Employing a superposition representation of the microcanonical density matrix the perturbation of the stationary diffusion process by a fixed point scatterer is treated approximately. The primary dipole distributions of carrier and current density are calculated and interpreted without additional assumptions. The stationarity of tho current is shown explicitly. The primary dipole is localized in a region limited by the mean free path. The classical diffusion process which follows removes this localization, the electrostatic screening by the ensemble of all electrons restores it. The ideas of Landauer are confirmed within a coherent theoretical scheme.
As in the Landauer-Büttiker approach to transport, a transmitter is, at fixed energy, characterized by its reflection and transmission coefficients. Generalizing a prior approach, we establish a variational principle to determine, without magnetic field, the distribution of the current over the different channels if the transmitter is coupled incoherently to its surroundings. For transmitters coupled with each other, a general demand of additivity defines the form of the variational functional. Contacts are treated as special transmitters, and, as a test, the results of the standard model are reproduced. A typical serial resistance is defined as the resistance within a long incoherently coupled chain, with no regard to contacts and reservoirs. This resistance is strictly additive. It is shown that well within the chain a relaxed current and density distribution is established that is independent of the conditions at the ends of the chain. This distribution coincides with the optimal distribution that minimizes the resistance of each of the single transmitters that are the building blocks of the chain. For a sufficiently long chain, the serial resistance is determined by the linear dependence of the inverse total transmission on the number of single transmitters. The relaxational behaviour of a long chain implies corresponding features of the reflection and transmission matrices in the asymptotic regime, especially a factorization of the transmission matrix, expressing memory loss with respect to the ingoing and outgoing channels.
Employing a superposition representation of the density matrix for a fixed energy the first order quantum corrections to the current driven by a weak constant force are calculated for independent charge carriers scattered by uncorrelated point-like scatterers. This complements a preceding treatment of the corresponding diffusion problem and demonstrates the Einstein equivalence as a property of the density matrix itself. The changes in kinetic energy caused by the force field lead to a reformulation of the correction terms which resemble now the known vertex structure of the Bethe-Salpeter equation. The influence of the force is considered explicitly in the propagator construction.Unter Benutzung einer Superpositionsdarstellung fur die Dichtematrix bei fixierter Energie werden fur unabhangige Ladungstriger Quantenkorrekturen erster Ordnung zu dem durch eine achwache konstante Kraft hervorgerufenen Strom berechnet. Die Streuzentren werden als punktformig und unkorreliert angenommen. Die Arbeit erganzt eine vorhergegangene Behandlung des entsprechenden Diffusionsproblems und weist die Einstein-Aquivalenz als eine Eigenschaft der Dichtematrix selbst nach. Die vom Kraftfeld bewirkten Anderungen der kinetischen Energie legen eine Umformulierung der Korrekturterme nahe, wodurch gleichzeitig die von der BetheSalpeter-Gleichung her bekannten mathematischen Vertex-Bildungen entstehen. Der EinfluB der Kraft wird explizit in der Ausbreitungsfunktion erfaBt.
A superposition method for the density matrix of stationary transport processes is developed where an arbitrary perturbation is superimposed on a weakly scattering background. Additional scatterers, areal perturbations of the grain boundary type and/or geometrical confinements in wires or films are candidates for applications. In the present paper an arbitrarily strong added scatterer is treated whose linear size remains small compared with the mean free path within the background. This problem is solved for a one-channel quantum wire and for the three-dimensional bulk. In both cases the evolving residual resistivity dipole (RRD) is determined. Already existing results are confirmed, generalized, and complemented by the inclusion of oscillatory density terms. A comparison of both the cases demonstrates the decisive role played by the topology of the problem. Within the scope of a completely formalized nonclassical transport theory, the internal mechanism producing the RRD is analysed. In this way it is shown that the voltage drop due to an added scatterer is given correctly, in the one-channel case, by an expression of the (R/T)-type quite similar to the original Landauer formula (LF). This derivation of a modified LF abandons the concept of dissipative reservoirs and ideal leads. The physical difference between ideal and resistive leads yields different results, too. These agree completely only for a sharp Fermi energy while, in the general case of finite temperatures, non-negligible energy dependences destroy the full equivalence of both approaches.
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