Coherent electron waves

Principle of electron holography. A bi-prism deviates the part of the highly coherent electron wave which passes through the vacuum with that having interacted with the specimen. The resulting set of interference fringes contains... 

Electron Nuclear Dynamics (48) departs from a variational form where the state vector is both explicitly and implicitly time-dependent. A coherent state formulation for electron and nuclear motion is given and the relevant parameters are determined as functions of time from the Euler equations that define the stationary point of the functional. Yngve and his group have currently implemented the method for a determinantal electronic wave function and products of wave packets for the nuclei in the limit of zero width, a "classical" limit. Results are coming forth protons on methane (49), diatoms in laser fields (50), protons on water (51), and charge transfer (52) between oxygen and protons. 

Propagation in a medium of a coherent optical wave packet whose longitudinal and transverse sizes are both of a few wavelength and whose field amplitude can induce relativistic motion of electrons is a novel challenging topic to be investigated in the general field of the so-called relativistic optics [11]. Theory and simulation have been applied to this problem for a few decades. A number of experiments have been performed since ultrashort intense laser pulses became available in many laboratories. 

Describing complex wave-packet motion on the two coupled potential energy surfaces, this quantity is also of interest since it can be monitored in femtosecond pump-probe experiments [163]. In fact, it has been shown in Ref. 126 employing again the quasi-classical approximation (104) that the time-and frequency-resolved stimulated emission spectrum is nicely reproduced by the PO calculation. Hence vibronic POs may provide a clear and physically appealing interpretation of femtosecond experiments reflecting coherent electron transfer. We note that POs have also been used in semiclassical trace formulas to calculate spectral response functions [3]. 

Modem electron microscopes with field emission electron sources provide brighter and more coherent electrons. Images with information of crystal stmctures up to 1 A can be achieved. A through-focus exit wave reconstmction method was developed by Coene et al. (1992 1996) to retrieve the complete exit wave function of electrons at the exit surface of the crystal. This method can be applied to thicker crystals which can not be treated as weak-phase object. It is especially useful for stud5dng defects and interfaces (Zandbergen etal, 1999). 

The criterium that the mean free path should be larger than the superconducting coherence length must be met. This is a very strict condition that implies also that the impurity interband scattering rate yab should be very small yah (1/2 )(KB/ft)Tc. Therefore most of the metals are in the dirty limit where the interband impurity scattering mixes the electron wave functions of electrons on different spots on bare Fermi surfaces and it reduces the system to an effective single Fermi surface. 

A suitable choice of the variational wave functions for various electron-phonon two-level systems is a long-standing problem in solid state physics as well as in quantum optics. For two-level reflection symmetric systems with intralevel electron-phonon interaction the approach with a variational two-center squeezed coherent phonon wave function was found to yield the lowest ground state energy. The two-center wave function was constructed as a linear combination of the phonon wave functions related to both levels introducing new VP. 

Electron radiation is a wave, which can be characterized by two physical terms amplitude A) and phase (6) Ae. Since electron radiation is coherent, when two waves meet, the resulting wave is a sum of the two waves, Ae = Aje -f A2e , and the resultant intensity is not necessarily bigger than any individual wave intensity but depends on the phase difference of the two waves. A phase-object refers to a specimen so thin that when a coherent plane wave passes through it, only the phase of the wave changes but the amplitude keeps its original value. Thus, there... 

X-ray photoelectron diffraction is the coherent superposition of a directly photo-emitted electron wave with the elastically scattered waves from near-neighboring atoms. This gives element-specific structural information about the near surface atoms in a single crystal [8-10]. The short inelastic mean free path of the electron waves at the kinetic energies of interest (15 to 1000 eV) leads to surface sensitivity and determination of the atomic geometry of the emitting atom. The known energies of narrow XPS core-level peaks lead to element specificity. The resolution of surface peaks and chemical shifts may even sometimes lead to a chemical state-specific structure determination. 

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 a transmission electron microscope, a highly coherent electron beam passes through a thin sample. The electron beam interacts with the sample and is transferred to the specimen s exit plane. The electron wave at the exit plane is magnified in order to form an image or alternatively a diffraction pattern of the sample. 

In diffraction mode, the projector lens system is adjusted in order to image the electron wave located at the back focal plane of the objective lens. What is seen on the screen is the intensity of this electron wave, which for coherent elastic scattering is called an electron diffraction pattern. 

If the impurity potential is smooth, the process of scattering on them proceeds quasi-classically. In this case no real scattering takes place and the impurity effect may be reduced to the appearance of a random phase of the electron wave function. As has been shown by Zawadowski (1), such impurities do not affect the thermodynamics of the one-dimensional system, in which, however, no phase transitions exist. The finite temperature of the transition arises due to three-dimensional effects which establish the coherent state in the whole volume. The impurities cause the phase shift on each thread, and, as a result, the coherence drops and the transition temperature diminishes. 

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