
}
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 della Unione matematica italiana
PY  - 2011
SP  - 1
EP  - 18
VL  - 4
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a0/
LA  - en
ID  - BUMI_2011_9_4_1_a0
ER  - 
%0 Journal Article
%A Morandi, Omar
%A Barletti, Luigi
%A Frosali, Giovanni
%T Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure
%J Bollettino della Unione matematica italiana
%D 2011
%P 1-18
%V 4
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a0/
%G en
%F BUMI_2011_9_4_1_a0
Morandi, Omar; Barletti, Luigi; Frosali, Giovanni. Perturbation Theory in Terms of a Generalized Phase-Space Quantization Procedure. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 1, pp. 1-18. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_1_a0/

[1] J. J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley, Reading, Mass. (1967).

[2] C. K. ZACHOS - D. B. FAIRLIE - T. L. CURTRIGHT (Eds.), Quantum mechanics in phase-space: an overview with selected papers, World Scientific Series in 20th Century Physics, vol. 34, World Scientific Publishing, Hackensack, NJ (2005). | MR | Zbl

[3] H.-W. Lee, Theory and application of the quantum phase-space distribution functions, Physics Reports, 259 (1995), 147. | DOI | MR

[4] R. J. Glauber, The Quantum Theory of Optical Coherence, Phys. Rev., 130 (1963), 2529. | MR

[5] W. R. Frensley, Boundary conditions for open quantum systems driven far from equilibrium, Rev. Mod. Phys., 62 (3) (1990), 745.

[6] C. Jacoboni - P. Bordone, The Wigner-function approach to non-equilibrium electron transport, Rev. Prog. Phys., 67 (2004), 1033-1071.

[7] R. Kosik - M. Nedjalkov - H. Kosina - S. Selberherr, A space dependent Wigner equation including phonon interaction, J. Comput. Electr., 1 (2002), 27.

[8] O. Morandi, Effective classical Liouville-like evolution equation for the quantum phase space dynamics, J. Phys. A: Math. Theor., 43 (2010), 365302. | DOI | MR | Zbl

[9] O. Morandi, Multiband Wigner-function formalism applied to the Zener band transition in a semiconductor, Phys. Rev. B, 80 (2009), 024301.

[10] L. Barletti - L. Demeio - G. Frosali, Multiband quantum transport models for semiconductor devices. In: C. Cercignani, E. Gabetta (Eds.) Transport Phenomena and Kinetic Theory, Birkhauser, Basel (2007), 55-89. | DOI | MR | Zbl

[11] J. Von Neumann, Mathematische Grundlagen der Quantomechanik, Springer Verlag, Berlin (1932). | fulltext EuDML

[12] L. Cohen, Generalized phase-space distribution functions, J. Math. Phys., 7 (1966), 781. | DOI | MR

[13] G. B. Folland, Harmonic Analysis in Phase Space, Princeton University Press, Princeton (1989). | DOI | MR | Zbl

[14] H. Haug - A.-P. Jauho, Quantum Kinetics in Transport and Optic of Semiconductor, Springer Series in Solid-State, Berlin (1996).

[15] S. Varro - J. Javanainen, Gauge-invariant relativistic Wigner functions, J. Opt. B: Quantum Semiclass. Opt., 5 (2003), 402. | DOI | MR | Zbl