Wigner函数的半经典传播
Semiclassical propagation of Wigner functions
摘要：
我们提出了一个全面的研究半经典相空间传播的维格纳表示，强调数值应用，特别是作为一个初始值表示。两个半经典近似方案进行了讨论：传播的维格纳函数的基础上van Vleck的近似取代刘维传播的量子点与振荡模式反映的经典轨迹对之间的干涉。采用相空间路径积分，而不是在量子点的焦散线解决艾里函数。我们适用于两个基准模型的非线性分子的潜力，莫尔斯振荡器和四次双井，测试它们在标准的任务，如计算自相关函数和传播相干态。半经典维格纳传播的性能即使在存在显著的量子效应的情况下也是非常好的，例如，在相干隧穿和传播薛定谔猫态，以及在四维相空间的经典混沌。我们建议选择一个有效的数值实现我们的方法，并将其集成在蒙特卡洛-大都市算法适用于高维系统。
英文摘要：
We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed: The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrödinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo--Metropolis algorithms suitable for high-dimensional systems.
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