Universality of excited three-body bound states in one dimension

Abstract

We study a heavy-heavy-light three-body system confined to one space dimension provided the binding energy of an excited state in the heavy-light subsystems approaches zero. The associated two-body resonance is characterized by (i) the structure of the weakly bound excited heavy-light state and (ii) the presence of deeply bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find strong indication for universal behavior of both three-body binding energies and wave functions close to different excited-state resonances in the heavy-light subsystems.

Proof of universality in one-dimensional few-body systems including anisotropic interactions

“…The universality of energies and wave functions of three-body bound states for finite-range interactions that are tuned to support a weakly-bound excited state in the heavy-light subsystems has been demonstrated numerically in Ref. [15]. An analytical proof as presented in this work would be desirable and might explain the reported [15] differences and similarities compared to the situation of a weakly-bound heavy-light ground state.…”

“…[15]. An analytical proof as presented in this work would be desirable and might explain the reported [15] differences and similarities compared to the situation of a weakly-bound heavy-light ground state.…”

Isogeometric Analysis of Bound States of a Quantum Three-Body Problem in 1D

“…In this section, we first present the heavy-light two-body and heavy-heavylight three-body problems that are modeled as the dimensionless stationary Schrödinger equations recently studied in [20,21]. We then generalize the problems for any mass ratios and unify them as a single differential eigenvalue problem.…”

“…Now, we consider the three-body problem with a heavy-light body ratio m h /m l = 20 that is studied in [20,21,33]. With such a mass ratio, κ in the unified problem ( 6) is a matrix with entries κ = (41/84, 0; 0, 2/21).…”

“…For instance, BO was used in [17,15] to study the Efimov effect in few-body systems. BO was adopted in [20,21] recently to establish the universality in a one-dimensional three-body system. A more efficient numerical method based on BO was developed using the tensor-product structure [33].…”