Narrow Results

Generalizing Dollard’s strategy, we investigate the structure of the scattering theory associated to any large time reference dynamics $U_D(t)$ allowing for the existence of Møller operators. We show that (for each scattering channel) $U_D(t)$ uniquely identifies, for $t\to \pm \infty$, asymptotic dynamics $U_{\pm }(t)$; they are unitary groups acting on the scattering spaces, satisfy the Møller interpolation formulas and are interpolated by the $S$-matrix. In view of the application to field theory models, we extend the result to the adiabatic procedure. In the Heisenberg picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg variables; their time evolution is induced by $U_{\pm }(t)$, which replace the usual free asymptotic dynamics. On the asymptotic states, (for each channel) the Hamiltonian can by written in terms of the asymptotic variables as $H=H_{\pm }(q_{out/in},p_{out/in})$, $H_{\pm }(q,p)$ the generator of the asymptotic dynamics. As an application, we obtain the asymptotic fields ${\psi }_{out/in}$ in repulsive Coulomb scattering by an LSZ modified formula; in this case, $U_{\pm }(t)=U_0(t)$, so that ${\psi }_{out/in}$ are free canonical fields and $H=H_0({\psi }_{out/in})$.

The lowest order contribution of the amplitude of the Dirac–Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given momentum and helicity. One studies the difficulties that arises when one passes from the amplitude to cross section.

The exact treatment of the two-body problem in momentum space in the presence of Coulomb forces is discussed. Convergence of the traditionally used renormalization approximation is investigated with respect to increasing ranges of the screened Coulomb potentials. The permissible energy range for this approximation is obtained for the first time in this work.

The scattering of a charged scalar field on Coulomb potential is studied using solutions of the Klein–Gordon equation which have a definite momentum. One obtains that the modulus of momentum is not conserved in the scattering process on de Sitter space.

We comment on a previous calculation¹ for the scattering amplitude for the Dirac field in an external Coulomb potential in the expanding de Sitter space. The result implies that for initial and final fermion states with identical momenta |p_i|=|p_f| the helicity of the particle is conserved. We make a classical analysis of the scattering problem in the small scattering angle approximation using the Bargmann–Michel–Telegdi equation and show that helicity conservation also manifests in the classical case. We also show that in Minkowski space there is a complete agreement between the classical and quantum polarization angle of the scattered particle.

We consider a double-layer system made of two parallel bilayer graphene sheets separated by a dielectric medium. We calculate the finite-temperature electrical conductivity of the first layer due to charged impurities located in two layers. We study the effects of temperature, interlayer distance, dielectric constants and impurity concentration, carrier concentration on the electrical conductivity. We show the importance of charged impurities located in layer II in determining electrical conductivity of the first layer for small interlayer distance. The results in this paper give us more understanding about the long-range charged impurity scattering in bilayer graphene under the effect of the second one.

In this research, the electron mobility in GaAs quasi-one-dimensional wires with the presence of ionized impurity at zero temperatures was investigated and the results were compared with the mobility of a two-dimensional electron gas system. GaAs is a non-magnetic semiconductor with a direct band gap. Here for the calculations, the Boltzmann transport equation is used in the relaxation time approximation, taking into account the ionized impurity potential. Focusing on ionized Coulomb scattering and the short-range disorder is our goal. Electron mobility was investigated based on related parameters (Fermi energy and width of nanowires), and its diagram was drawn. In the end, the results of this research were compared with electron mobility in completely two-dimensional electronic systems. As expected, the numerical results showed that the electron mobility in extensive wires converges to the electron gas mobility of a fully two-dimensional plane.