Motion of Nonlinear Excitations in Quasi-One-Dimensional Electron-Phonon Systems

在这个项目中，我们主要用数值模拟的方法研究了聚乙炔和类似的导电聚合物中实现的准一维电子-声子系统的孤子动力学。晶格位移被经典地处理，而电子波函数被量子力学计算。为了使总能量最小，由一组自洽方程来确定承载静态孤子的初始状态。通过施加均匀的电场使孤子运动起来。运动由晶格位移的运动方程和电子波函数的含时薛定谔方程决定。这种方法的优点是我们不需要假定运动孤子的形状，因为它是受物理力以自然的方式运动的。主要结果是：(1)孤子的饱和速度是系统声速的3-4倍；(2)运动…的宽度更多的孤子是速度的递减函数，在饱和速度下，最大衰减率为10%~20%。(3)在饱和速度下，孤子的动能看起来发散很弱。(4)运动孤子周围的振幅振动模的频率随着速度的增加而增加，表明孤子的内部结构随着速度的增加而变得更加坚硬。(5)当存在位点型短程杂质时，孤子的有效势具有与孤子宽度相同数量级的宽度。(6)当存在键型无序时，孤子的有效势是阶梯状的，因此是非定域的。这是因为本文所考虑的孤子是连接两个简并基态的拓扑孤子。(7)在晶格位移的运动方程中引入唯象阻尼项，在静电场的作用下，孤子的速度取一个固定值。根据定态速度与电场的比例关系，估算了孤子的迁移率。指出理想聚乙炔的室温电导率可以与铜等优良金属的电导率相媲美。由于孤子的有限宽度，发现在离链离子掺杂的情况下，孤子的激活能随掺杂浓度的增加而迅速下降。较少

In this project, the dynamics of solitons in quasi-one-dimensional electron-phonon systems, typically realized in polyacetylene and similar conducting polymers, are investigated mainly in terms of numerical simulations. The lattice displacement is treated classically, while the electronic wave functions are calculated quantum mechanically. The initial state bearing a static soliton is determined by a set of self-consistent equations which are derived so as to minimize the total energy. The soliton is put in motion by applying a uniform electric field. The motion is determined by equation of motions for the lattice displacements and by the time-dependent Schrodinger equations for the electronic wave functions. The advantage of the present method is that we need not assume the shape of a moving soliton, since it is moved by a physical force in a natural way.The main results are(1)Soliton has a saturation velocity to 3 to 4 times of the sound velocity of the system.(2)The width of a movin … More g soliton is a decreasing function of the velocity and the maximum reduction rate is 10 to 20 % at the saturation velocity.(3)The kinetic energy of the soliton looks to diverge weakly at the saturation velocity.(4)The frequency of the amplitude oscillation mode around a moving soliton increases with the velocity, indicating that the inner structure of the soliton becomes harder with increasing velocity.(5)When there is a site-type short-ranged impurity, the effective potential for a soliton has a width of the same order of magnitude as the soliton width.(6)When there is a bond-type disorder, the effective potential for a soliton is step-like and therefore non-local. This is because the soliton considered in this work is a topological soliton connecting two degenerate ground states.(7)Introducing a phenomenological damping in the equation of motion for the lattice displacements, the soliton velocity takes a stationary value in the presence of a static electric field. From the proportionality relation between the stationary velocity and the electric field, the mobility of a soliton is estimated. It is pointed out that the room-temperature conductivity of an ideal polyacetylene can have a value comparable to those of good metals such as copper.The actibation energy of a soliton in the presence of ionized off-chain dopants is found to decreased rather rapidly with increasing the dopant concentration because of the finite width of the soliton. Less