中文摘要：

基于一维分子晶体系统的Holstein模型,采用压缩-相干态展开方法,计及电子-声子间量子关联和重整化平移修正,分析和研究电子-双声子相互作用对极化子-孤子系统基态性质和量子涨落的影响.推导了一维极化子-孤子系统的封闭形式非线性方程.应用非线性项展开方法,给出非线性方程的解析解和相关基态特性结果.研究表明,仅当电子-双声子耦合强度g1〈0时非线性方程才有孤波解,此时声子量子涨落效应随着压缩的增加,极化子-孤子系统基态能量变得更负,孤子局域减少,孤子态更加稳定;另一方面,电子密度涨落〈Δ2n〉和声子坐标-动量的不确定量〈Δ2p〉〈Δ2q〉比无声子压缩效应的大,极化子结合能变得更负.特别是,当g1〈0时,双声子效应的量子涨落〈Δ2n〉与〈Δ2p〉〈Δ2q〉的值比单声子情况有明显增加.

英文摘要：

On the basis of the Hamiltonian of the Holstein one-dimensional molecular crystals, using the squeezed-coherent state expansion method, the influence of the electron-two phonon interaction on the properties of the ground state and quantum fluctuation for the polaron-soliton system were investigated by including the quantum correlation between the polarons and the squeezed phonons, and the renormalized displacement correction. The nonlinear Schrfinger equation for one-dimensional polaron- soliton state has been found in a closed form. By the use of the nonlinear expansion, wehave given the analytical solution of the corresponding nonlinear equation so as to obtain the ground state energy, the quantum fluctuation and the polaron energy of the polaron-soliton system in analytical form. We have found that, when the electron-two phonon coupling strength g1 〈 0, the nonlinear Schrfinger equation has the solitary wave solution. As a result, the ground state energy and the polaron energy are more negative than the electron-single phonon coupling. At the same time, the stability of the polaron-soliton state is enhanced and the soliton localization is decreased . Particularly, when g1 〈 0, the quantum fluctuation（Δ^2 n） and （Δ^2p） （Δ^2 q） for the twophonon effect are larger than the one-phonon one and the polaron energy for the two-phonons effect is more negative compared with the one-phonon one.