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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 33, Issue: 2, page 329-349
- ISSN: 0764-583X

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topCastella, 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 -

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