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Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems

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Abstract

We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.

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Authors and Affiliations

  1. Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

    Benjamin Schlein & Horng-Tzer Yau

  2. Institute of Mathematics, University of Munich, Theresienstr. 39, D-80333, Munich, Germany

    László Erdős

Authors
  1. László Erdős
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  2. Benjamin Schlein
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  3. Horng-Tzer Yau
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Correspondence to Horng-Tzer Yau.

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Mathematics Subject Classification (2000)

5Q55; 81Q15; 81T18; 81V70

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Erdős, L., Schlein, B. & Yau, HT. Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems. Invent. math. 167, 515–614 (2007). https://doi.org/10.1007/s00222-006-0022-1

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  • DOI: https://doi.org/10.1007/s00222-006-0022-1

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