一维分子晶体激子-孤子运动的激子运动学和动力学非线性效应

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

基于一维分子晶体相邻分子间静态作用势和分子间的(电)偶极-偶极相互作用,采用分子投影算符表示一维分子晶体激子系统的模型哈密顿量.在谐振近似下,根据激子运动学和动力学非线性效应的理解,推导了晶格运动和激子-孤子运动的非线性Klein-Gordon(K-G)耦合运动方程组.发现激子运动学和动力学非线性效应不但对孤子波函数Ф的Ф3,Ф2■2Ф/■x2有重要贡献,且导致重要的高阶非线性项,分别对Ф5非线性和Ф7非线性方程给出了解析解.详细分析Ф非线性方程的Bell型孤子和Kink型孤子解结果,发现激子运动学和动力学非线性效应对激子的有效质量m有显著增加贡献,对激子-孤子能量(Ω)有更负的修正,孤子局域范围更小.对Bell型孤子以超声速(v>cs)沿一维键传播,而Kink型孤子以亚声速传播(v<cs),它们分别出现在激子能带底部和顶部.

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.