Cooperative scattering of scalar waves by optimized configurations of point scatterers

We investigate multiple scattering of scalar waves by an ensemble of $N$ resonant point scatterers in three dimensions. For up to $N = 21$ scatterers, we numerically optimize the positions of the individual scatterers, such as to maximize the total scattering cross section for an incoming plane wave, on the one hand, and to minimize the decay rate associated to a long-lived scattering resonance, on the other hand. In both cases, the optimimum is achieved by configurations where all scatterers are placed on a line parallel to the direction of the incoming plane wave. The associated maximal scattering cross section increases quadratically with the number of scatterers for large $N$, whereas the minimal decay rate -- which is realized by configurations that are not the same as those that maximize the scattering cross section -- decreases exponentially as a function of $N$. Finally, we also analyze the stability of our optimized configurations with respect to small random displacements of the scatterers. These results demonstrate that optimized configurations of scatterers bear a considerable potential for applications such as quantum memories or mirrors consisting of only a few atoms.Comment: 21 pages, 9 figure

Individual scatterers as microscopic origin of equilibration between spin- polarized edge channels in the quantum Hall regime

The equilibration length between spin-polarized edge states in the Quantum Hall regime is measured as a function of a gate voltage applied to an electrode on top of the edge channels. Reproducible fluctuations in the coupling are observed and interpreted as a mesoscopic fingerprint of single spin-flip scatterers which are turned on and off. A model to analyze macroscopic edge state coupling in terms of individual scatterers is developed, and characteristic values for these scatterers in our samples are extracted. For all samples investigated, the distance between spin-flip scatterers lies between the Drude and the quantum scattering length.Comment: 4 pages, 2 figure

Magneto-electric point scattering theory for metamaterial scatterers

We present a new, fully analytical point scattering model which can be applied to arbitrary anisotropic magneto-electric dipole scatterers, including split ring resonators (SRRs), chiral and anisotropic plasmonic scatterers. We have taken proper account of reciprocity and radiation damping for electric and magnetic scatterers with any general polarizability tensor. Specifically, we show how reciprocity and energy balance puts constraints on the electrodynamic responses arbitrary scatterers can have to light. Our theory sheds new light on the magnitude of cross sections for scattering and extinction, and for instance on the emergence of structural chirality in the optical response of geometrically non-chiral scatterers like SRRs. We apply the model to SRRs and discuss how to extract individual components of the polarizability matrix and extinction cross sections. Finally, we show that our model describes well the extinction of stereo-dimers of split rings, while providing new insights in the underlying coupling mechanisms.Comment: 12 pages, 3 figure

Disordered Bose Einstein Condensates with Interaction

We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wave function of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers or strong interactions the wave function extends over the whole interval. High density of scatterers and weak interaction, on the other hand, leads to localization of the wave function in a fragmented subset of the interval.Comment: Contribution to the proceedings of ICMP12, Aalborg, Denmark, August 6-11, 2012. Minor amendments; subsection 4.4 on the thermodynamic limit adde

Non‐Rayleigh Statistics of Ultrasonic Backscattered Echo from Tissues

The envelope of the backscattered signal from tissues can exhibit non‐Rayleigh statistics if the number density of scatterers is small or if the variations in the scattering cross sections are random. The K distribution which has been used extensively in radar, is introduced to model this non‐Rayleigh behavior. The generalized K distribution is extremely useful since it encompasses a wide range of distributions such as Rayleigh, Lognormal, and Rician. Computer simulations were conducted using a simple one‐dimensional discrete scatteringmodel to investigate the properties of the echo envelope. In addition to cases of low number densities, significant departures from Rayleigh statistics were seen as the scattering cross sections of the scatterers become random. The validity of this model was also tested using data from tissue mimicking phantoms. Results indicate that the density function of the envelope can be modeled by the K distribution and the parameters of the K distribution can provide information on the nature of the scattering region in terms of the number density of the scatterers as well as the scattering cross sections of the scatterers in the range cell. [Work was supported by NSF Grant No. BCS‐9207385.

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Universal bounds on the selfaveraging of random diffraction measures

We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers. The rate is given in terms of a universal function that depends on the point set only through the minimal distance between points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a central limit theorem