Geometrically induced two-particle binding in a wave guide

TL;DR

This paper demonstrates that certain wave guide geometries can induce binding of two interacting particles even when a single particle cannot be trapped, highlighting the role of geometry and boundary conditions in quantum confinement.

Contribution

It introduces a new example of a wave guide where two particles bind due to geometry, unlike single particles, and compares effects of boundary conditions on binding.

Findings

Two-particle binding occurs in wave guides that do not bind single particles.

Neumann boundary conditions are more conducive to binding for two particles than for one.

Geometric features can induce two-particle bound states independently of single-particle binding.

Abstract

For mathematical models of quantum wave guides we show that in some situations two interacting particles can be trapped more easily than a single particle. In particular, we give an example of a wave guide that can not bind a single particle, but does have a geometrically induced bound state for two particles that attract each other. We also show that Neumann boundary conditions are `stickier' for two interacting particles than for a single one.