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arXiv · 1801.04799

Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials

Maximilian Jeblick·Peter Pickl
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Abstract

We present a microscopic derivation of the time-dependent Gross-Pitaevskii equation starting from an interacting N-particle system of Bosons. We prove convergence of the reduced density matrix corresponding to the exact time evolution to the projector onto the solution of the respective Gross-Pitaevskii equation. Our work extends a previous result by one of us (P.P.[44]) to interaction potentials which need not to be nonnegative, but may have a sufficiently small negative part. One key estimate in our proof is an operator inequality which was first proven by Jun Yin, see [49].

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Maximilian Jeblick, Peter Pickl. 2018-01-15. Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials. https://arxiv.org/abs/1801.04799

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