Subleading Soft Factor for String Disk Amplitudes

We investigate the behavior of superstring disk scattering amplitudes in the presence of a soft external momentum at finite string tension. We prove that there are no $\alpha'$-corrections to the field theory form of the subleading soft factor $S^{(1)}$. At the end of this work, we also comment on the possibility to find the corresponding subleading soft factors in closed string theory using our result and the KLT relations.Comment: 15 pages, v2: minor changes, new references, version accepted by JHE

Persistent current induced by magnetic impurities

We calculate the average persistent current in a normal conducting, mesoscopic ring in the diffusive regime. In the presence of magnetic impurities, a contribution to the persistent current is identified, which is related to fluctuations in the electron spin density. Assuming a spin-flip scattering rate which is comparable to the Thouless energy E_c and low temperature, this new contribution to the persistent current is of the order $I\sim E_c^2/(kT\phi_0)$, which is considerably larger than the persistent current induced by the electron-electron interaction.Comment: 19 pages, 7 figures, accepted by Z. Phys.

Persistent Currents versus Phase Breaking in Mesoscopic Metallic Samples

Persistent currents in mesoscopic normal metal rings represent, even a decade after their first experimental observation, a challenge to both, theorists and experimentalists. After giving a brief review of the existing -- experimental and theoretical -- results, we concentrate on the (proposed) relationship of the size of the persistent current to the phase breaking rate. In particular, we consider effects induced by noise, scattering at two-level systems, and magnetic impurities.Comment: accepted by JLT

Quantum Coherence in an Exactly Solvable One-dimensional Model with Defects

Using the Quantum Inverse Scattering Method we construct an integrable Heisenberg-XXZ-model, or equivalently a model for spinless fermions with nearest-neighbour interaction, with defects. Each defect involves three sites with a fine tuning between nearest-neighbour and next-nearest-neighbour terms. We investigate the finite size corrections to the ground state energy and its dependence on an external flux as a function of a parameter $\nu$, characterizing the strength of the defects. For intermediate values of $\nu$, both quantities become very small, although the ground state wavefunction remains extended.Comment: accepted by Europhys. Lett., latex, 7 pages. A postscript version including the figures is available at: http://www.physik.uni-augsburg.de/theo2/Publications

Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills

Recent developments in the determination of the planar S-matrix of N=4 Super Yang-Mills are closely related to its Yangian symmetry. Here we provide evidence for a yet unobserved additional symmetry: the Yangian level-one helicity operator.Comment: 8 pages, v2: minor change

Soft Black Hole Absorption Rates as Conservation Laws

The absorption rate of low-energy, or soft, electromagnetic radiation by spherically symmetric black holes in arbitrary dimensions is shown to be fixed by conservation of energy and large gauge transformations. We interpret this result as the explicit realization of the Hawking-Perry-Strominger Ward identity for large gauge transformations in the background of a non-evaporating black hole. Along the way we rederive and extend previous analytic results regarding the absorption rate for the minimal scalar and the photon.Comment: 20 Pages, 1 figur

Density functional theory for a model quantum dot: Beyond the local-density approximation

We study both static and transport properties of model quantum dots, employing density functional theory as well as (numerically) exact methods. For the lattice model under consideration the accuracy of the local-density approximation generally is poor. For weak interaction, however, accurate results are achieved within the optimized effective potential method, while for intermediate interaction strengths a method combining the exact diagonalization of small clusters with density functional theory is very successful. Results obtained from the latter approach yield very good agreement with density matrix renormalization group studies, where the full Hamiltonian consisting of the dot and the attached leads has to be diagonalized. Furthermore we address the question whether static density functional theory is able to predict the exact linear conductance through the dot correctly - with, in general, negative answer.Comment: 8 page

Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous dependence of weak solutions on data in the deterministic case, we develop a definition of random entropy solution. We establish existence, uniqueness, measurability and integrability results for these random entropy solutions, generalizing \cite{Mishr478,MishSch10a} to possibly degenerate hyperbolic-parabolic problems with random data. We next address the numerical approximation of random entropy solutions, specifically the approximation of the deterministic first and second order statistics. To this end, we consider explicit and implicit time discretization and Finite Difference methods in space, and single as well as Multi-Level Monte-Carlo methods to sample the statistics. We establish convergence rate estimates with respect to the discretization parameters, as well as with respect to the overall work, indicating substantial gains in efficiency are afforded under realistic regularity assumptions by the use of the Multi-Level Monte-Carlo method. Numerical experiments are presented which confirm the theoretical convergence estimates.Comment: 24 Page