Momentum relaxation time

Fig. 1.17. The temperature-dependence of angular momentum relaxation time (+) in nitrogen [71] and accompanying density change due to cooling (0).

Specific values of r are helpful for identifying the nature of the scattering process. For example, if the momentum relaxation time is proportional to a given... 

In order to find the Green s function g, we consider the diffusive case when the Usadel equation is applicable. This equation can be used provided the condition Jr strong ferromagnets like Fe and in this case one should use a more general Eilenberger equation for a quantitative... 

FEMTOSECOND ELLIPSOMETRY A NEW TOOL FOR THE MEASUREMENT OF HOT ELECTRON MOMENTUM RELAXATION TIMES IN METALS... 

The measurement of hot electron momentum relaxation times in metals... 

It is possible to reconcile the dilTerence by asserting that a time scale argument applies, namely, the reduced FPE applies on short time scales whereas the reduced Smoluchowski equation applies on time scales that are long compared to the momentum relaxation time scales. The question of the magnitude of these differences is addressed in the next section. For most chemical reactions, the FPE results will be used, except for the diffusive contribution to recombination dynamics considered in the next section. 

This has the projjerty that /1(0) = 1 — Ay/toy and A(co) = 0. Thus at frequencies above the barrier momentum relaxation time the kinetic theory result for the encounter flux is found, whereas at lower frequency the action of the retarded backflow leads to a reduction in the encounter flux. 

Note, however, that electrical conductivity is related to the momentum relaxation time, whereas the thermal conductivity is related to the energy relaxation time. They are usually close at room temperature or at very low temperatures. 

Here rp(k) is the momentum relaxation time which is due to the electron-phonon and electron-impurity scattering,stands for the electron distribution functions of spin a, h(k) is the DP term which serves as an effective magnetic field and is composed of the Dresselhaus term [10] due to the bulk inversion asymmetry (BIA) and the Rashba term [11] due to the structure inversion asymmetry (SIA),... 

T is the mean momentum relaxation time. It describes the time it takes for the... 

Tjn denotes the mean time between subsequent collisions (momentum relaxation time). The electrons move with a constant drift velocity which is proportional to the applied electric field strength, E, such that... 

In TMS, the value of Pjj tracks that of Pj. The mobility drop observed near the critical temperature T is caused by a smaller momentum relaxation time t. Within the range of temperatures studied, the mobility ratio r = Pj /yQ seems clustered around 1.0 0.10. If a single scattering mechanism is responsible for the observed electron mobility in TMS, it must be such that the momentum relaxation time T is independent of the kinetic energy of the carriers. 

However, the maximum size of the time step must be short enough such that the force on the particles and the gradient of the diffusion tensor remain constant during the time step. There is no lower limit on the time step however, one must only study time correlations of the displacement that are longer than the momentum relaxation time. 

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