Cáceres Manuel O, Nizama Marco
Comision Nacional de Energia Atomica, Centro Atomico Bariloche and Instituto Balseiro, Universidad Nacional de Cuyo, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina.
CONICET, Centro Atomico Bariloche, Av. E. Bustillo 9500, CP8400, Bariloche, Argentina.
Phys Rev E. 2022 Apr;105(4-1):044131. doi: 10.1103/PhysRevE.105.044131.
The 1D random Boltzmann-Lorentz equation has been connected with a set of stochastic hyperbolic equations. Therefore, the study of the Boltzmann-Lorentz gas with disordered scattering centers has been transformed into the analysis of a set of stochastic telegrapher's equations. For global binary disorder (Markovian and non-Markovian) exact analytical results for the second moment, the velocity autocorrelation function, and the self-diffusion coefficient are presented. We have demonstrated that time-fluctuations in the lost of energy in the telegrapher's equation, can delay the entrance to the diffusive regime, this issue has been characterized by a timescale t_{c} which is a function of disorder parameters. Indeed, producing a longer ballistic dynamics in the transport process. In addition, fluctuations of the space probability distribution have been studied, showing that the mean value of a stochastic telegrapher's Fourier mode is a good statistical object to characterize the solution of the random Boltzmann-Lorentz gas. In a different context, the stochastic telegrapher's equation has also been related to the run-and-tumble model in Biophysics. Then a discussion devoted to the potential applications when swimmers' speed and tumbling rate have time fluctuations has been pointed out.
一维随机玻尔兹曼 - 洛伦兹方程已与一组随机双曲方程相关联。因此，对具有无序散射中心的玻尔兹曼 - 洛伦兹气体的研究已转化为对一组随机电报员方程的分析。对于全局二元无序（马尔可夫和非马尔可夫），给出了二阶矩、速度自相关函数和自扩散系数的精确解析结果。我们已经证明，电报员方程中能量损失的时间波动可以延迟进入扩散区域，这个问题由一个时间尺度(t_{c})来表征，它是无序参数的函数。实际上，在输运过程中产生了更长的弹道动力学。此外，还研究了空间概率分布的波动，表明随机电报员傅里叶模式的平均值是表征随机玻尔兹曼 - 洛伦兹气体解的一个良好统计对象。在不同的背景下，随机电报员方程也与生物物理学中的奔跑 - 翻滚模型相关。然后指出了在游泳者速度和翻滚速率存在时间波动时的潜在应用的讨论。
