ACH - Models in Chemistry 134. (1997)

5. szám - RESEARCH ARTICLES - Sibert III, E. L.–Borondo, F.: A time dependent view of the statistics of spectral intensities

С ц - MODELS IN CHEMISTRY 134 (5), pp 595-618 (1997) A time dependent view of the statistics of spectral intensities Edwin L. Sibert III1 and Florentino Borondo2 1Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin, Madison Madison, WI53706, USA 2Departmento de Quimica, C-IX, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain Received October 22, 1996 The intensities of spectrally resolved eigenstates are obtained for a two-dimensional model Hamiltonian, and the results are compared to predictions of random matrix theory and maximal entropy treatments. It is shown that when the statistics of spectral intensities are examined from a time dependent perspective, where the short time dynamics places constraints on the intensity distributions, one can readily separate useful dynamical information from that which is purely random in nature. Introduction Correlating the dynamics and spectroscopy of highly excited polyatomic molecules with features of the potential energy surface is an ongoing challenge in physical chemistry. Over the last two decades tremendous strides have been made at low and intermediate energies where high resolution spectroscopy and powerful new numerical methods have combined to yield a relatively clear picture of energy flow in polyatomic molecules [1, 2]. At higher energies, many of the standard spectroscopic techniques used at lower energies for interpreting and elucidating spectra fail, and other approaches must be used [3-11]. An essential feature of these newer approaches is the statistical treatment of the level spacings and intensities of molecular transitions. In this paper, we will use statistical arguments to argue and present an example in support of the idea that in strongly mixing systems there may be a well defined time before which one can obtain fruitful dynamical information. After this time the dynamics appears statistical. We define this time by using statistical measures of state mixing that have evolved out a random matrix theory [12]. The intensity distributions of a model Hamiltonian are considered. This Hamiltonian describes two coupled quartic oscillators [13-17]. The classical phase space of this system has negligible 1217-8969/97/$ 5.00 © 1997 Akadémiai Kiadó, Budapest

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