A Stationary Phase Approach to the Weak Coupling Schrödinger Equation |
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Authors: | Sivan Rottenstreich |
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Institution: | (1) Department of Mathematics, Georgetown University, St. Mary’s Building, Washington, DC 20057-1233, USA |
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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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Keywords: | weak coupling Schr?dinger stationary phase |
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