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QUANTUM BOUND STATES FOR A DERIVATIVE NONLINEAR SCHRÖDINGER MODEL AND NUMBER THEORY

B. BASU-MALLICK

Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India

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TANAYA BHATTACHARYYA

Theory Group, Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700064, India

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, and

DIPTIMAN SEN

Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560012, India

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https://doi.org/10.1142/S0217732304015075Cited by:3 (Source: Crossref)

Abstract

A derivative nonlinear Schrödinger model is shown to support localized N-body bound states for several ranges (called bands) of the coupling constant η. The ranges of η within each band can be completely determined using number theoretic concepts such as Farey sequences and continued fractions. For N≥3, the N-body bound states can have both positive and negative momenta. For η>0, bound states with positive momentum have positive binding energy, while states with negative momentum have negative binding energy.

Keywords:

PACS: 03.65.Ge, 02.30.Ik, 02.10.De, 05.45.Yv

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