Quantum lattice solitons

The number state method is used to study soliton bands for three anharmonic quantum lattices: (i) The discrete nonlinear Schrödinger equation, (ii) The Ablowitz-Ladik system, and (iii) A fermionic polaron model. Each of these systems is assumed to have f{hook}-fold translational symmetry in one spatial dimension, where f{hook} is the number of freedoms (lattice points). At the second quantum level (n = 2) we calculate exact eigenfunctions and energies of pure quantum states, from which we determine binding energy (E_b), effective mass (m^*) and maximum group velocity (V_m) of the soliton bands as functions of the anharmonicity in the limit f{hook} ? 8. For arbitrary values of n we have asymptotic expressions for E_b, m^*, and V _m as functions of the anharmonicity in the limits of large and small anharmonicity. Using these expressions we discuss and describe wave packets of pure eigenstates that correspond to classical solitons. © 1994.