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Binding Energies for Discrete Nonlinear Schrödinger Equations

P. D. Miller and A. C. Scott
Program in Applied Mathematics
The University of Arizona, Tucson AZ 85721 USA

J. Carr and J. C. Eilbeck
Department of Mathematics
Heriot-Watt University, Edinburgh EH14 4AS, UK


The standard quantum discrete nonlinear Schrödinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. If f goes to infinity at a sufficiently small level of anharmonicity, the value for soliton binding energy from quantum field theory (QFT) in the continuum limit is recovered. For fixed f, however, the QFT result always fails for sufficiently large and small anharmonicity. Corresponding calculations are discussed for the quantized Ablowitz-Ladik equation at the second quantum level with periodic boundary conditions.