@article{M2AN_1999__33_2_329_0,
author = {Castella, Fran\c cois},
title = {On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {33},
year = {1999},
pages = {329-349},
mrnumber = {1700038},
zbl = {0954.82023},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_1999__33_2_329_0}
}
Castella, François. On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 33 (1999) pp. 329-349. http://gdmltest.u-ga.fr/item/M2AN_1999__33_2_329_0/
[1] , Fundamental aspects of Quantum Transport, in Handbook on Semiconductors, T.S. Moss Ed., North-Holland (1982).
[2] and , On a hierarchy of macroscopic models for semi-conductors. J. Math. Phys. 37 (1996) 3306-3333. | MR 1401227 | Zbl 0868.45006
[3] , and , On the distribution of free path lengths for the periodic Lorentz gas. Comm. Math. Phys. 190 (1998) 491-508. | MR 1600299 | Zbl 0910.60082
[4] and , Path Integral Approach to Brownian Motion. Physica A 121 (1983) 587-616. | MR 726154 | Zbl 0585.60082
[5] , Lecture, University of Paris 6 (1997).
[6] , Ph.D. thesis, University of Paris VI, France (1997).
[7] and , The Von-Neumann equation with deterministic potential converges towards the Quantum Boltzmann equation. Preprint (1999).
[8] , , and , Caldeira-Leggett Master equation. Work in progress (1999).
[9] , and , Mécanique Quantique, I et II, Enseignement des Sciences, Vol. 16. Hermann (1973).
[10] and , Linear Boltzmann equation as scaling limit of quantum Lorentz gas. Preprint (1998). | Zbl 0894.35027
[11] , and , The Boltzmann Equation for a one-dimensional Quantum Lorentz gas. Preprint (1998). | Zbl 0940.35167
[12] , and , On the weak coupling limit for a Fermi gas in a random potential. Rev. Math, Phys,5 (1993) 209-298. | Zbl 0816.46079
[13] , Foundations of Classical and Quantum Statistical Mechanics. Pergamon, Braunschweig (1969).
[14] and , Phys. Rev. 108 (1957) 590-611. | Zbl 0092.21901
[15] and , Phys. Rev. 109 (1958) 1892. | Zbl 0092.21902
[16] , Nonequilibrium thermodynamics and its statistical foundations. Monographs on Physics and Chemistry of Materials. Oxford Science Publications (1983). | MR 602695
[17] , J. Phys. Soc. Jap. 12 (1957) 570. | MR 98482
[18] and , Sur les mesures de Wigner. Revista Matematica ibero americana 9 (1993) 553-618. | MR 1251718 | Zbl 0801.35117
[19] , Mathematical Methods in Solid State and Superfluid Theory, Oliver and Boyd Eds. (1968) 157.
[20] and , Space homogeneous solutions to the Cauchy problem for the semi-conductor Boltzmann equation. SIAM J. Math. Anal. 28 (1997) 1294-1308. | MR 1474215 | Zbl 0896.45006
[21] , and , Semiconductor equations. Springer-Verlag, Wien (1990). | MR 1063852 | Zbl 0765.35001
[22] and , The drift-diffus ion limit for electron-phonon interaction in semiconductors. Math. Mod. Meth. Appl. Sci. 7 (1997) 707-729. | MR 1460701 | Zbl 0884.45006
[23] , Global existence of solutions for the non-linear Boltzmann equation of semiconductors physics. Rev. Mat. Iberoam. 6 (1990) 43-59. | MR 1086150 | Zbl 0728.45010
[24] , Asymptotic Analysis of a scaled Wigner equation and Quantum Scattering. Transp. Theor. Stat. Phys. 24 (1995) 591-629. | MR 1321368 | Zbl 0870.45003
[25] , A semi-classical picture of quantum scattering. Ann. Sci. Ec. Norm. Sup. 29 (1996) 149-183. | Numdam | MR 1373932 | Zbl 0858.35106
[26] , Festschrift zum 60 Geburtstage A. Sommerfelds. Hirzel, Leipzig (1928) 30.
[27] , Non-Equilibrium Statistical Mechanics. Interscience, New-York (1962). | MR 187841 | Zbl 0106.43301
[28] , Derivation of the transport equation for electrons moving through random impurities. J. Stat. Phys. 17 (1997) 385-412. | MR 471824 | Zbl 0964.82508
[29] , Physica 21 (1955) 517-540. | MR 71346 | Zbl 0065.19505
[30] , Physica 23 (1957) 441. | MR 89576 | Zbl 0079.19405
[31] , in Fundamental Problems in Statistical Mechanics, E.G.D. Cohen Ed. (1962) 157.
[32] , Stochastic processes in physics and chemistry, Lecture Notes in Mathematics. North-Holland 888 (1981). | MR 648937 | Zbl 0511.60038
[33] , Quantum Statistical Mechanics, P.H.E. Meijer Ed., Gordon and Breach, New-York (1966).