caa a22 4500 467891176 CHVBK 20180406152749.0 cr unu---uuuuu 170328e20060701xx s 000 0 eng 10.1007/s10955-006-9157-0 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9157-0 Rottenstreich Sivan Department of Mathematics, Georgetown University, St. Mary's Building, 20057-1233, Washington, DC, USA aut A Stationary Phase Approach to the Weak Coupling Schrödinger Equation [Elektronische Daten] [Sivan Rottenstreich] 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. Springer Science + Business Media, Inc., 2006 weak coupling nationallicence Schrödinger nationallicence stationary phase nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/1(2006-07-01), 47-86 0022-4715 124:1<47 2006 124 10955 https://doi.org/10.1007/s10955-006-9157-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9157-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rottenstreich Sivan Department of Mathematics, Georgetown University, St. Mary's Building, 20057-1233, Washington, DC, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 124/1(2006-07-01), 47-86 0022-4715 124:1<47 2006 124 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer