Résultats de convergence et de non-convergence de l’équation de Von-Neumann périodique vers l’équation de Boltzmann quantique.
- [1] CNRS et IRMAR - Université de Rennes 1 - Campus de Beaulieu, 35042 Rennes Cedex - France.
Séminaire Équations aux dérivées partielles (1999-2000)
- Volume: 1999-2000, page 1-16
Access Full Article
topHow to cite
topCastella, François. "Résultats de convergence et de non-convergence de l’équation de Von-Neumann périodique vers l’équation de Boltzmann quantique.." Séminaire Équations aux dérivées partielles 1999-2000 (1999-2000): 1-16. <http://eudml.org/doc/10995>.
@article{Castella1999-2000,
affiliation = {CNRS et IRMAR - Université de Rennes 1 - Campus de Beaulieu, 35042 Rennes Cedex - France.},
author = {Castella, François},
journal = {Séminaire Équations aux dérivées partielles},
language = {fre},
pages = {1-16},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Résultats de convergence et de non-convergence de l’équation de Von-Neumann périodique vers l’équation de Boltzmann quantique.},
url = {http://eudml.org/doc/10995},
volume = {1999-2000},
year = {1999-2000},
}
TY - JOUR
AU - Castella, François
TI - Résultats de convergence et de non-convergence de l’équation de Von-Neumann périodique vers l’équation de Boltzmann quantique.
JO - Séminaire Équations aux dérivées partielles
PY - 1999-2000
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1999-2000
SP - 1
EP - 16
LA - fre
UR - http://eudml.org/doc/10995
ER -
References
top- J. Bourgain, F. Golse, B. Wennberg, On the distribution of free path lengths for the periodic Lorentz gas, Comm. Math. Phys., Vol. 190, p. 491-508 (1998). Zbl0910.60082MR1600299
- R.W. Boyd, Nonlinear Optics, Academic Press (1992).
- F. Castella, On the derivation of a Quantum Boltzmann Equation from the periodic Von-Neumann equation, Math. Mod. An. Num., Vol. 33, N. 2, p. 329-350 (1999). Zbl0954.82023MR1700038
- F. Castella, Travail en cours.
- F. Castella, P. Degond, From the Von-Neumann equation to the Quantum Boltzmann equation in a deterministic framework, C. Rend. Acad. Sci., t. 329, sér. I, p. 231-236 (1999). Zbl0930.35146MR1711066
- F. Castella, P. Degond, From the Von-Neumann equation to the Quantum Boltzmann equation in a deterministic framework, Preprint (1999). Zbl1034.82033MR1711066
- F. Castella, A. Plagne, A distribution result for slices of sums of squares, soumis. Zbl1019.11025
- F. Castella, A. Plagne, A non-convergence result from the periodic Schrödinger equation towards the Quantum Boltzmann equation, travail en cours. Zbl1080.82014
- M. Combescot, Is there a generalized Fermi Golden Rule ?, Preprint (1999).
- L. Erdös, H.T. Yau, Linear Boltzmann equation as scaling limit of quantum Lorentz gas, A paraître dans CPAM. Zbl0894.35027
- T.G. Ho, L.J. Landau, A.J. Wilkins, On the weak coupling limit for a Fermi gas in a random potential, Rev. Math. Phys., Vol. 5, N. 2, p. 209-298 (1993). Zbl0816.46079MR1223523
- R. Jancel, Foundations of Classical and Quantum Statistical Mechanics, Pergamon, Braunschweig (1969). MR247817
- W. Kohn, J.M. Luttinger, Phys. Rev., Vol. 108, p. 590 (1957). Zbl0092.21901MR96408
- J.B. Keller, G. Papanicolaou, L. Ryzhik, Transport equations for elastic and other waves in random media, Preprint (1996). Zbl0954.74533MR1427483
- R. Kubo, J. Phys. Soc. Jap., Vol. 12 (1958).
- L.J. Landau, Observation of Quantum Particles on a Large Space-Time Scale, J. Stat. Phys., Vol. 77, N. 1-2, pp. 259-309 (1994). Zbl0860.60097MR1300536
- G. Lindblad, On the generators of Quantum dynamical semigroups, Comm. Math. Phys., Vol. 48, pp. 119-130 (1976). Zbl0343.47031MR413878
- A. C. Newell, J. V. Moloney, Nonlinear Optics, Advanced Topics in the Interdisciplinary Mathematical Sciences, Addison-Wesley Publishing Company (1992). MR1163192
- F. Nier, Asymptotic Analysis of a scaled Wigner equation and Quantum Scattering, Transp. Theor. Stat. Phys., Vol. 24, N. 4 et 5, p. 591-629 (1995). Zbl0870.45003MR1321368
- F. Nier, A semi-classical picture of quantum scattering, Ann. Sci. Ec. Norm. Sup., 4. Sér., t. 29, p. 149-183 (1996). Zbl0858.35106MR1373932
- W. Pauli, Festschrift zum 60. Geburtstage A. Sommerfelds, p. 30, Hirzel, Leipzig (1928).
- M. Reed, B. Simon, Methods of modern mathematical physics, Academic Press (1972). Zbl0242.46001MR493419
- M. Sargent, M.O. Scully, W.E. Lamb, Laser Physics, Addison-Wesley (1977).
- H. Spohn, Derivation of the transport equation for electrons moving through random impurities, J. Stat. Phys., Vol. 17, N. 6, p. 385-412 (1977). Zbl0964.82508MR471824
- H. Spohn, Kinetic equations from Hamiltonian dynamics : Markovian limits, Rev. Mod. Phys., Vol. 53, N. 3, pp. 569-615 (1980). MR578142
- H. Spohn, Large Scale Dynamics of interacting particles, Springer, Berlin (1991). Zbl0742.76002
- L. Van Hove, Physica, Vol. 21 p. 517 (1955). Zbl0065.19505MR71346
- L. Van Hove, Physica, Vol. 23 p. 441 (1957). MR89576
- L. Van Hove, in Fundamental Problems in Statistical Mechanics, E.G.D. Cohen ed., p. 157 (1962).
- R. Zwanzig, Quantum Statistical Mechanics, P.H.E. Meijer ed., Gordon and Breach, New-York (1966).
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.