论文标题
通用力量法缩放在转弯点附近
Universal Power Law Scaling Near the Turning Points
论文作者
论文摘要
我们通过分析和数字显示，转向点附近的粒子的速度$ v_ \ pm $ x_0 $ nishes vanishes，i。 e。 $ v_ \ pm \ rightarrow 0 $ as $ x \ rightarrow x_0 $，根据电源法缩放$ \ left | v_ \ pm \ pm \ right | \ propto \ left | x_0-x \右|^β$，其中指数$β= 1/2 $独立于粒子质量及其作用的力。我们还表明，在转弯点附近的每个小间隔$ dx $上花费任何粒子的时间差异为$τ\ propto \ left | x_0-x \ right |^priend |^t $，指数$ν= -1/2 $。我们在这里发现的行为与在发生相变的系统附近发现的幂律缩放非常相似。
We show analytically and numerically that, the velocity $v_\pm$ of a particle near the turning points $x_0$ vanishes, i. e. $v_\pm\rightarrow 0$ as $x\rightarrow x_0$, according to the power law scaling $\left|v_\pm\right| \propto \left|x_0-x\right|^β$, where the exponent $β=1/2$ is independent of the particle mass and the force acting on it. We also show that, the time spends it any particle at each small interval $dx$ near the turning points diverges as $τ\propto \left|x_0-x\right|^ν$, with the exponent $ν=-1/2$. Behavior we find here is very similar to power law scaling that had been found near the critical points for systems which undergo a phase transition.
