High-Altitude Particle Acceleration and Radiation in Pulsar Slot Gaps

We explore the pulsar slot gap electrodynamics up to very high altitudes, where for most relatively rapidly rotating pulsars both the standard small-angle approximation and the assumption that the magnetic field lines are ideal stream lines break down. We address the importance of the electrodynamic conditions at the slot gap boundaries and the occurrence of a steady-state drift of charged particles across the slot gap field lines at very high altitudes. These boundary conditions and the deviation of particle trajectories from stream lines determine the asymptotic behavior of the scalar potential at all radii from the polar cap to near the light cylinder. As a result, we demonstrate that the steady-state accelerating electric field must approach a small and constant value at high altitude above the polar cap. This parallel electric field is capable of maintaining electrons moving with high Lorentz factors (a few times 10^7) and emitting curvature gamma-ray photons up to nearly the light cylinder. By numerical simulations, we show that primary electrons accelerating from the polar cap surface to high altitude in the slot gap along the outer edge of the open field region will form caustic emission patterns on the trailing dipole field lines. Acceleration and emission in such an extended slot gap may form the physical basis of a model that can successfully reproduce some pulsar high-energy light curves.Comment: 26 pages, 2 figures, to appear in the Astrophysical Journal, May 10, 200

Functional control of network dynamics using designed Laplacian spectra

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. Spectral graph theory has traditionally prioritized unweighted networks. Here, we introduce a complementary framework, providing a mathematically rigorous weighted graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer spectra can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces chimera states in Kuramoto-type oscillator networks, completely suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. Our approach can be generalized to design continuous band gaps through periodic extensions of finite networks.Comment: 9 pages, 5 figure

Phase Transitions in the Pooled Data Problem

In this paper, we study the pooled data problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we identify an exact asymptotic threshold on the required number of tests with optimal decoding, and prove a phase transition between complete success and complete failure. In addition, we present a novel noisy variation of the problem, and provide an information-theoretic framework for characterizing the required number of tests for general random noise models. Our results reveal that noise can make the problem considerably more difficult, with strict increases in the scaling laws even at low noise levels. Finally, we demonstrate similar behavior in an approximate recovery setting, where a given number of errors is allowed in the decoded labels.Comment: Accepted to NIPS 201

Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport

We show that it is possible to have a topological phase in two-dimensional quasicrystals without any magnetic field applied, but instead introducing an artificial gauge field via dynamic modulation. This topological quasicrystal exhibits scatter-free unidirectional edge states that are extended along the system's perimeter, contrary to the states of an ordinary quasicrystal system, which are characterized by power-law decay. We find that the spectrum of this Floquet topological quasicrystal exhibits a rich fractal (self-similar) structure of topological "minigaps," manifesting an entirely new phenomenon: fractal topological systems. These topological minigaps form only when the system size is sufficiently large because their gapless edge states penetrate deep into the bulk. Hence, the topological structure emerges as a function of the system size, contrary to periodic systems where the topological phase can be completely characterized by the unit cell. We demonstrate the existence of this topological phase both by using a topological index (Bott index) and by studying the unidirectional transport of the gapless edge states and its robustness in the presence of defects. Our specific model is a Penrose lattice of helical optical waveguides - a photonic Floquet quasicrystal; however, we expect this new topological quasicrystal phase to be universal.Comment: 12 pages, 8 figure