Noise from metallic surfaces -- effects of charge diffusion

Non-local electrodynamic models are developed for describing metallic surfaces for a diffusive metal. The electric field noise at a distance z_0 from the surface is evaluated and compared with data from ion chips that show anomalous heating with a noise power decaying as z_0^{-4}. We find that high surface diffusion can account for the latter result.Comment: 16 pages, 2 figures. Revised version focusing on charge diffusing and anomalous heatin

Interference in presence of Dissipation

We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces a 2 loop RG for the Caldeira-Legget environment. In the latter case the Aharonov-Bohm (AB) oscillation amplitude is exponential in -R^2 where R is the ring's radius. For either a charge or an electric dipole coupled to a dirty metal we find that the metal induces dissipation, however the AB amplitude is ~ R^{-2} for large R, as for free particles. Cold atoms with a large electric dipole may show a crossover between these two behaviors.Comment: 5 pages, added motivations and reference

Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Mediation and Social Justice: Risks and Opportunities

Published in cooperation with the American Bar Association Section of Dispute Resolutio

Competition in a system of Brownian particles: Encouraging achievers

We introduce and study analytically and numerically a simple model of inter-agent competition, where underachievement is strongly discouraged. We consider $N\gg 1$ particles performing independent Brownian motions on the line. Two particles are selected at random and at random times, and the particle closest to the origin is reset to it. We show that, in the limit of $N\to \infty$, the dynamics of the coarse-grained particle density field can be described by a nonlocal hydrodynamic theory which was encountered in a study of the spatial extent of epidemics in a critical regime. The hydrodynamic theory predicts relaxation of the system toward a stationary density profile of the "swarm" of particles, which exhibits a power-law decay at large distances. An interesting feature of this relaxation is a non-stationary "halo" around the stationary solution, which continues to expand in a self-similar manner. The expansion is ultimately arrested by finite-$N$ effects at a distance of order $\sqrt{N}$ from the origin, which gives an estimate of the average radius of the swarm. The hydrodynamic theory does not capture the behavior of the particle farthest from the origin -- the current leader. We suggest a simple scenario for typical fluctuations of the leader's distance from the origin and show that the mean distance continues to grow indefinitely as $\sqrt{t}$. Finally, we extend the inter-agent competition from $n=2$ to an arbitrary number $n$ of competing Brownian particles ($n\ll N$). Our analytical predictions are supported by Monte-Carlo simulations.Comment: 9 pages, 10 figure