Transverse Shubnikov–de Haas effect and the manifestation of quantum diffraction

A quantum diffraction interpretation of the transverse Shubnikov–de Haas effect is presented. Within the framework of the conventional theory of this effect, we show that the matrix element for the electron transition from an initial state to a final state used in calculating the transverse electrical conductivity can be represented as a diffraction-type amplitude distribution. The squared modulus of this matrix element under certain conditions exhibits the Fraunhofer diffraction pattern. It is shown that the oscillating part of the transverse conductivity has the same form as the amplitude for Fraunhofer diffraction by an annular aperture.

Optical characteristics of finite temperature quantum electron gas

In this paper we study the propagation of elliptically polarized transverse electromagnetic waves in a quasineutral plasma with arbitrary degenerate electron fluid ranging from classical dilute to fully degenerate density regimes by using the appropriate collisional magnetohydrodynamics model, which incorporates the adiabatic quantum equation of states for high-frequency electron fluid compression and the Bohm quantum potential responsible for the collective quantum diffraction effect. Three distinct propagation modes are categorized corresponding to electron density regimes of dilute, intermediate, and fully degenerate plasmas. One of these modes is found to be purely of quantum mechanical origin and disappears in the absence of the quantum diffraction effect. The present generalized magnetohydrodynamics theory qualitatively describes key features of optical parameters and experimental data of dilute classical, semiconducting, and in fully degenerate plasmas. Different optical parameters, such as the refractive and absorption index of the new mode are investigated. It is shown that the optical response of the magnetized plasma with arbitrary degeneracy is essentially governed by three characteristic frequencies, namely, collision, plasmon, and cyclotron frequencies. The profound experimental minimum in the refractive index of arbitrary degenerate quantum plasmas and its dependence on the characteristic frequencies is studied in detail. Current investigation is of fundamental importance in high energy density and fusion plasma diagnostics and may provide key knowledge on the characteristics of astrophysical dense matter.

Classical scattering and stopping power in dense plasmas: the effect of diffraction and dynamic screening

In the present work, classical electron–ion scattering, Coulomb logarithm, and stopping power are studied taking into account the quantum mechanical diffraction effect and the dynamic screening effect separately and together. The inclusion of the quantum diffraction effect is realized at the same level as the well-known first-order gradient correction in the extended Thomas–Fermi theory. In order to take the effect of dynamic screening into account, the model suggested by Grabowski et al. in 2013 is used. Scattering as well as stopping power of the external electron (ion) beam by plasma ions (electrons) and scattering of the plasma's own electrons (ions) by plasma ions (electrons) are considered differently. In the first case, it is found that in the limit of the non-ideal plasma with a plasma parameter Γ → 1, the effects of quantum diffraction and dynamic screening partially compensate each other. In the second case, the dynamic screening enlarges scattering cross-section, Coulomb logarithm, and stopping power, whereas the quantum diffraction reduces their values. Comparisons with the results of other theoretical methods and computer simulations indicate that the model used in this work gives a good description of the stopping power for projectile velocities $v\,{\rm \lesssim}\, 1.5 v_{{\rm th}}$, where vth is the thermal velocity of the plasma electrons.

Quantum diffraction grating: A possible new description of nuclear elastic scattering

The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. Introduction of the generalized functions into the quantum scattering theory clarifies the problem and allows to propose new interpretations of nuclear elastic scattering phenomenon. The derived new forms of the full elastic scattering amplitudes and possibility of splitting them suggest existence of dynamical quantum diffraction grating around the nuclei. Particularly important fact is that this grating existing in the space around the nucleus makes considerable contribution to the experimental elastic differential cross-section. All these might be quite important in analyses of nuclear elastic scattering data and so require to be stated in a more detailed and clear way.