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Binding energies for discrete nonlinear Schrödinger equations

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 → ∞ at a sufficiently small level of anharmonicity (γ), 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 γ sufficiently large and also for γ sufficiently small. Corresponding calculations are discussed for the quantized Ablowitz-Ladik equation at the second quantum level with periodic boundary conditions.