图 1  二维棘轮外势$ V(x, y) $的结构示意图

Fig. 1.  The schematic diagram of two-dimensional ratchet potential $ V(x, y) $.

图 2  非保守外力$ {F_x} $和$ {F_y} $的结构示意图, 非保守力参量$ a = 0.4 $

Fig. 2.  The schematic diagram of non-conservative forces $ {F_x} $ and $ {F_y} $, where non-conservative force parameter $ a = 0.4 $.

图 3  不同弹簧原长$ L $下平均速度$ \left\langle {{V_x}} \right\rangle $随非保守力参数$ a $的变化曲线, 其中$ D = 0.1 $, $ k = 2 $

Fig. 3.  The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the non-conservative force parameter $ a $ under different original length of the spring L, where $ D = 0.1 $, $ k = 2 $.

图 4  非保守力$ {F_x} $随参数$ a $的变化曲线

Fig. 4.  The curve of the non-conservative force $ {F_x} $ varying with the parameter $ a $.

图 5  不同噪声强度$ D $下平均速度$ \left\langle {{V_x}} \right\rangle $随弹簧原长$ L $的变化曲线, 其中$ a = 0.4 $, $ k = 2 $

Fig. 5.  The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the original length of the spring $ L $ under different noise intensity $ D $, where $ a = 0.4 $, $ k = 2 $.

图 6  耦合粒子的位置随时间演化图像, 其中$ a = 0.4 $, $ k = 2 $, $ L = 3.5 $, $ D = 0.1 $

Fig. 6.  Trajectories for the coupled particles as a function of time, where $ a = 0.4 $, $ k = 2 $, $ L = 3.5 $, $ D = 0.1 $.

图 7  不同耦合强度下平均速度$ \left\langle {{V_x}} \right\rangle $随热噪声$ D $的变化曲线, 其中$ a = 0.4 $, $ L = 1 $

Fig. 7.  The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the noise $ D $ under different coupling strength, where $ a = 0.4 $, $ L = 1 $.

图 8  不同非保守外力参量$ a $下平均速度$ \left\langle {{V_x}} \right\rangle $随弹性系数$ k $的变化曲线, 其中$ D = 0.1 $, $ L = 1 $

Fig. 8.  The curves of the mean velocity $ \left\langle {{V_x}} \right\rangle $ varying with the spring coefficient $ k $ under different non-conservative force parameter $ a $, where $ D = 0.1 $, $ L = 1 $.

图 9  耦合粒子的位置随时间演化图像, 其中$ a = 0.3 $, $ k = 0.3 $, $ L = 1 $, $ D = 0.1 $

Fig. 9.  Trajectories for the coupled particles as a function of time, where $ a = 0.3 $, $ k = 0.3 $, $ L = 1 $, $ D = 0.1 $.