Current browse context:
cond-mat.quant-gas
Change to browse by:
References & Citations
Condensed Matter > Quantum Gases
Title: Efimov effect for two particles on a semi-infinite line
(Submitted on 26 Jan 2022 (v1), last revised 16 Sep 2022 (this version, v2))
Abstract: The Efimov effect (in a broad sense) refers to the onset of a geometric sequence of many-body bound states as a consequence of the breakdown of continuous scale invariance to discrete scale invariance. While originally discovered in three-body problems in three dimensions, the Efimov effect has now been known to appear in a wide spectrum of many-body problems in various dimensions. Here we introduce a simple, exactly solvable toy model of two identical bosons in one dimension that exhibits the Efimov effect. We consider the situation where the bosons reside on a semi-infinite line and interact with each other through a pairwise $\delta$-function potential with a particular position-dependent coupling strength that makes the system scale invariant. We show that, for sufficiently attractive interaction, the bosons are bound together and a new energy scale emerges. This energy scale breaks continuous scale invariance to discrete scale invariance and leads to the onset of a geometric sequence of two-body bound states. We also study the two-body scattering off the boundary and derive the exact reflection amplitude that exhibits a log-periodicity. This article is intended for students and non-specialists interested in discrete scale invariance.
Submission history
From: Satoshi Ohya [view email][v1] Wed, 26 Jan 2022 11:00:00 GMT (56kb)
[v2] Fri, 16 Sep 2022 13:00:00 GMT (64kb)
Link back to: arXiv, form interface, contact.