Rozenbaum V M, Korochkova T Ye, Shapochkina I V, Trakhtenberg L I
Chuiko Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Generala Naumova str. 17, Kiev 03164, Ukraine.
Department of Physics, Belarusian State University, Prospekt Nezavisimosti 4, Minsk 220050, Belarus.
Phys Rev E. 2021 Jul;104(1-1):014133. doi: 10.1103/PhysRevE.104.014133.
We consider the motion of a Brownian particle in a sawtooth potential dichotomously modulated by a spatially harmonic perturbation. An explicit expression for the Laplace transform of the Green function of an extremely asymmetric sawtooth potential is obtained. With this result, within the approximation of small potential-energy fluctuations, the integration of the relations for the average particle velocity is performed in elementary terms. The obtained analytical result, its high-temperature, low-frequency, and high-frequency asymptotics, as well as numerical calculations performed for a sawtooth potential of an arbitrary symmetry, indicate that in such a system, the frequency-temperature controlling the magnitude and direction of the ratchet velocity becomes possible. We clarify the mechanism of the appearance of additional regions of nonmonotonicity in the frequency dependence of the average velocity, which leads to the appearance of additional ratchet stopping points. This mechanism is a consequence of the competition between the sliding time along the steep slope of the highly asymmetric sawtooth potential and the correlation time of the dichotomous noise.
我们考虑一个布朗粒子在由空间谐波扰动进行二分调制的锯齿形势场中的运动。得到了一个极不对称锯齿形势场的格林函数的拉普拉斯变换的显式表达式。基于此结果，在小势能涨落的近似下，以基本项完成了平均粒子速度关系的积分。所得到的解析结果、其高温、低频和高频渐近线，以及针对任意对称性的锯齿形势场进行的数值计算表明，在这样一个系统中，控制棘轮速度大小和方向的频率 - 温度是可能的。我们阐明了平均速度的频率依赖性中出现额外非单调性区域的机制，这导致了额外棘轮停止点的出现。这种机制是沿着高度不对称锯齿形势场陡坡的滑动时间与二分噪声的关联时间之间竞争的结果。
