2011/07/31 by F. F. Bellotti, F F Bellotti, T. Frederico +9 · 23 citations
Mathematics · Physics and Astronomy · #Boson #Bound state #Cold Atom Physics and Bose-Einstein Condensates #Fermion #Identical particles #Phase diagram #Physics of Superconductivity and Magnetism #Quantum Mechanics and Non-Hermitian Physics #Scaling #Universality (dynamical systems) #Upper and lower bounds #cond-mat.quant-gas #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.1088/0953-4075/44/20/205302
published in Journal of Physics B Atomic Molecular and Optical Physics 44(20), 205302 (IOP Publishing) · 21 pages, 8 figures, 4 tables, final version
openalex publication_date 2011/09/26 · arxiv created 2011/10/03 · arxiv updated 2011/10/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle and the two different two-body subsystems are characterized by two-body energies and masses. The three-body energy in units of one of the two-body energies is a universal function of the other two-body energy and the mass ratio. We derive convenient analytical formulae for calculations of the three-body energy as a function of these two independent parameters and exhibit the results as universal curves. In particular, we show that the three-body system can have any number of stable bound states. When the mass ratio of the distinct to identical particles is greater than 0.22, we find that at most two stable bound states exist, while for two heavy and one light mass an increasing number of bound states is possible. The specific number of stable bound states depends on the ratio of two-body bound state energies and on the mass ratio, and we map out an energy–mass phase diagram of the number of stable bound states. Realizable systems of both fermions and bosons are discussed in this framework.