1994/06/22 by A. C. Scott, Alwyn Scott, J. C. Eilbeck +2 · 5 citations
Physics and Astronomy · #Advanced Fiber Laser Technologies #Condensed matter physics #Lattice (music) #Nonlinear Photonic Systems #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #hep-th
paper · pdf · doi:10.1016/0167-2789(94)90115-5
21 pages, 1 figure
arxiv created 1994/06/22 · openalex publication_date 1994/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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-fold translational symmetry in one spatial dimension, where f 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\rm b), effective mass (m*) and maximum group velocity (V\rm m) of the soliton bands as functions of the anharmonicity in the limit f → ∞. For arbitrary values of n we have asymptotic expressions for E\rm b, m*, and V\rm 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.