Showing papers on "Einstein relation published in 1988"

The Einstein relation in Kane-type semiconductors

Abstract: An attempt is made to investigate the Einstein relation for the diffusivity‐mobility ratio of the carriers in degenerate Kane‐type semiconductors, taking n‐Cd3As2 as an example, on the basis of a newly derived dispersion relation of the conduction electrons allowing various types of anisotropies in the band parameters within the framework of k⋅p formalism. It is found that the above ratio increases with increasing carrier degeneracy and is in quantitative agreement with the suggested experimental method of determining the Einstein relation in degenerate semiconductors having an arbitrary dispersion relation. In addition, the corresponding results for an isotropic three‐band Kane model are also obtained from the expressions derived.

On the diffusivity-mobility ratio in ultrathin films of bismuth in the presence of crossed electric and magnetic fields

Abstract: The Einstein relation is studied for the diffusivity-mobility ratio of the carriers in ultrathin films of bismuth in the presence of crossed electric and magnetic fields at very low temperatures, and the numerical results are presented for McClure and Choi, hybrid, Cohen, Lax, and ellipsoidal parabolic energy bands by formulating the respective modified carrier energy spectra. It is found that this ratio increases with decreasing film thickness, increasing electron concentration, and decreasing magnetic field. The quantum oscillations of the ratio show up much more significantly in the McClure than in the other models.

Probabilistic interpretation of the Einstein relation

Abstract: We present a probabilistic picture for the Einstein relation which holds for arbitrarily connected structures The diffusivity is related to mean first-passage times, while the conductance is given as a direct-passage probability The fractal Einstein relation is an immediate consequence of our result In addition, we derive a star-triangle transformation for Markov chains and calculate the exact values of the fracton (spectral) dimension for treelike structures We point to the relevance of the probabilistic interpretation for simulation and experiment

Concentration dependence of surface diffusion coefficients in clustering systems.

Abstract: Using an extended Einstein relation, we discuss the concentration dependence of the surface diffusion coefficient in clustering systems. We explain the difference between the surface diffusion coefficient measured by microscopic mass transport techniques (terrace-cluster coexistence surface diffusion) compared to coefficients extracted for a simple hopping process (adatom on terrace surface diffusion). For Sn and Ga on Si the adatom on terraces surface diffusion coefficient is shown to be concentration independent. Literature data for surface diffusion of Ag/Ge(111) and O/W(110) show a concentration dependence which is in good agreement with the dependence predicted for the terrace-cluster surface diffusion.

Some identities and relations for transport coefficients of dense fluids

Abstract: The transport coefficients appearing in the dense fluid kinetic theory by the author are cast in the forms of time correlation functions suitable for numerical simulation methods. The Einstein relation for the diffusion coefficient and friction constant is found to follow exactly from the collision integral for the diffusion coefficient in the dense fluid kinetic theory. By assuming that the momentum and the force (or configuration) relax at different rates in the dilute and dense regimes of density, it is shown that the self‐diffusion coefficient and the viscosity have two different relations, i.e., the one predicted by the mean free path theory and the Stokes–Einstein‐type relation. The intrinsic viscosity of a polymer solution is shown to scale like mν/2a, where ν is an index and ma is the molecular weight, if the momentum relaxation time of the polymer scales like (∼(l−2a))ν/2 with ∼(l−2a) denoting the mean square end‐to‐end distance. If ν=1, the scaling follows Flory’s prediction for instrinsic visco...

Reversible diffusion process and einstein relation

Abstract: Starting from a general partial differential operator of second order, we give the condition of reversibility and construct the reversible diffusion process generated by it. The flow current density of the process was defined and the Einstein formula proved.

The first-order concentration dependence of the mutual diffusion coefficient of Brownian particles

Abstract: The first‐order concentration dependence of the mutual diffusion coefficient of spherical Brownian particles in a suspension has previously been calculated essentially within the framework of the Smoluchowski equation in the configuration space of a pair of particles. After these calculations are reviewed, the same quantity is here treated on the basis of the Fokker–Planck equation in the phase space of a pair of particles which is considered to have a wider range of validity than the Smoluchowski equation. Two methods are used in the treatment. In one method the mobility of the particles is determined by solving the Fokker–Planck equation in a stationary state which is reached by application of the same external force on each particle. In the other method a known expression for the mobility in terms of time‐correlation functions is evaluated by solving the time‐dependent Fokker–Planck equation in the absence of external forces. The mobility thus obtained is transformed into the diffusion coefficient with the aid of the generalized Einstein relation. It is found that both methods lead to the same result for the diffusion coefficient as derived from the Smoluchowski equation. Implications of the present calculations are also discussed.