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Scaling Limits of Schrödinger Quantum Mechanics

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Dynamics of Dissipation

Part of the book series: Lecture Notes in Physics ((LNP,volume 597))

Abstract

We outline the status of rigorous derivations of certain classical evolution equations as limits of Schrödinger dynamics. We explain two recent results jointly with H.T. Yau in more details. The first one is the derivation of the linear Boltzmann equation as the long time limit of the one-body Schrödinger equation with a random potential. The second one is the mean field limit of high density bosons with Coulomb interaction that leads to the nonlinear Hartree equation.

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Author information

Authors and Affiliations

  1. School of Mathematics, GeorgiaTech, Atlanta, GA, 30332, USA

    L. Erdős

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  1. L. Erdős
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Editors and Affiliations

  1. Institute of Physics, University of Zielona Góra, pl. Słowiański 6, 65069, Zielona Góra, Poland

    Piotr Garbaczewski

  2. Institute of Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50205, Wrocław, Poland

    Robert Olkiewicz

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© 2002 Springer-Verlag Berlin Heidelberg

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Erdős, L. (2002). Scaling Limits of Schrödinger Quantum Mechanics. In: Garbaczewski, P., Olkiewicz, R. (eds) Dynamics of Dissipation. Lecture Notes in Physics, vol 597. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46122-1_19

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  • DOI: https://doi.org/10.1007/3-540-46122-1_19

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  • Print ISBN: 978-3-540-44111-3

  • Online ISBN: 978-3-540-46122-7

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