On the Number of Solutions of Exponential Congruences

For a prime $p$ and an integer $a \in \Z$ we obtain nontrivial upper bounds on the number of solutions to the congruence $x^x \equiv a \pmod p$, $1 \le x \le p-1$. We use these estimates to estimate the number of solutions to the congruence $x^x \equiv y^y \pmod p$, $1 \le x,y \le p-1$, which is of cryptographic relevance

Dynamical r-matrices and the chiral WZNW phase space

The dynamical generalization of the classical Yang-Baxter equation that governs the possible Poisson structures on the space of chiral WZNW fields with generic monodromy is reviewed. It is explained that for particular choices of the chiral WZNW Poisson brackets this equation reduces to the CDYB equation recently studied by Etingof--Varchenko and others. Interesting dynamical r-matrices are obtained for generic monodromy as well as by imposing Dirac constraints on the monodromy.Comment: Talk given at XXIII International Colloquium on Group Theoretical Methods in Physics, July 31 - August 5, 2000, Dubna, Russia. LaTeX, 9 page

Photocount statistics in mesoscopic optics

We report the first observation of the impact of mesoscopic fluctuations on the photocount statistics of coherent light scattered in a random medium. Poisson photocount distribution of the incident light widens and gains additional asymmetry upon transmission through a suspension of small dielectric spheres. The effect is only appreciable when the average number of photocounts becomes comparable or larger than the effective dimensionless conductance g of the sample.Comment: Thoroughly revised text and figures, new data set, new figure adde

A Two-loop Test of Buscher's T-duality I

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.Comment: 28 pp, Latex, references adde

Dusty Cometary Globules in W5

We report the discovery of four dusty cometary tails around low mass stars in two young clusters belonging to the W5 star forming region. Fits to the observed emission profiles from 24 micron observations with the Spitzer Space Telescope give tail lifetimes < 30 Myr, but more likely < 5 Myr. This result suggests that the cometary phase is a short lived phenomenon, occurring after photoevaporation by a nearby O star has removed gas from the outer disk of a young low mass star (see also Balog et al. 2006; Balog et al. 2008).Comment: 11 pages, 3 figures. Accepted for publication to ApJ Letter

The two dimensional XY model at the transition temperature: A high precision Monte Carlo study

We study the classical XY (plane rotator) model at the Kosterlitz-Thouless phase transition. We simulate the model using the single cluster algorithm on square lattices of a linear size up to L=2048.We derive the finite size behaviour of the second moment correlation length over the lattice size xi_{2nd}/L at the transition temperature. This new prediction and the analogous one for the helicity modulus are confronted with our Monte Carlo data. This way beta_{KT}=1.1199 is confirmed as inverse transition temperature. Finally we address the puzzle of logarithmic corrections of the magnetic susceptibility chi at the transition temperature.Comment: Monte Carlo results for xi/L in table 1 and 2 corrected. Due to a programming error,these numbers were wrong by about a factor 1+1/L^2. Correspondingly the fits with L_min=64 and 128 given in table 5 and 6 are changed by little.The central results of the paper are not affected. Wrong sign in eq.(52) corrected. Appendix extende

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.Comment: 69 pages, Late

Electron-phonon coupling in potassium-doped graphene: Angle-resolved photoemission spectroscopy

The electron-phonon coupling in potassium-doped graphene on Ir(111) is studied via the renormalization of the pi* band near the Fermi level, using angle-resolved photoemission spectroscopy. The renormalization is found to be fairly weak and almost isotropic, with a mass enhancement parameter of lambda= 0.28(6) for both the K-M and the K-G direction. These results are found to agree well with recent first principles calculations.Comment: 5 pages, 3 figure

Nonlinear integral equations for finite volume excited state energies of the O(3) and O(4) nonlinear sigma-models

We propose nonlinear integral equations for the finite volume one-particle energies in the O(3) and O(4) nonlinear sigma-models. The equations are written in terms of a finite number of components and are therefore easier to solve numerically than the infinite component excited state TBA equations proposed earlier. Results of numerical calculations based on the nonlinear integral equations and the excited state TBA equations agree within numerical precision.Comment: numerical results adde