The femtosecond inter-Landau-level dynamics of a two-dimensional electron gas in a large magnetic field is investigated by degenerate four-wave mixing on modulation doped quantum wells. We observe a large transfer of oscillator strength to the lowest Landau level, and unusual dynamics due to Coulomb correlation. We interpret the effects using a model based on shakeup of the electron gas.

We show that there exists multi-vortex, non-radial, finite energy solutions to the magnetic Ginzburg-Landau equations on all of R2. We use Lyapunov-Schmidt reduction to construct solutions which are invariant under rotations by 2π k (but not by rotations in O(2) in general) and reflections in the x− axis for some k ≥ 7. 1 Ginzburg-Landau equations 1.

The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau equations. We propose a discretization scheme which leads to a faithful discretization of the reduced dynamics of the original differential equations.

s of courses Giovanni ALBERTI “Concentration phenomena for functionals of Ginzburg-Landau type. A variational approach” In these lectures I will describe an approach by Γ-convergence to certain concentration phenomena for minimizers of functionals of Ginzburg-Landau type, as developped in [ABO2] and [JS]. Consider the functionals

In this paper, we establish the global fast dynamics for the time-dependent Ginzburg}Landau equations of superconductivity. We show the squeezing property and the existence of "nite-dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in ̧2] ̧2 for the Ginzburg}Landau equations in two spatial dimensions. Copyright ( 1999 John Wiley & Sons, ...