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weak-couplinglimit.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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On the derivation of a quantum Boltzmann equationfrom the periodic Von-Neumann equation
François Castella
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 2 / March 1999

Published online by Cambridge University Press:

15 August 2002, pp. 329-349

Print publication:

March 1999
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We present the semi-conductor Boltzmann equation,which is time-reversible, and indicate that it can be formally derivedby considering the large time and small perturbing potential limitin the Von-Neumann equation (time-reversible). We then rigorously computethe corresponding asymptotics in the case of the Von-Neumann equation onthe Torus. We show that the limiting equation we obtain does not coincidewith the physically realistic model. The former is indeedan equation of Boltzmann type, yet with memory in time, so that it appearsto be time-reversible. We comment on this point, and further describethe properties of the limiting equation.