Takatsuka Kazuo, Takahashi Satoshi, Koh Yang Wei, Yamashita Takefumi
Department of Basic Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902, Tokyo, Japan.
J Chem Phys. 2007 Jan 14;126(2):021104. doi: 10.1063/1.2431178.
The mechanism of energy quantization is studied for classical dynamics on a highly anharmonic potential, ranging from integrable, mixed, and chaotic motions. The quantum eigenstates (standing waves) are created by the phase factors (the action integrals and the Maslov index) irrespective of the integrability, when the amplitude factors are relatively slowly varying. Indeed we show numerically that the time Fourier transform of an approximate semiclassical correlation function in which the amplitude factors are totally removed reproduces the spectral positions (energy eigenvalues) accurately in chaotic regime. Quantization with the phase information alone brings about dramatic simplification to molecular science, since the amplitude factors in the lowest order semiclassical approximation diverge exponentially in a chaotic domain.
针对高度非谐势上的经典动力学，研究了能量量子化机制，其涵盖可积、混合和混沌运动。当振幅因子相对缓慢变化时，量子本征态（驻波）由相位因子（作用量积分和马斯洛夫指数）产生，与可积性无关。实际上，我们通过数值表明，在完全去除振幅因子的近似半经典关联函数的时间傅里叶变换，在混沌区域能准确再现谱位置（能量本征值）。仅用相位信息进行量子化给分子科学带来了极大简化，因为在最低阶半经典近似中，振幅因子在混沌域呈指数发散。
