Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 104, Issue 1-2, Pages 387-447Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1010374114551
Keywords
density matrix; Liouville equation; Pauli Master Equation; time-dependent scattering theory; Fermi's Golden Rule; oscillatory integrals in large dimensions
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In this paper, we investigate the rigorous convergence of the Density Matrix Equation (or Quantum Lionville Equation) towards the Quantum Boltzmann Equation (or Pauli Master Equation). We start from the Density Matrix Equation posed on a cubic box of size L with periodic boundary conditions, describing the quantum motion of a particle in the box subject to an external potential V. The physics motivates the introduction of a damping term acting on the off-diagonal part of the density matrix, with a characteristic damping time alpha (-1). Then, the convergence can be proved by letting successively L tend to infinity and alpha to zero. The proof relies heavily on a lemma which allows to control some oscillatory integrals posed in large dimensional spaces. The present paper improves a previous announcement [CD].
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