Thin Ohmic or superconducting strip with an applied ac electric current

The complex impedance, currents, and electric and magnetic fields are calculated as functions of resistivity and frequency or London depth for a long thin strip with applied ac current. Both Ohmic and superconducting strips are considered. While the inductance per unit length of the strip depends on the strip length logarithmically, the sheet current, magnetic field, resistance, and magnetic susceptibility are independent of this length. It is found that the enhancement of resistance by the skin effect in thin Ohmic strips is much weaker (logarithmic) than in thick wires.Comment: 4 pages, 3 figures, for Phys. Rev.

T>0 ensemble state density functional theory revisited

A logical foundation of equilibrium state density functional theory in a Kohn-Sham type formulation is presented on the basis of Mermin's treatment of the grand canonical state. it is simpler and more satisfactory compared to the usual derivation of ground state theory, and free of remaining open points of the latter. It may in particular be relevant with respect to cases of spontaneous symmetry breaking like non-collinear magnetism and orbital order.Comment: 7 pages, no figure

Rapid computation of far-field statistics for random obstacle scattering

In this article, we consider the numerical approximation of far-field statistics for acoustic scattering problems in the case of random obstacles. In particular, we consider the computation of the expected far-field pattern and the expected scattered wave away from the scatterer as well as the computation of the corresponding variances. To that end, we introduce an artificial interface, which almost surely contains all realizations of the random scatterer. At this interface, we directly approximate the second order statistics, i.e., the expectation and the variance, of the Cauchy data by means of boundary integral equations. From these quantities, we are able to rapidly evaluate statistics of the scattered wave everywhere in the exterior domain, including the expectation and the variance of the far-field. By employing a low-rank approximation of the Cauchy data's two-point correlation function, we drastically reduce the cost of the computation of the scattered wave's variance. Numerical results are provided in order to demonstrate the feasibility of the proposed approach

Dynamical scaling in Ising and vector spin glasses

We have studied numerically the dynamics of spin glasses with Ising and XY symmetry (gauge glass) in space dimensions 2, 3, and 4. The nonequilibrium spin-glass susceptibility and the nonequilibrium energy per spin of samples of large size L_b are measured as a function of anneal time t_w after a quench to temperatures T. The two observables are compared to the equilibrium spin-glass susceptibility and the equilibrium energy, respectively, measured as functions of temperature T and system size L for a range of system sizes. For any time and temperature a nonequilibrium time-dependent length scale L*(t_w,T) can be defined by comparing equilibrium and nonequilibrium quantities. Our analysis shows that for all systems studied, an "effective dynamical critical exponent" parametrization L*(t_w,T) = A(T) t^(1/z(T)) fits the data well at each temperature within the whole temperature range studied, which extends from well above the critical temperature to near T = 0 for dimension 2, or to well below the critical temperature for the other space dimensions studied. In addition, the data suggest that the dynamical critical exponent z varies smoothly when crossing the transition temperature.Comment: 14 pages, 13 figures, 9 table

Cohomology of Line Bundles: A Computational Algorithm

We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds of interest are complete intersections of hypersurfaces in toric varieties supporting additional vector bundles.Comment: 11 pages, 1 figure, 2 tables; v2: typos and references corrected; v3: proof-related statements updated, cohomCalg implementation available at http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg