Local Random Matrix Theory LRMT

The harmonic picture of forces in a molecule is a good approximation because nuclei are much heavier than the electron, so the low-energy wave functions for nuclear motion can 

However, even for the harmonic level of approximation one can contemplate that certain paths of motion are more facile than others. Such paths follow resonances in which a few quanta in one mode are converted into quanta of other modes, such that the total mode energy is nearly conserved. 

The local ways of hopping are quantified through a local density of states. This local density is crucial in determining the rate and manner of energy flow in the interior states. It measures the likelihood that a resonance local transfer can occur. 

Rice and Jortner among others have argued that the density of levels in the state space can be treated as a continuum, allowing the use of the golden rule formalism to describe this IVR in the intra-molecular energy transfer processes. Such an approach will be presented later in Chapter 15. 

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Section II provides a summary of Local Random Matrix Theory (LRMT) and its use in locating the quantum ergodicity transition, how this transition is approached, rates of energy transfer above the transition, and how we use this information to estimate rates of unimolecular reactions. As an illustration, we use LRMT to correct RRKM results for the rate of cyclohexane ring inversion in gas and liquid phases. Section III addresses thermal transport in clusters of water molecules and proteins. We present calculations of the coefficient of thermal conductivity and thermal diffusivity as a function of temperature for a cluster of glassy water and for the protein myoglobin. For the calculation of thermal transport coefficients in proteins, we build on and develop further the theory for thermal conduction in fractal objects of Alexander, Orbach, and coworkers [36,37] mentioned above. Part IV presents a summary. 

For moderate-sized molecules with tens of vibrational modes, vibrational energy flow is conveniently described in a vibrational quantum number space. A statistical theory for the vibrational Hamiltonian, called Local Random Matrix Theory (LRMT), exploits the local coupling in the state space. LRMT predicts... 

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