Transport coherent scattering

In short, incoherent scattering allows one to determine the self-diffusivity, Ds, whereas coherent scattering gives access to the transport diffusivity, Du from experiments performed at equihbrium. When the scattering is both incoherent and coherent, then both diffusivities can in principle be determined simultaneously. 

Landauer proposed in 1957 the first mesoscopic theoretical approach to charge transport [176]. Transport is treated as a scattering problem, ignoring initially all inelastic interactions. Phase coherence is assumed to be preserved within the entire conductor. Transport properties, such as the electrical conductance, are intimately related to the transmission probability for an electron to cross the system. Landauer considered the current as a consequence of the injection of electrons at one end of a sample, and the probability of the electrons reaching the other end. The total conductance is determined by the sum of all current-carrying eigenmodes and their transmission probability, which leads to the Landauer formula of a ID system ... 

Nan, X., Potma, E. O., and Xie, X. S. 2006. Nonperturhative chemical imaging of organelle transport in living cells with coherent anti-Stokes Raman scattering microscopy. Biophys. J. 91 728-35. 

In order to obtain estimates of quantum transport at the molecular scale [105], electronic structure calculations must be plugged into a formalism which would eventually lead to observables such as the linear conductance (equilibrium transport) or the current-voltage characteristics (nonequilibrium transport). The directly measurable transport quantities in mesoscopic (and a fortiori molecular) systems, such as the linear conductance, are characterized by a predominance of quantum effects—e.g., phase coherence and confinement in the measured sample. This was first realized by Landauer [81] for a so-called two-terminal configuration, where the sample is sandwiched between two metalhc electrodes energetically biased to have a measurable current. Landauer s great intuition was to relate the conductance to an elastic scattering problem and thus to quantum transmission probabilities. 

A very effective method to describe scattering and transport is the Green function (GF) method. In the case of non-interacting systems and coherent transport single-particle GFs are used. In this section we consider the matrix Green function method for coherent transport through discrete-level systems. 

This technique is based on the fact that voids in the material act as optical scatters. The analysis of the coherent light backscattering pattern of the material allows the measurement of the mean free transport light path, L, which is related to the mean distance between scatters, that is voids in our case. 

Let us estimate an order of electron conductivity value. As far as electron transport is provided through extended states of conduction band, which are not far from a mobility edge, the extreme disorder of electron scattering takes place, where between any two acts of scattering the phase coherence of electron wave turned out to be lost. In this case, according to Mott [8, 10] one may expect that pre-exponent coefficient po will correspond to the minimum metallic conductivity quantity,... 

In separation or catalytic applications, it is the transport diffusivity, Dt, which matters (this quantity is also named Fickian or chemical diffusivity). Transport diffusivities are traditionally obtained under non-equilibrium conditions [2], but they can be measured at equilibrium by coherent QENS [5]. Coherent neutron scattering is in principle more comphcated than incoherent scattering, but under certain conditions transport diffusivities can be extracted from the neutron data. 

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