On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation

Castella, François. " On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation." ESAIM: Mathematical Modelling and Numerical Analysis 33.2 (2010): 329-349. <http://eudml.org/doc/197395>.

@article{Castella2010,
abstract = { We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet with memory in time, so that it appears to be time-reversible. We comment on this point, and further describe the properties of the limiting equation. },
author = {Castella, François},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Quantum Boltzmann equation; Von-Neumann equation; Fermi Golden Rule; time-irreversibility; memory effects; weak-coupling limit.; quantum Boltzmann equation; Fermi golden rule; weak-coupling limit; semi-conductor Boltzmann equation; von Neumann equation; asymptotics},
language = {eng},
month = {3},
number = {2},
pages = {329-349},
publisher = {EDP Sciences},
title = { On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation},
url = {http://eudml.org/doc/197395},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Castella, François
TI - On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 2
SP - 329
EP - 349
AB - We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet with memory in time, so that it appears to be time-reversible. We comment on this point, and further describe the properties of the limiting equation.
LA - eng
KW - Quantum Boltzmann equation; Von-Neumann equation; Fermi Golden Rule; time-irreversibility; memory effects; weak-coupling limit.; quantum Boltzmann equation; Fermi golden rule; weak-coupling limit; semi-conductor Boltzmann equation; von Neumann equation; asymptotics
UR - http://eudml.org/doc/197395
ER -