论文标题
Davydov量子分子链模型中的异常扩散
Anomalous diffusion in Davydov quantum molecular chain model
论文作者
论文摘要
我们讨论了Davydov一维链分子中的异常松弛过程，该过程由激子和声音声子场作为链中的热储层组成。我们使用liouville-von neumann操作员的复杂频谱表示为激子得出动力学方程。由于一维，动量空间将分为无连接不可约合子空间的无限集，彼此动态独立。因此，动量松弛仅在每个子空间内朝着麦克斯韦分布。我们获得了具有传输系数，声速和扩散系数的流体动力模式，该模式在每个子空间中定义。此外，由于声速度具有动量依赖性，因此相混合会影响激发子的空间分布外，除了扩散过程外。由于相混合，激子的均方位移的增加速率随时间和长时间限制而差异线性增加。
We discuss anomalous relaxation processes in Davydov one-dimensional chain molecule that consists of an exciton and an acoustic phonon field as a thermal reservoir in the chain. We derive a kinetic equation for the exciton using the complex spectral representation of the Liouville-von Neumann operator. Due to the one-dimensionality, the momentum space separates into infinite sets of disjoint irreducible subspaces dynamically independent of one another. Hence, momentum relaxation occurs only within each subspace toward the Maxwell distribution. We obtain a hydrodynamic mode with transport coefficients, a sound velocity and a diffusion coefficient, defined in each subspace. Moreover, because the sound velocity has momentum dependence, phase mixing affects the broadening of the spatial distribution of the exciton in addition to the diffusion process. Due to the phase mixing the increase rate of the mean-square displacement of the exciton increases linearly with time and diverges in the long-time limit.
