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arXiv:1911.09635

Commutative diagram of the Gross-Pitaevskii approximation

Stefan Adams, Chiranjib Mukherjee, Vogel, Quirin

Published Nov 21, 2019• 0 citations
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Abstract

It is well-known that the Gross-Pitaevskii variational formula describes the ground-state energy per particle of $N$-indistinguishable trapped particles (Bosons) in a dilute state in the large system size $N\to\infty$. The goal of the present article is to prove that the Gross--Pitaevskii formula also appears in the iterated limit of zero temperature and large system size of the product ground-state energy per particle of the $N$-particle Hamiltonian operator. For fixed particle number $N$, we moreover identify the low-temperature limit of the Brownian model with mutual intersection-local-time interaction as the ground-product-state energy per particle of the corresponding $N$-body system with repulsive Dirac interaction. This proves the conjectures of Adams, König and Bru from arXiv:math/0411660 and arXiv:math/0512305.

DOI
10.48550/arxiv.1911.09635

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It is well-known that the Gross-Pitaevskii variational formula describes the ground-state energy per particle of NNN-indistinguishable trapped particles (Bosons) in a dilute state in the large system size N→∞N\to\inftyN→∞. The goal of the present article is to prove that the Gross--Pitaevskii formula also appears in the iterated limit of zero temperature and large system size of the product ground-state energy per particle of the NNN-particle Hamiltonian operator. For fixed particle number NNN, we moreover identify the low-temperature limit of the Brownian model with mutual intersection-local-time interaction as the ground-product-state energy per particle of the corresponding NNN-body system with repulsive Dirac interaction. This proves the conjectures of Adams, König and Bru from arXiv:math/0411660 and arXiv:math/0512305.
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