Dependence of Multiphonon Transitions on Interaction Strength and Temperature

Institute of Physics, University of Tartu, Riia 142, 51014 Tartu, Estonia 

A non-perturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the time-dependent non-stationary displacement correlation function of atoms. A non-linear integral equation for this function is derived and solved numerically for 3- and 4-phonon processes. We have found that the rate exhibits a critical behavior it sharply increases near a specific (critical) value(s) of the interaction. 

The temperature dependence of non-radiative transitions, caused by linear diagonal and quadratic non-diagonal vibronic interactions, is also investigated on the basis of the non-perturbative quantum theory. It was found that the usual increase of the transition rate with temperature does not hold near some critical values of the non-diagonal interaction and temperature. At these critical values the rate is high (comparable to the mean phonon frequency) and its temperature dependence has a maximum. The results may be important for understanding the mechanisms of catalysis in chemical reactions. 

Multiphonon transitions in molecular systems and in solids are usually described by the perturbation theory [1-12]. This theory works only if the interaction causing the process is weak. However, very often this interaction is rather strong. To explain the results of measurements in such a case, a non-perturbative theory is needed. 

ADVANCES IN QUANTUM CHEMISTRY, VOLUME 44 ISSN 0065-3276 DOI 10.1016/S0065-3276(03)44010-0 

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Critical Dependence of Multiphonon Transitions on Interaction Strength and Temperature... 

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