Quantum Walks of SU(2)_k Anyons on a Ladder

We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information of the coin and nonlocal fusion degrees of freedom on every second time step, such that the entanglement between the position states and the exponentially growing auxiliary degrees of freedom is lost. The computational complexity of numerical calculations reduces drastically from the fully coherent anyonic quantum walk model, allowing for relatively long simulations for anyons which are spin-1/2 irreps of SU(2)_k Chern-Simons theory. We find that for Abelian anyons, the walk retains the ballistic spreading velocity just like particles with trivial braiding statistics. For non-Abelian anyons, the numerical results indicate that the spreading velocity is linearly dependent on the number of time steps. By approximating the Kraus generators of the time evolution map by circulant matrices, it is shown that the spatial probability distribution for the k=2 walk, corresponding to Ising model anyons, is equal to the classical unbiased random walk distribution.Comment: 12 pages, 4 figure

Braiding Interactions in Anyonic Quantum Walks

The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the effects of braiding statistics in anyonic quantum walks in quasi-one dimensional ladder geometries. For anyons which correspond to spin-1/2 irreps of the quantum groups $SU(2)_k$, the non-Abelian species $(1<k<\infty)$ gives rise to entanglement between the walker and topological degrees of freedom which is quantified by quantum link invariants over the trajectories of the walk. The decoherence is strong enough to reduce the walk on the infinite ladder to classical like behaviour. We also present numerical results on mixing times of $SU(2)_2$ or Ising model anyon walks on cyclic graphs. Finally, the possible experimental simulation of the anyonic quantum walk in Fractional Quantum Hall systems is discussed.Comment: 13 pages, submitted to Proceedings of the 2nd International Conference on Theoretical Physics (ICTP 2012

Wave-Based Subsurface Guide Star

Astronomical or optical guide stars are either natural or artificial point sources located above the Earth's atmosphere. When imaged from ground-based telescopes, they are distorted by atmospheric effects. Knowing the guide star is a point source, the atmospheric distortions may be estimated and, deconvolved or mitigated in subsequent imagery. Extending the guide star concept to wave-based measurement systems to include acoustic, seismo-acoustic, ultrasonic, and radar, a strong artificial scatterer (either acoustic or electromagnetic) may be buried or inserted, or a pre-existing or natural sub-surface point scatterer may be identified, imaged, and used as a guide star to determine properties of the sub-surface volume. That is, a data collection is performed on the guide star and the sub-surface environment reconstructed or imaged using an optimizer assuming the guide star is a point scatterer. The optimization parameters are the transceiver height and bulk sub-surface background refractive index. Once identified, the refractive index may be used in subsequent reconstructions of sub-surface measurements. The wave-base guide star description presented in this document is for a multimonostatic ground penetrating radar (GPR) but is applicable to acoustic, seismo-acoustic, and ultrasonic measurement systems operating in multimonostatic, multistatic, multibistatic, etc., modes

Data-efficient Neuroevolution with Kernel-Based Surrogate Models

Surrogate-assistance approaches have long been used in computationally expensive domains to improve the data-efficiency of optimization algorithms. Neuroevolution, however, has so far resisted the application of these techniques because it requires the surrogate model to make fitness predictions based on variable topologies, instead of a vector of parameters. Our main insight is that we can sidestep this problem by using kernel-based surrogate models, which require only the definition of a distance measure between individuals. Our second insight is that the well-established Neuroevolution of Augmenting Topologies (NEAT) algorithm provides a computationally efficient distance measure between dissimilar networks in the form of "compatibility distance", initially designed to maintain topological diversity. Combining these two ideas, we introduce a surrogate-assisted neuroevolution algorithm that combines NEAT and a surrogate model built using a compatibility distance kernel. We demonstrate the data-efficiency of this new algorithm on the low dimensional cart-pole swing-up problem, as well as the higher dimensional half-cheetah running task. In both tasks the surrogate-assisted variant achieves the same or better results with several times fewer function evaluations as the original NEAT.Comment: In GECCO 201

Abundances of Disk Planetary Nebulae in M31 and the Radial Oxygen Gradient

We have obtained spectra of 16 planetary nebulae in the disk of M31 and determined the abundances of He, N, O, Ne, S and Ar. Here we present the median abundances and compare them with previous M31 PN disk measurements and with PNe in the Milky Way. We also derive the radial oxygen gradient in M31, which is shallower than that in the Milky Way, even accounting for M31's larger disk scale length.Comment: 2 pages, 1 figure, 1 table, to appear in the proceedings of IAU Symposium No. 283, Planetary Nebulae: An Eye to the Futur

Statistical dynamics of a non-Abelian anyonic quantum walk

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.Comment: 7 pages, 5 figure