论文标题
由短脉冲驱动的阻尼不足的谐波振荡器：分析分析
Underdamped harmonic oscillator driven by a train of short pulses: Analytical analysis
论文作者
论文摘要
周期性短脉冲驱动的不足阻尼谐波振荡器（UHO）的理论模型可能在经典，半经典和量子物理学中发现了很多应用。我们在这里介绍了两种不同形式的分析解决方案：{\ it Time-priodic solutions}和{\ it谐波解决方案}，用于一维经典的UHO，由三种不同的短脉冲火车驱动。它们是狄克梳子，一列方形脉冲和一列与脉冲到脉冲时间间隔$ t $和脉冲宽度$2τ$的高斯脉冲火车。当脉冲宽度$2τ\ rightarrow 0 $按预期时，针对正方形和高斯脉冲的两种解决方案接近狄拉克梳子的溶液。特别是，可以用重复频率$ω_ {\ rm r} =2π/t $的谐波项来表示狄拉克梳和高斯脉冲的谐波解决方案。提出的分析解决方案将提供一种实践方法来确定系统参数，例如换档振荡频率$ω= \ sqrt {ω_0^2-γ^2} $，固有频率$ω_0$，以及非线性弯曲式拟合力的$ gript for $γ$的$ω_0$ $和$ 2 $ 2 $ 2
A theoretical model of an underdamped harmonic oscillator (UHO) driven by periodic short pulses may find plenty of applications in classical, semiclassical, and quantum physics. We present here two different forms of analytical solutions: {\it time-periodic solutions} and {\it harmonic solutions} for one-dimensional classical UHO driven by three different trains of short pulses. They are a Dirac comb, a train of square pulses, and a train of Gaussian pulses with the same pulse-to-pulse time interval $T$ and pulse width $2τ$. Two solutions for square and Gaussian pulses approach to that of the Dirac comb when the pulse width $2τ\rightarrow 0$ as expected. In particular, the harmonic solutions for Dirac comb and Gaussian pulses could be expressed approximately with harmonic terms of the repetition frequency $ω_{\rm R} = 2π/T$ up to the second order. The presented analytical solutions would provide a practical way to determine experimentally the system parameters such as the underdamped oscillation frequency $ω= \sqrt{ω_0^2-γ^2}$, the natural frequency $ω_0$, and the damping rate $γ$, by nonlinear curve fitting procedures for different driving force parameters of $T$ and $2τ$.
