Validity of the Kirchhoff approximation for the scattering of electromagnetic waves from dielectric, doubly periodic surfaces.

Accuracy of Kirchhoff approximation (KA) for rough-surface electromagnetic wave scattering is studied by comparison with accurate numerical solutions in the context of three-dimensional dielectric surfaces. The Kirchhoff tangent plane approximation is examined without resorting to the principle of stationary phase. In particular, it is shown that this additional assumption leads to zero cross-polarized backscattered power, but not the tangent plane approximation itself. Extensive numerical results in the case of a bisinusoidal surface are presented for a wide range of problem parameters: height-to-period, wavelength, incidence angles, and dielectric constants. In particular, this paper shows that the range of validity inherent in the KA includes surfaces whose curvature is not only much smaller, but also comparable to the incident wavelength, with errors smaller than 5% in total reflectivity, thus presenting a detailed and reliable source for the validity of the KA in a three-dimensional fully polarimetric formulation.

Two-particle irreducible effective action approach to nonlinear current-conserving approximations in driven systems.

Using closed-time-path two-particle irreducible coarse-grained effective action (CTP 2PI CGEA) techniques, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the CTP 2PI CGEA is invariant under a simultaneous gauge transformation of the external field and the full Schwinger-Keldysh propagator, and that this property holds even when the loop expansion of the CTP 2PI CGEA is truncated at arbitrary order. The effective action approach provides a systematic way of calculating the propagator and response functions of the system, via the Schwinger-Dyson equation and the Bethe-Salpeter equations, respectively. We show that, due to the invariance of the CTP 2PI CGEA under external gauge transformations, the response functions calculated from it satisfy the Ward-Takahashi hierarchy, thus warranting the conservation of the electronic current beyond the expectation value level. We also clarify the connection between nonlinear response theory and the WT hierarchy, and discuss an example of an ad hoc approximation that violates it. These findings may be useful in the study of current fluctuations in correlated electronic pumping devices.

Counting defects in an instantaneous quench.

We consider the formation of defects in a nonequilibrium second-order phase transition induced by an instantaneous quench to zero temperature in a type II superconductor. We perform a full nonlinear simulation where we follow the evolution in time of the local order parameter field. We determine how far into the phase transition theoretical estimates of the defect density based on the Gaussian approximation yield a reliable prediction for the actual density. We also characterize quantitatively some aspects of the out of equilibrium phase transition.