@article{SEDP_1999-2000____A20_0, author = {Castella, Fran\c{c}ois}, title = {R\'esultats de convergence et de non-convergence de l{\textquoteright}\'equation de {Von-Neumann} p\'eriodique vers l{\textquoteright}\'equation de {Boltzmann} quantique.}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:20}, pages = {1--16}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {1999-2000}, zbl = {02124217}, language = {fr}, url = {http://archive.numdam.org/item/SEDP_1999-2000____A20_0/} }
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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:20 PY - 1999-2000 SP - 1 EP - 16 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_1999-2000____A20_0/ LA - fr ID - SEDP_1999-2000____A20_0 ER -
%0 Journal Article %A Castella, François %T Résultats de convergence et de non-convergence de l’équation de Von-Neumann périodique vers l’équation de Boltzmann quantique. %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:20 %D 1999-2000 %P 1-16 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_1999-2000____A20_0/ %G fr %F SEDP_1999-2000____A20_0
Castella, 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 (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (1999-2000), Exposé no. 20, 16 p. http://archive.numdam.org/item/SEDP_1999-2000____A20_0/
[BGW] 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). | MR | Zbl
[Bo] R.W. Boyd, Nonlinear Optics, Academic Press (1992).
[Ca1] 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). | Numdam | MR | Zbl
[Ca2] F. Castella, Travail en cours.
[CD1] 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). | MR | Zbl
[CD2] F. Castella, P. Degond, From the Von-Neumann equation to the Quantum Boltzmann equation in a deterministic framework, Preprint (1999). | MR | Zbl
[CP1] F. Castella, A. Plagne, A distribution result for slices of sums of squares, soumis. | Zbl
[CP2] F. Castella, A. Plagne, A non-convergence result from the periodic Schrödinger equation towards the Quantum Boltzmann equation, travail en cours.
[Co] M. Combescot, Is there a generalized Fermi Golden Rule ?, Preprint (1999).
[EY] L. Erdös, H.T. Yau, Linear Boltzmann equation as scaling limit of quantum Lorentz gas, A paraître dans CPAM.
[HLW] 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). | MR | Zbl
[Ja] R. Jancel, Foundations of Classical and Quantum Statistical Mechanics, Pergamon, Braunschweig (1969). | MR
[KL] W. Kohn, J.M. Luttinger, Phys. Rev., Vol. 108, p. 590 (1957). | MR | Zbl
[KPR] J.B. Keller, G. Papanicolaou, L. Ryzhik, Transport equations for elastic and other waves in random media, Preprint (1996). | MR | Zbl
[Ku] R. Kubo, J. Phys. Soc. Jap., Vol. 12 (1958).
[La] 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). | MR | Zbl
[Li] G. Lindblad, On the generators of Quantum dynamical semigroups, Comm. Math. Phys., Vol. 48, pp. 119-130 (1976). | MR | Zbl
[NM] A. C. Newell, J. V. Moloney, Nonlinear Optics, Advanced Topics in the Interdisciplinary Mathematical Sciences, Addison-Wesley Publishing Company (1992). | MR
[Ni1] 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). | MR | Zbl
[Ni2] F. Nier, A semi-classical picture of quantum scattering, Ann. Sci. Ec. Norm. Sup., 4. Sér., t. 29, p. 149-183 (1996). | Numdam | MR | Zbl
[Pa] W. Pauli, Festschrift zum 60. Geburtstage A. Sommerfelds, p. 30, Hirzel, Leipzig (1928).
[RS] M. Reed, B. Simon, Methods of modern mathematical physics, Academic Press (1972). | MR | Zbl
[SSL] M. Sargent, M.O. Scully, W.E. Lamb, Laser Physics, Addison-Wesley (1977).
[Sp1] H. Spohn, Derivation of the transport equation for electrons moving through random impurities, J. Stat. Phys., Vol. 17, N. 6, p. 385-412 (1977). | MR | Zbl
[Sp2] H. Spohn, Kinetic equations from Hamiltonian dynamics : Markovian limits, Rev. Mod. Phys., Vol. 53, N. 3, pp. 569-615 (1980). | MR
[Sp3] H. Spohn, Large Scale Dynamics of interacting particles, Springer, Berlin (1991). | Zbl
[VH1] L. Van Hove, Physica, Vol. 21 p. 517 (1955). | MR | Zbl
[VH2] L. Van Hove, Physica, Vol. 23 p. 441 (1957). | MR
[VH3] L. Van Hove, in Fundamental Problems in Statistical Mechanics, E.G.D. Cohen ed., p. 157 (1962).
[Zw] R. Zwanzig, Quantum Statistical Mechanics, P.H.E. Meijer ed., Gordon and Breach, New-York (1966).