Dynamically assisted Sauter-Schwinger effect in inhomogeneous electric fields

Via the worldline instanton method, we study electron-positron pair creation by a strong electric field of the profile $E/\cosh^2(kx)$ superimposed by a weaker pulse $E'/\cosh^2(\omega t)$. If the temporal Keldysh parameter $\gamma_\omega=m\omega/(qE)$ exceeds a threshold value $\gamma_\omega^{\rm crit}$ which depends on the spatial Keldysh parameter $\gamma_k=mk/(qE)$, we find a drastic enhancement of the pair creation probability -- reporting on what we believe to be the first analytic non-perturbative result for the interplay between temporal and spatial field dependences $E(t,x)$ in the Sauter-Schwinger effect.Comment: 13 pages, 4 figure

Homotopy theory of Hopf Galois extensions

We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H-Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.Comment: 28 page

Electronic Dynamics Due to Exchange Interaction with Holes in Bulk GaAs

We present an investigation of electron-spin dynamics in p-doped bulk GaAs due to the electron-hole exchange interaction, aka the Bir-Aronov-Pikus mechanism. We discuss under which conditions a spin relaxation times for this mechanism is, in principle, accessible to experimental techniques, in particular to 2-photon photoemission, but also Faraday/Kerr effect measurements. We give numerical results for the spin relaxation time for a range of p-doping densities and temperatures. We then go beyond the relaxation time approximation and calculate numerically the spin-dependent electron dynamics by including the spin-flip electron-hole exchange scattering and spin-conserving carrier Coulomb scattering at the level of Boltzmann scattering integrals. We show that the electronic dynamics deviates from the simple spin-relaxation dynamics for electrons excited at high energies where the thermalization does not take place faster than the spin relaxation time. We also present a derivation of the influence of screening on the electron-hole exchange scattering and conclude that it can be neglected for the case of GaAs, but may become important for narrow-gap semiconductors.Comment: 14 pages, 5 figures, formatted using SPIE templat