Ohmic dissipation

In the case of ohmic dissipation the product in (5.44) can be calculated explicitly and one obtains for the quantum correction factor... 

To make further progress, it is standard practice to take this definition of the spectral density and replace it by a continuous form based on physical intuition. A form that is often used for the spectral density is a product of ohmic dissipation qco (which corresponds to Markovian dynamics) times an exponential cutoff (which reflects the fact that frequencies of the normal modes of a finite system have an upper cutoff) ... 

The last term in (5.45) accounts for quantum corrections to the classical escape rate (5.32) [Dakhnovskii and Ovchinnikov 1985 Grabert and Weiss, 1984 Melnikov and Meshkov, 1983 Wolynes, 1981]. In the case of ohmic dissipation the product in (5.45) can be calculated explicitly and one obtains for the quantum correction factor... 

Fig. 38 Electronic transmission and corresponding current in the weak-coupling limit with ohmic dissipation (s = 1) in the bath. Parameters N = 20, Jo/wc =...

In Section IV, we turn to our model system, namely a classical or quantal dissipative free particle. We focus the study on the so-called Ohmic dissipation case, in which the noise is white and the particle equation of motion can be given the form of a classical nonretarded Langevin equation in the high-temperature regime (the Brownian particle then undergoes normal diffusive... 

In fact, the validity of Eqs. (90) and (91) is not restricted to the simple (i.e., nonretarded) Langevin model as defined by Eq. (73). These formulas can be applied in other classical descriptions of Brownian motion in which a time-dependent diffusion coefficient can be defined. This is for instance, the case in the presence of non-Ohmic dissipation, in which case the motion of the Brownian particle is described by a retarded Langevin equation (see Section V). 

In the Ohmic dissipation model with a Lorentzian cutoff function, y(oo) is given by Eq. (28), and Eq. (102) reads... 

In this section, we extend the previous study to the case of non-Ohmic dissipation, in the presence of which the particle damped motion is described by a truly retarded equation even in the classical limit, and either localization or anomalous diffusion phenomena are taking place. Such situations are encountered in various problems of condensed matter physics [28]. 

Non-Ohmic dissipation models are defined by a generalized friction coefficient varying at small angular frequencies like a power-law characterized by the exponent 8—1 (with 6 / 1) ... 

In the quantum case, the effective temperature Teff = ( peff)-1 can be obtained from Eq. (130), an equation which also allows one to define 7 err at T 0 for 1 < 8 < 2. Since Dit) is a monotonic increasing function of T, Eq. (130) yields for reff(T, tw) a uniquely defined value, as in the Ohmic dissipation case. 

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