Dynamics and chaos of molecules

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Recently, Takatsuka [1] has proposed a modified semiclassical correlation function that is free of the annoying amplitude factor. We refer this function to the amplitude-free correlation function (AFC), which is written in terms of the Action Decomposed Function [2], AFC is composed of only what we call turn-back orbits. Calculation of the turn-back orbits is by far easier than the periodic orbits. The role of the turn-back orbits in describing a standing wave is physically understandable. As an analogy, one may think of the motion of a string, one of the ends of which is spatially fixed on a wall and the other end is shaken. If the phases of ingoing and outcoming waves reflecting at t = 0 match with each other, they should form a stationary state. Here in this talk, we numerically verify that this theory gives really accurate spectrum in a unified manner both to integrable and nonintegrable systems by showing numerically how the AFC actually reproduces the correct eigenvalues of strongly chaotic systems [3]. This epoch-making method can be readily applied to large systems that could not be quantized otherwise.