Local Random Matrix Theory

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... 

Leitner DM, Wolynes PG. 1997. Vibrahonal mixing and energy flow in polyatomic molecules Quantitative prediction using local random matrix theory. J. Phys. Chem. A 101 541-548. 

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