Two-particle bound states at interfaces and corners

We study two interacting quantum particles forming a bound state in d-dimensional free space, and constrain the particles in k directions to (0, infinity)(k) x Rd-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 (2020) [6] to dimensions d > 1. (C)2022 The Author(s). Published by Elsevier Inc.

Automated summary

We study the interaction between two quantum particles forming a bound state in d-dimensional free space. The particles are constrained in k directions and subject to Neumann boundary conditions. We prove that the ground state energy decreases strictly as k increases, indicating that the particles tend to stick to the corner where all boundary planes intersect. Additionally, we show that the resulting Hamiltonian, after removing the free part of the kinetic energy, has only a finite number of eigenvalues below the essential spectrum.