Ohmic dissipation model

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

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 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... 

The Ohmic model memory kernel admits an infinitely short memory limit y(t) = 2y5(t), which is obtained by taking the limit a>c —> oo in the memory kernel y(t) = yG)ce c [this amounts to the use of the dissipation model as defined by Eq. (23) for any value of ]. Note that the corresponding limit must also be taken in the Langevin force correlation function (29). In this limit, Eq. (22) reduces to the nonretarded Langevin equation ... 

The formal similitude between Eq. (30) and Ohm s law in an electrical circuit justifies the term of Ohmic model given to the dissipation model as defined by the spectral density (23). 

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). 

Here we apply the LAND-map approach to compute of the time dependent average population difference, A t) = az t)), between the spin states of a spin-boson model. Here az = [ 1)(1 — 2)(2 ]. Within the limits of linear response theory, this model describes the dissipative dynamics of a two level system coupled to an environment [59,63-65]. The environment is represented by an infinite set of harmonic oscillators, linearly coupled to the quantum subsystem. The characteristics of the system-bath coupling are completely described by the spectral density J(w). In the following, we shall restrict ourselves to the case of an Ohmic spectral density... 

This is the simplest model of an electrocatalyst system where the single energy dissipation is caused by the ohmic drop of the electrolyte, with no influence of the charge transfer in the electrochemical reaction. Thus, fast electrochemical reactions occur at current densities that are far from the limiting current density. The partial differential equation governing the potential distribution in the solution can be derived from the Laplace Equation 13.5. This equation also governs the conduction of heat in solids, steady-state diffusion, and electrostatic fields. The electric potential immediately adjacent to the electrocatalyst is modeled as a constant potential surface, and the current density is proportional to its gradient ... 

It is evident from the previous discussion that significantly sim-phfied modeling of the current distribution can often be achieved once scaling analysis has identified the controlling dissipative mechanisms in the cell. It has been shown that the current distribution in most common systems can be characterized in terms of three major dissipative processes ohmic (within the electrolyte across the cell), mass transport (across the concentration bmmdary layer), and surface activation (on the electrode). These are designated in terms of the corresponding resistances R q,R q, and R. The Wa number characterizes the cmrent distribution in terms of the relative importance of two of the three resistances the surface (Jfg)and the ohmic (Rq ) resistances.Clearly,more complete characterization of the system requires the comparison of two additional resistance ratios and the formulation of two additional dimensionless parameters. ... 

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