Large-scale collective motion at finite thermal excitations
This chapter uses a Kramers-Moyal expansion to derive from short time propagators transport equations of Fokker-Planck type for global motion. Because of the inherent non-linearities, the transport coefficients may vary strongly with the collective coordinates. In this sense the resulting equation for the phase space density differs markedly from that of Kramers, implying modifications in the probability distribution of the collective coordinates. Of particular importance are consequences for the limit of over-damped motion, where one faces problems typical for multiplicative noise. This influences the relation of equations for the collective density distribution to those of Langevin type for the collective variables themselves. Microscopic computations of transport coefficients are presented in their variation both with nuclear shapes and with temperature. Problems related to level crossings are discussed, together with general thermal aspects of global motion.
Keywords: Kramers-Moyal expansion, Fokker-Planck equation, Kramers equation, coordinate dependent transport coefficients, over-damped motion, multiplicative noise, Langevin equation, level crossings, global motion
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