Vibron Solitons and Coherent Polarization in an Exactly Tractable Oscillator-Lattice System: Applications to Solitons in Helical Proteins and Frohlich's Idea of Biological Activity

An exactly tractable, nonlinearly coupled oscillator-lattice system is studied. This is a quasi one-dimensional (1d) model system in which each anharmonic oscillator in an oscillator system is coupled linearly with one another and nonlinearly with acoustic-type harmonic lattice vibrations. Such an oscillator system is shown to include, under certain circumstances, Frenkel excitons with exciton transfer by dipole-dipole interactions. When the on-site oscillator potential is of single-minimum type, the effect of oscillator-lattice interactions is mainly classified into two types: One is to modulate vibrons, which are elementary excitations in the lattice-free oscillator system, to yield vibron solitons governed by a discrete version of the 1d nonlinear Klein-Gordon equation, and the other is to produce coherent polarization and kinks that are stabilized by lattice deformation provided that the oscillator on-site potential contains positive quartic anharmonicity. The former is applied to solitons in α helical proteins to show that Davydov’s idea can be formulated in a more physically reasonable and quantitatively correct form by the present model system. The latter is shown to be a working microscopic model to study Fröhlich’s idea of biological activity due to the existence of coherent polarization field.