Quantum lattice solitons

Alwyn C. Scott, J. C. Eilbeck, H. Gilhøj

Research output: Contribution to journalArticle


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 (Eb), effective mass (m*) and maximum group velocity (Vm) 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 Eb, 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.

Original languageEnglish
Pages (from-to)194-213
Number of pages20
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
Publication statusPublished - 15 Nov 1994

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    Scott, A. C., Eilbeck, J. C., & Gilhøj, H. (1994). Quantum lattice solitons. Physica D: Nonlinear Phenomena, 78(3-4), 194-213.