Departamento de Física, Universidad Nacional de Colombia, Bogotá DC, Colombia.
J Chem Phys. 2010 Jun 7;132(21):214102. doi: 10.1063/1.3425881.
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 Schrodinger 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.
我们提出了在 Wigner 表象中进行半经典相空间传播的综合研究，重点是数值应用，特别是作为初始值表示。讨论了两种半经典逼近方案。基于范弗莱克近似的 Wigner 函数传播子用具有振荡模式的量子点代替刘维尔传播子，该模式反映了经典轨迹对之间的干涉。相反，使用相空间路径积分，可以根据艾里函数解决量子点中的焦散现象。我们将这两种方法应用于两个非线性分子势的基准模型，即莫尔斯振荡器和四次双阱，以在计算自相关函数和传播相干态等标准任务中对它们进行测试。即使在存在明显的量子效应（例如，相干隧穿和传播薛定谔猫态）和四元相空间中的经典混沌的情况下，半经典 Wigner 传播的性能也非常好。我们为我们的方法的有效数值实现以及将其集成到适合高维系统的蒙特卡罗- metropolis 算法中提出了一些选择。
