Universal Bound States of Two Particles in Mixed Dimensions or Near a Mirror

Abstract

Some novel TWO-body effects analogous to the well-known THREE-body Efimov effect are predicted. In the systems considered, particle A is constrained on a TRUNCATED or BENT one-dimensional line or two-dimensional plane, or on one side of a flat mirror in three dimensions (3D). The constraining potential is fine-tuned such that particle A's ground state wave function is a constant in the region in which it is constrained. Particle B moves in 3D and interacts with particle A resonantly. An infinite sequence of giant two-body bound states are found in each case.

5 pages, 2 figures