Derivation of the time dependent Gross-Pitaevskii equation for a class of non purely positive potentials
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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].
Type
Journal articlePermalink
https://hdl.handle.net/10161/17128Collections
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Show full item recordScholars@Duke
Peter Pickl
Visiting Professor of Global Studies
Starting with the autumn term 2018 I will teach the foundational mathematics and integrated
science courses in the undergraduate program at DKU. In the coming years, other classes
on several topics of mathematics and mathematical physics will be taught.

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