论文标题
定期驱动的四分之一振荡器中的工作统计数据：经典动力学和量子动力学
Work statistics in the periodically driven quartic oscillator: classical versus quantum dynamics
论文作者
论文摘要
在纳米镜系统的热力学中，经典机械描述之间的关系特别重要。为了审查这种对应关系，我们研究了由经典外部力量的周期性外力驱动的非谐波振荡器，在量子力学的框架内，幅度逐渐变化。驾驶引起的振荡器的能量变化与系统工作的概率分布密切相关。随着驱动器的振幅$λ（t）$从零增加到最大$λ_{max} $，然后再次回到零重新汇率和最终的汉密尔顿重合。利息的主要数量是概率密度$ p（e_f | e_i）$，用于从初始能源$ e_i $过渡到最终能源$ e_f $。在经典的情况下，具有$ e_f \ neq e_i $的非对角性转变主要是由于分离质交叉的机制而出现的。我们表明，摆近似中的近似分析结果符合数值模拟。在量子案例中，数值确切的结果与使用Floquet理论的分析参数相辅相成。对于经典和量子案例，我们提供了$ p（e_f | e_i）$的周期性变化的直观解释，并具有最大振幅$λ_{max} $。
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. The energy change of the oscillator induced by the driving is closely related to the probability distribution of work for the system. With the amplitude $λ(t)$ of the drive increasing from zero to a maximum $λ_{max}$ and then going back to zero again initial and final Hamiltonian coincide. The main quantity of interest is then the probability density $P(E_f|E_i)$ for transitions from initial energy $E_i$ to final energy $E_f$. In the classical case non-diagonal transitions with $E_f\neq E_i$ mainly arise due to the mechanism of separatrix crossing. We show that approximate analytical results within the pendulum approximation are in accordance with numerical simulations. In the quantum case numerically exact results are complemented with analytical arguments employing Floquet theory. For both classical and quantum case we provide an intuitive explanation for the periodic variation of $P(E_f|E_i)$ with the maximal amplitude $λ_{max}$ of the driving.
