Vibron solitons

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Abstract
Starting from a general Hamiltonian describing the dynamics of vibrons coupled to acoustic phonons, equations of motion for the dynamical variables are obtained by eliminating the phonon degrees of freedom. Specific results are obtained for the form of this Hamiltonian proposed by Takeno. Vibron number is not conserved in general, which distinguishes our study from others based on the Fröhlich Hamiltonian in which the analogous bosons are conserved. Solitary-wave solutions are found for approximate continuum wave equations obtained employing a coherent-state ansatz under a rotating-wave approximation. Regimes of validity are determined, and within these regimes physically meaningful quantities are computed, including energy–wave-vector relations, frequency–wave-vector relations, binding energies, and effective masses. The role of these in spectroscopy is discussed. Several instabilities are encountered and their origins traced. Certain of these are argued to be generic and intrinsic to the physics of the problem, while others can be shown to be artifacts of the particular model chosen for specific calculations. The modification of our results caused by discreteness corrections is considered, and the role of thermal fluctuations is discussed.

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