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arXiv · 2212.00144

Trial states for Bose gases: singular scalings and non-integrable potentials

Alessandro Olgiati
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Abstract

We review two results in which trial states for bosonic Hamiltonians were discussed. The problem of finding a trial state for a system with a hard-core potential in the Gross-Pitaevskii regime was recently solved by proving a link with the problem of finding a trial state for a system with a more regular potential in a less singular scaling, one of the type $N^{-1+3\beta}V(N^\beta\cdot)$ with $\beta\in(0,1)$. For both of these models we present the main result for the upper bound to the ground state energy, and discuss the key steps in the proof.

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Alessandro Olgiati. 2022-11-30. Trial states for Bose gases: singular scalings and non-integrable potentials. https://arxiv.org/abs/2212.00144

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