Generalized Einstein relations

Roichman Y, Tessler N (2002) Generalized Einstein relation for disordered semiconductors -implications for device performance. Appl Phys Lett 80 1948... 

The time-dependent VACF is obtained by numerically Laplace inverting the frequency-dependent VACF, which is related to the frequency-dependent friction through the following generalized Einstein relation given by Eq. (81) ... 

The frequency (z)-dependent velocity correlation function Cv(z) is related to the frequency dependent friction by the well-known generalized Einstein relation,... 

Actually, if we focus our attention on Eq. (180) and we consider the case where the correlation function <1> ( ) has the analytical form of Eq. (148), with 2 < p < 3, we reach the conclusion that the conductivity of the system would become infinite in this case, given the fact that the form of Eq. (148) makes non integrable the correlation function . The current /(f) is the time derivative of ( (f)). Thus, time differentiating Eq. (182) and using Eq. (163), we see that j(t) oc f8 1. Hence the generalized Einstein relation of Eq. (182) is not a problem for subdiffusion [76], since the current tends to vanish in the time asymptotic limit. It becomes a problem for superdiffusion, since in this case the current tends to diverge for t > oo. 

Roichman Y. and Tessler N. (2002), Generalized Einstein relation for disordered semicondnctors—implications for device performance , Appl. Phys. Lett. 80, 1948-1950. 

In Eq. (3), 039 and 023 are the cross sections for stimulated emission and absorption. For narrow-line absorption and emission spectra, these two cross sections are equal. For broadband spectra with emission bandwidth greater than kT, the cross sections are connected by a generalized Einstein relation (6J. The final term in Eq. (3) accounts for possible excited-state absorption from the upper laser level to higher excited-states indicated by the dashed level in Fig. 1. If aesa > a32> absorption from level 3 dominates stimulated emission and laser action is not possible. 

Waldman, M. Mason, E.A., Generalized Einstein relations from a three temperature theory of gaseous ion transport, Chem. Phys. 1981, 58, 121-144. 

Like mobUity, the diffusion of ions is modified at high E/N it is accelerated because of field heating and becomes anisotropic (1.3.4). Both D and can still be related to mobility by generalized Einstein relations (GER) that use longitudinal (I ll) and transverse (Tx) temperatures to characterize the random component of ion motion in those directions. Such relations are found by solution of Boltzmann equation assuming some basis functions.In the simplest two-T treatment (1.3.9) using Gaussian functions with temperatures T and T ... 

Robson, R.E., On the generalized Einstein relation for gaseous ions in an electrostatic field. J. Phys. B 1976, 9, L337. 

Note that since the charge concentrations n and p in (4) and (5) are the concentrations of free carriers and and are the mobilities of free charge carriers, the classical Einstein relation (f>n,p = kTp Jq) is applicable. Only if we were to define n and p as the concentration of free and trapped carriers would we have to use the generalized Einstein relation [32, 33]. 

Additionally, we may provide a formulatirMi of the generalized Einstein relation (90) that links the conductivity, the chemical diffusion coefficient, and the chemical... 

This last equation corresponds to the generalized Einstein relation given in (90). 

Here tb is a relaxation time for the Brownian velocities, and rg is far smaller than t, even in the nominal t 0 limit of Eq. 4.25. Diffusion coefficients and mobility tensors are related by a generalized Einstein relation... 

---