Related papers: Two-Particle Bound States at Interfaces and Corners

Two-Particle Bound States at Interfaces and Corners

URL: http://arxiv.org/abs/2105.04874v3
Date: Wed, 16 Mar 2022 08:18:20 GMT
Title: Two-Particle Bound States at Interfaces and Corners
Authors: Barbara Roos, Robert Seiringer
Abstract summary: We study two quantum particles forming a bound state in $d$-dimensional free space. We constrain the particles in $k$ directions to $(0,infty)k times mathbbRd-k$, with Neumann boundary conditions.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We study two interacting quantum particles forming a bound state in $d$-dimensional free space, and constrain the particles in $k$ directions to $(0,\infty)^k \times \mathbb{R}^{d-k}$, with Neumann boundary conditions. First, we prove that the ground state energy strictly decreases upon going from $k$ to $k+1$. This shows that the particles stick to the corner where all boundary planes intersect. Second, we show that for all $k$ the resulting Hamiltonian, after removing the free part of the kinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper generalizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413--1444, 2020) to dimensions $d>1$.

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