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arXiv · 2202.12765

Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity

Daniele Ferretti·Alessandro Teta
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Abstract

We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the standard approach, one obtains the Ter-Martirosyan Skornyakov Hamiltonian which is unbounded from below. In order to avoid such instability problem, we introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles, i.e., the impurity and a boson, when another boson approaches the common position of the first two particles. We show that the Hamiltonian defined with such regularized interaction is self-adjoint and bounded from below if the strength of the three-body force is sufficiently large. The method of the proof is based on a careful analysis of the corresponding quadratic form.

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Daniele Ferretti, Alessandro Teta. 2022-02-25. Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity. https://doi.org/10.1007/s11785-023-01358-4

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