Quantum Theory of Vibron Solitons -Coherent States of a Vibron-Phonon System and Self-Localized Modes-

A quantum theory of dynamical self-trapping in a quasi-one-dimensional (1d) lattice of vibrons by phonons is presented to explore possible existence of soliton-like entities in α-helical proteins and related model dynamical 1d lattices. The theory developed here distinguishes itself from others based on the Fröhlich-type Hamiltonian and the use of the continuum approximation in the following two respects: (1) By virtue of the number-nonconserving nature of vibrons, coherent states can be taken as a natural basis for studying a soliton-like state in quantum mechanics. (2) A self-localized mode, movable or stationary, appearing below the bottom of the frequency band of phonon-free vibrons can be identified as a soliton in the lattice system. To solve integro-differential-difference equations, an adiabatic approximation and the lattice-Green's functions are used.