Quasi-particle decay

Transport (TMTSF)2X. In a metallic system where phonons and impurities play little role in the scattering rate of carriers, the temperature dependence of resistivity is controlled by electron-electron scattering rate. In a Fermi liquid, it is then governed by the decay rate of quasi-particles. Dropping the logarithmic factors due to either the special geometry of the Fermi surface or the proximity of the SDW transition, one gets a quadratic temperature dependence of the form [29, 34, 75] ... 

Finally, let us consider in Fig.12 our findings for the decay rate of the quasi-particles (hole in the valence bands) in Si, and again compare with our C results. First, we note that below a threshold Im(E j ) = 0 the lifetime (2 ImE is infinite. The mechanism... 

Studies have been reported of the complex equilibria present in electrolytically produced supersaturated solutions of Zn2+ in aqueous KOH. Light-scattering and NMR techniques indicate the excess zinc to be present as a solute, rather than a colloid, and the predominant species appears to be the [Zn(OH)4]2 ion.606 However, Raman and potentiometric studies indicate that initially, quasi-colloidal particles, based on Zn(OH)2 and molecules of solvation, are present.607 These particles undergo a first-order decay to yield a solution containing the species [Zn(0H)2(H20)2], [Zn(0H)3H20] and [Zn(OH)4]2-, the actual constitution depending on the concentration. The non-colloidal zinc species are tetrahedral, rather than planar or octahedral. Stability constants for the ions [Zn(OH)n](" 2) ( = 1-3) have been reported.608... 

In the standard overdamped version of the Kramers problem, the escape of a particle subject to a Gaussian white noise over a potential barrier is considered in the limit of low diffusivity—that is, where the barrier height AV is large in comparison to the diffusion constant K [14] (compare Fig.6). Then, the probability current over the potential barrier top near xmax is small, and the time change of the pdf is equally small. In this quasi-stationary situation, the probability current is approximately position independent. The temporal decay of the probability to find the particle within the potential well is then given by the exponential function [14, 22]... 

Figure 1. (a) Transverse local photonic DOS (%) for the two-level atom in the centers of the four zigzag CNs (x is the dimensionless frequency), (b) Two-particle local photonic DOS functions S (solid lines) and f (dashed lines) taken at the peak frequencies of if 00 [see (a)], as functions of the distances between the two atoms on the axes of the (10,0) (lines 1 x=0.29), (11,0) (lines 2 v=0.25) and (12,0) (lines 3 x=0.24) CNs (see Ref. [5] for more details), (c) Optical absorbtion lineshapes for the atom at different distances outside the metallic (9,0) CN, demonstrating the formation of the atomic quasi-ID polariton state as the atom approaches the CN surface (see Ref. [10] for more details), (d) Upper-level population decay probability of initially excited atom A (lines 1) and initially unexcited atom B (lines 2), and the two-qubit atomic entanglement (lines 3), as functions of dimensionless time r for the two atoms in the center of the metallic (9,0) CN separated from each other by the distance of 6.3/U = 22.2 A (see Ref. [6] for more details). 

The most commonly used technique for determining 5 is photon correlation spectroscopy (PCS) [also known as quasi-elastic light scattering (QELS)]. PCS has become one of the standard tools of the trade for the colloid chemist. In this technique concentration fluctuations arising from the diffusive motion of the dispersion particles give rise to fluctuations in the dielectric constant of the medium are monitored photometrically. These fluctuations decay exponentially with a time constant related to the diffusion coefficient, Ds, of the scatterer, which can in turn be related to its hydrodynamic radius through the Stokes-Einstein equation ... 

Gaspard and Rice have also calculated the decay of an ensemble of particles for d=2. As for two-dimensional mappings (see Fig. 9), the decay occurs over two different time scales and it may be approximated here by a biexponential curve for intermediate times. However, an extremely slow decay still occurs after a very long time, as shown in Fig. 10, which is due to the slow depletion of the quasi-invariant set. As a... 

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