By Rainer Klages
This publication offers an outstanding, balanced and recent assessment of the topic matter.
Highly urged for college kids of non equilibrium statistical mechanics.
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Extra resources for Microscopic Chaos, Fractals And Transport in Nonequilibrium Statistical Mechanics (Advanced Series in Nonlinear Dynamics)
Kla95; Kla96b; Kla99a] on the basis of detailed numerical evidence; for proofs of the first result for b = 0 and of the last result see also Ref. [Kel07]. Interestingly, in the case of b = 0 very recently another exact solution for all parameter values of the diffusion coefficient has been derived by generalizing cycle expansion techniques [Cri06]. Similarly to the transition matrix methods reported in Chapter 2 (see also below), previously periodic orbit theory seemed restricted to Markov partition values of the slope [Cvi07].
15) which approaches the equilibrium one if u → 0, has an eigenvalue λ0 (u) which is no longer equal to one. It is just this quantity which contains all information we need to solve our problem, that of calculating the cumulant rates ck . 17) May 8, 2007 4:1 World Scientific Book - 9in x 6in 34 klages˙book Deterministic drift-diffusion where in turn λ0 (u) = lim n→∞ 1 log Qn (u) . 18) 2) As a calculational device, the problem is reinterpreted in terms of one-dimensional electrostatics: The probability density can then be considered as an electric field strength, and a jump at a discontinuity of such a density is therefore regarded as a charge at that point.
1. primary regimes of Fig. 1 can be detected. Such higher-order topological effects may eventually form the key to understand the full structure in the parameter dependence of the cumulant rates. We note that in the case of b = 0 a closely related argument has been used to understand the complicated structure of the diffusion coefficient D(a, 0) for our model in May 8, 2007 4:1 World Scientific Book - 9in x 6in 44 Deterministic drift-diffusion the region 2 < a < 3, cf. 2. We furthermore remark that J(a, b) = b for a ∈ N and J(a, b) = b for 2b ∈ N, which yields the exact boundaries in Fig.
Microscopic Chaos, Fractals And Transport in Nonequilibrium Statistical Mechanics (Advanced Series in Nonlinear Dynamics) by Rainer Klages