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N-boson spectrum from a discrete scale invariance

Kievsky, A, Timofeyuk, NK and Gattobigio, M (2014) N-boson spectrum from a discrete scale invariance PHYSICAL REVIEW A, 90 (3), ARTN 03250.

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We present an analysis of the N-boson spectrum computed using a soft two-body potential, the strength of which has been varied in order to cover an extended range of positive and negative values of the two-body scattering length a close to the unitary limit. The spectrum shows a tree structure of two states, one shallow and one deep, attached to the ground state of the system with one less particle. It is governed by a unique universal function Δ(ξ), already known in the case of three bosons. In the three-particle system the angle ξ, determined by the ratio of the two- and three-body binding energies E3/E2=tan2ξ, characterizes the discrete scale invariance of the system. Extending the definition of the angle to the N-body system as EN/E2=tan2ξ, we study the N-boson spectrum in terms of this variable. The analysis of the results, obtained for up to N=16 bosons, allows us to extract a general formula for the energy levels of the system close to the unitary limit. Interestingly, a linear dependence of the universal function as a function of N is observed at fixed values of a. We show that the finite-range nature of the calculations results in the range corrections that generate a shift of the linear relation between the scattering length a and a particular form of the universal function. We also comment on the limits of applicability of the universal relations.

Item Type: Article
Subjects : Physics
Divisions : Faculty of Engineering and Physical Sciences > Physics
Authors :
Kievsky, A
Timofeyuk, NK
Gattobigio, M
Date : 4 September 2014
DOI : 10.1103/PhysRevA.90.032504
Copyright Disclaimer : ©2014 American Physical Society. All rights reserved.
Uncontrolled Keywords : Science & Technology, Physical Sciences, Optics, Physics, Atomic, Molecular & Chemical, Physics, LARGE SCATTERING LENGTH, FEW-BODY SYSTEMS, EFIMOV SPECTRUM, BOUND-STATES, UNIVERSALITY, HELIUM, PARTICLES, CLUSTERS, PHYSICS
Related URLs :
Additional Information : ©2014 American Physical Society. All rights reserved.
Depositing User : Symplectic Elements
Date Deposited : 22 Mar 2016 17:38
Last Modified : 31 Oct 2017 18:08

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