BINDING-ENERGIES FOR DISCRETE NONLINEAR SCHRODINGER-EQUATIONS

The standard quantum discrete nonlinear Schrodinger equation with periodic boundary conditions and an arbitrary number of freedoms (f) is solved exactly at the second and third quantum levels. If f --> infinity at a sufficiently small level of anharmonicity (gamma), 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 gamma sufficiently large and also for gamma sufficiently small. Corresponding calculations are discussed for the quantized Ablowitz-Ladik equation at the second quantum level with periodic boundary conditions.