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Clusters of bound particles in the derivativeδ-function Bose gas

Authors
Journal
Nuclear Physics B
0550-3213
Publisher
Elsevier
Publication Date
Volume
871
Issue
2
Identifiers
DOI: 10.1016/j.nuclphysb.2013.02.016
Keywords
  • Field Theory And Statistical Systems
Disciplines
  • Mathematics
  • Physics

Abstract

Abstract In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative δ-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative δ-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant.

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