Smoluchowski equation approach for quantum Brownian motion in a tilted periodic potential
Smoluchowski equation approach for quantum Brownian motion in a tilted periodic potential
复制标题
DOI：
10.1103/physreve.78.031114
复制
发表时间：
2008-09-01
影响因子：
2.4
通讯作者：
Cleary, Liam
中科院分区：
文献类型：
--
作者：
Coffey, William T.;Kalmykov, Yuri P.;Cleary, Liam
通过求解分布函数在位态空间中时间演化的量子Smoluchowski方程，在高温弱浴-粒子耦合极限下处理了一维倾斜余弦周期势中粒子非惯性布朗运动的量子修正。已经提出的两种不同形式的量子Smoluchowski方程的理论预测，即J. Ankerhold等人。中国生物医学工程学报，2003,19(2):481 - 481。理论物理。A 40, F91(2007)]-在点约瑟夫森结动力学的特定应用中进行了详细的比较。各种特性（平稳分布、电流-电压特性、平均首次通过时间、线性交流响应）通过连续分数和有限积分表示来评估，通常用于经典斯摩鲁霍夫斯基方程。在给定电压下，直流电-电压特性表现为增强电流，阻抗曲线的谐振峰表现为Q因子的增强，这些与经典行为的偏差分别是势垒顶部附近相对高温的非耗散隧道效应（降低势垒高度）和耗散隧道效应（降低约瑟夫森振荡的阻尼）的表现。
Quantum corrections to the noninertial Brownian motion of a particle in a one-dimensional tilted cosine periodic potential are treated in the high-temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the distribution function in configuration space. The theoretical predictions from two different forms of the quantum Smoluchowski equation already proposed viz., J. Ankerhold et al. [Phys. Rev. Lett. 87, 086802 (2001)] and W. T. Coffey et al. [J. Phys. A 40, F91 (2007)]-are compared in detail in a particular application to the dynamics of a point Josephson junction. Various characteristics (stationary distribution, current-voltage characteristics, mean first passage time, linear ac response) are evaluated via continued fractions and finite integral representations in the manner customarily used for the classical Smoluchowski equation. The deviations from the classical behavior, discernible in the dc current-voltage characteristics as enhanced current for a given voltage and in the resonant peak in the impedance curve as an enhancement of the Q factor, are, respectively, a manifestation of relatively high-temperature nondissipative tunneling (reducing the barrier height) and dissipative tunneling (reducing the damping of the Josephson oscillations) near the top of a barrier.