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A Stationary Phase Approach to the Weak Coupling Schrödinger Equation

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Abstract

We study the dynamics of a quantum particle governed by a linear Schrödinger equation with a scaled Gaussian potential. In the weak coupling limit the average dynamics of such a particle can be described by a linear Boltzmann equation. In this work we prove a bound for the rate at which the average dynamics of the quantum particle approach linear Boltzmann equation dynamics. For the so called simple diagrams, we use a stationary phase approach to establish an asymptotic expansion that provides the bound. Our stationary phase approach also provides a simple, formal method for computing the Boltzmann limit. Our work uses and extends results developed by L. Erdös and H.T. Yau.

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Authors and Affiliations

  1. Department of Mathematics, Georgetown University, St. Mary’s Building, Washington, DC, 20057-1233, USA

    Sivan Rottenstreich

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  1. Sivan Rottenstreich
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Correspondence to Sivan Rottenstreich.

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Rottenstreich, S. A Stationary Phase Approach to the Weak Coupling Schrödinger Equation. J Stat Phys 124, 47–86 (2006). https://doi.org/10.1007/s10955-006-9157-0

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  • DOI: https://doi.org/10.1007/s10955-006-9157-0

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