Phase coherence length

Static defects scatter elastically the charge carriers. Electrons do not loose memory of the phase contained in their wave function and thus propagate through the sample in a coherent way. By contrast, electron-phonon or electron-electron collisions are inelastic and generally destroy the phase coherence. The resulting inelastic mean free path, Li , which is the distance that an electron travels between two inelastic collisions, is generally equal to the phase coherence length, the distance that an electron travels before its initial phase is destroyed ... 

At low temperatures, in a sample of very small dimensions, it may happen that the phase-coherence length in Eq.(3) becomes larger than the dimensions of the sample. In a perfect crystal, the electrons will propagate ballistically from one end of the sample and we are in a ballistic regime where the laws of conductivity discussed above no more apply. The propagation of an electron is then directly related to the quantum probability of transmission across the global potential of the sample. 

When the electron s phase coherence length Le, i.e. the typical distance for the electron to travel without losing its phase, is of the order of the dot mean free path such a system is called mesoscopic. The regime ensuring Le 3> Ld is called ballistic. 

Here we present a quantum mechanical model to calculate the experimentally observed interference patterns [3,5]. We include two-dimensional potential fluctuations, temperature effects as well as the back-scattering from the potential fluctuations. The latter effect alters the interference patterns strongly when the scattering center is located close (within the phase coherence length) to the sample boundaries. Constructive and deconstructive interference arise when the position of the scattering potential in the direction of the detector QPC is changed by 1/4 of the Fermi wavelength. 

For an adequate description of the electron beam propagation the effect of back-scattering is also taken into account. Electrons propagating in the direction of the detector can be subjected to multiple reflections by the potential fluctuations and the sample boundaries before they reach the detector QPC. When the length of their trajectories is smaller than the phase coherence length these electrons influence the observed interference patterns strongly. For the structure under consideration this... 

The CDW phase coherence length measured by X-ray diffraction increases rapidly below T, For high-quality crystals at about 100 K the longitudinal coherence becomes longer than 1 pirn. At temperatures below 100 K the transverse coherence decreased by applying a current for a while. 

It should be pointed out that the model presented is appropriate for three dimensions. In the one-dimensional case all states are localized by disorder because a particular interrelation between the phase and the amplitude of the wave function implies the localization of the wave function within the phase coherence length. We shall return to this point in Section 3.7. 

Mesoscopic materials form the subset of nanostructured materials for which the nanoscopic scale is large compared with the elementary constituents of the material, i. e. atoms, molecules, or the crystal lattice. For the specific property under consideration, these materials can be described in terms of continuous, homogeneous media on scales less than that of the nanostructure. The term mesoscopic is often reserved for electronic transport phenomena in systems structured on scales below the phase-coherence length A0 of the carriers. 

Adaptive optics requires a reference source to measure the phase error distribution over the whole telescope pupil, in order to properly control DMs. The sampling of phase measurements depends on the coherence length tq of the wavefront and of its coherence time tq. Both vary with the wavelength A as A / (see Ch. 1). Of course the residual error in the correction of the incoming wavefront depends on the signal to noise ratio of the phase measurements, and in particular of the photon noise, i.e. of the flux from the reference. This residual error in the phase results in the Strehl ratio following S = exp —a ). 

The nematic phase of all the compounds CBn is characterized by a coherence length of about 1.4 times the elongated structure of the molecule. Based on this behaviour local associations in form of dimers with cyano-phenyl interactions were postulated. For the smectic A phase a partial bilayer arrangement of the molecules (SAd) is most likely. But there are also example for the smectic A phase with a monolayer (Sai) or a bilayer (Sa2) arrangement of the molecules as well as a commensurate structure A large number of X-ray measurements were carried out in the liquid crystalline state to clear up the structural richness and variability (see Chap. 2, this Vol. [52]). 

Inwa (x/c)2(lw)nsin2(irz/2/c), where lQ is the coherence length (distance for accrual of a it phase mismatch). 

Under the simulation conditions, the HMX was found to exist in a highly reactive dense fluid. Important differences exist between the dense fluid (supercritical) phase and the solid phase, which is stable at standard conditions. One difference is that the dense fluid phase cannot accommodate long-lived voids, bubbles, or other static defects, whereas voids, bubbles, and defects are known to be important in initiating the chemistry of solid explosives.107 On the contrary, numerous fluctuations in the local environment occur within a time scale of tens of femtoseconds (fs) in the dense fluid phase. The fast reactivity of the dense fluid phase and the short spatial coherence length make it well suited for molecular dynamics study with a finite system for a limited period of time chemical reactions occurred within 50 fs under the simulation conditions. Stable molecular species such as H20, N2, C02, and CO were formed in less than 1 ps. 

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