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Gapless Superconductivity
Published in R. D. Parks, Superconductivity, 2018
Here the first term is the ordinary impurity scattering potential while the second term is the so-called exchange interaction. S denotes the spin operator of the localized magnetic moment. It is important to note that from the criterion given in Section II, it follows that the spin exchange interaction is a time-reversal breaking perturbation. The significant differences in the energy shifts caused by U1ρ3 and U2S · α have been noticed previously by Suhl and Matthias and Baltensperger (20,21). The first satisfactory treatment based on the above model was given by Abrikosov and Gor’kov (1). They were able to obtain the Green’s function which describes the equilibrium as well as nonequilibrium properties of the system. In particular, they predicted the existence of the gapless region in which the excitation spectrum begins continuously from zero energy. This prediction was subsequently confirmed in a beautiful experiment by Woolf and Reif (22). In the case of rare earth impurities such as Gd which have unfilled f-shells, the agreement between theory and experiment was good, while in the case of transition metal impurities such as Fe and Mn, a density of states larger at low excitation energies than theoretically expected was observed. Although we shall not discuss critically the AG theory, here, there are several assumptions which have been made in the calculation and which we will mention here. The correlations among the impurity spins are neglected (23,6).The scattering amplitude due to the exchange interaction is treated in Born approximation.
Radiation, Diffraction, and Scattering
Published in J. David, N. Cheeke, Fundamentals and Applications of Ultrasonic Waves, 2017
Scattering of acoustic waves can in principle be calculated from Huygens principle. The scattering amplitude is usually described by the scattering cross-section that represents the apparent area of the scattering object.
Functional integral approach to the transfer function of a stochastic scattering channel
Published in Waves in Random and Complex Media, 2020
Octavio Cabrera, Damián H. Zanette
As it stands in Equation (3), the transfer function does not take into account the possibility that the transmitted signal is shifted in phase at each scattering event. This effect can be incorporated to our description by adding a complex phase to the scattering amplitude, , where is the frequency-dependent phase shift introduced by scatterer k. In turn, when defining the scattering amplitude density through Equation (4), the scattering phase shift induces the appearance of a phase in the density, . Thus, the scattering amplitude density becomes a complex quantity.