The kinematic and dynamic nonlinear effects in the exciton-soliton motion in one-dimensional molecular crystals

Abstract

Based on the static interaction potential and the (electrical) dipole-dipole interaction between neighboring molecules, the Hamiltonian model of the exciton system in one-dimensional molecular crystal can be expressed by means of the molecular projection operators. In the case of approximate resonance, according to our findings with respect to the kinematics and dynamics effects of the exciton motion, the Klein-Gordon-type equation set for the time evolution of the exciton_soliton and lattice motion has been obtained. With regard to the solitary wave function , it was found that the kinematics and dynamics effects of exciton motion not only greatly contributed to its nonlinear terms 3 and 2{2}\{ξ2}, but also led to its important high-order nonlinear terms. We solved its 5 and 7　nonlinear equation in an analytical form. In particular the solitary wave solution for the 5-nonlinear equation has been studied in detail under the Bell-type and kink-type boundary conditions. Then we found that the kinematics and dynamics effects of exciton motion contributed remarkably to the increase of exciton effective mass, and makes further negative correction to the exciton-soliton energy Ω. As for the Bell-type soliton movement in supersonic speed v＞cs and the Kink-type soliton movement in subsonic speed v＜cs, and the types of the soliton bound states appear to be situated at the bottom and the top of the exciton energy band respectively.