Energy diffusion regime

The situation is analogous to the so-called energy diffusion regime in the Kramers picture of reactions in solution except that here the molecule acts as its own solvent [E. W. Schlag, J. Grotemeyer, and R. D. Levine, Chem. Phys. Lett. 190, 521 (1992)]. 

Generalized Langevin equation, 3,70, 94 energy diffusion regime of GLE, 18, 20-21... 

Only at smaller temperature V 1 MeV when the emissivity of the direct Urea process has dropped according to the typical T6 dependence, most of the neutrino energy will be released within a small time. Neutrinos in the diffusion regime can escape from the surface in the time... 

Rayleigh quotient method has been used only in the spatial diffusion limited regime but not in the energy diffusion limited regime (see the next Seetion). 

Equation (7.206) disregards the small contribution to the heat flow arising from the kinetic energy of the Brownian particles. Equation (7.206) is mathematically and thermodynamically coupled and describes specifically the coupled evolutions of the temperature field and the velocity-coordinate probability distribution of the Brownian particles. However, for larger times than the characteristic time /3 1, the system is in the diffusion and thermal diffusion regime. 

This ensures the correct connection between the one-dimensional Kramers model in the regime of large friction and multidimensional unimolecular rate theory in that of low friction, where Kramers model is known to be incorrect as it is restricted to the energy diffusion limit. For low damping, equation (A3.6.29) reduces to the Lindemann-Hinshelwood expression, while in the case of very large damping, it attains the Smoluchowski limit... 

Berezhkovskii A M and Zitserman V Yu 1993 Multi-dimensional Kramers theory of the reaction rate with highly anisotropio friotion. Energy diffusion for the fast coordinate versus overdamped regime for the slow coordinate Chem. Phys. Lett. 212 413-19... 

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