Noid W G, Loring Roger F
Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA.
J Chem Phys. 2005 May 1;122(17):174507. doi: 10.1063/1.1888485.
The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.
针对零温度下共振耦合的非简谐振荡器的量子力学模型，计算了与红外振动回波相关的非线性响应函数。通过将普朗克常数除以2π并令其趋于零，从量子响应函数确定经典力学响应函数，从而能够比较任意数量的非简谐振荡器之间的共振振动耦合对量子和经典振动回波的影响。量子响应函数表现出一种时间依赖性，它既反映了非简谐性又反映了共振耦合，而经典响应函数仅通过一个与时间无关的振幅依赖于非简谐性，并且其时间依赖性仅由共振耦合控制。此外，经典响应函数随时间无界增长，这是一种与经典力学非线性相关的现象，在量子力学中不存在。这种无界增长先前在没有共振振动能量转移的系统的响应函数中已被识别，并且在存在振动之间的共振耦合时也会持续出现。经典和量子响应函数之间的定量一致性仅限于与非简谐性成反比的持续时间的时间尺度。
