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Convergence in Higher Mean of a Random Schrödinger to a Linear Boltzmann Evolution

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Abstract

We study the macroscopic scaling and weak coupling limit for a random Schrödinger equation on \(\mathbb{Z}^3\). We prove that the Wigner transforms of a large class of “macroscopic” solutions converge in r th mean to solutions of a linear Boltzmann equation, for any 1 ≤  r  <  ∞. This extends previous results where convergence in expectation was established.

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Authors and Affiliations

  1. Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ, 08544-1000, USA

    Thomas Chen

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  1. Thomas Chen
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Correspondence to Thomas Chen.

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Communicated by H.-T. Yau

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Chen, T. Convergence in Higher Mean of a Random Schrödinger to a Linear Boltzmann Evolution. Commun. Math. Phys. 267, 355–392 (2006). https://doi.org/10.1007/s00220-006-0085-2

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  • DOI: https://doi.org/10.1007/s00220-006-0085-2

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