Departamento de Química. Universidad de Los Andes, Mérida 5101, Venezuela.
Phys Rev E. 2019 Nov;100(5-1):052117. doi: 10.1103/PhysRevE.100.052117.
This article discusses the numerical result predicted by the quantum Langevin equation of the generalized diffusion function of a Brownian particle immersed in an Ohmic quantum bath of harmonic oscillators. The time dependence of the standard deviation of the reduced Wigner function of the system, obtained by integrating the whole function in the momentum space, is determined as well. The complexity of the equations leads to resort to a much simpler calculation based in the position correlation function. They are done for the three possible regimes of the system, namely, periodic, aperiodic, and overdamped. It is found in the periodic case that the generalized diffusion is a discontinuous function exhibiting negative values during short time periods of time. This counterintuitive result, found theoretically in other systems and waiting for its experimental confirmation, can be perfectly explained in the framework of the quantum Langevin equation. Its oscillatory behavior is primordially due to the response to the external field while its quantum origin contributes only in its magnitude. The results are compared to those of the continuum limit which exhibits similar behavior.
本文讨论了布朗粒子在简谐振子欧姆量子浴中广义扩散函数的量子朗之万方程所预测的数值结果。通过在动量空间中积分整个函数，还确定了系统的约化维格纳函数的标准偏差随时间的变化。由于方程的复杂性，我们需要借助一种更为简单的基于位置相关函数的计算方法。我们针对系统的三种可能状态，即周期性、非周期性和过阻尼状态，进行了计算。在周期性状态下，发现广义扩散是一个不连续的函数，在短时间内会出现负值。这一与直觉相悖的结果在其他系统中已经从理论上得到了证实，目前正在等待实验验证，它可以在量子朗之万方程的框架内得到完美的解释。其振荡行为主要是由于对外场的响应，而其量子起源仅在其幅度上有所贡献。我们将结果与连续极限的结果进行了比较，它们表现出相似的行为。
