Emergence of a confined state in a weakly bent wire

In this paper we use a simple straightforward technique to investigate the emergence of a bound state in a weakly bent wire. We show that the bend behaves like an infinitely shallow potential well, and in the limit of small bending angle and low energy the bend can be presented by a simple 1D delta function potential.Comment: 4 pages, 3 Postscript figures (uses Revtex); added references and rewritte

Scatterer that leaves "footprints" but no "fingerprints"

We calculate the exact transmission coefficient of a quantum wire in the presence of a single point defect at the wire's cut-off frequencies. We show that while the conductance pattern (i.e., the scattering) is strongly affected by the presence of the defect, the pattern is totally independent of the defect's characteristics (i.e., the defect that caused the scattering cannot be identified from that pattern).Comment: 4 pages, 3 figure

Existence and representation of diophantine and mixed diophantine solutions to linear equations and inequalities

AbstractIn this paper we present necessary and sufficient conditions for the existence of solutions to more general systems of linear diophantine equations and inequalities than have previously been considered. We do this in terms of variants and extensions of generalized inverse concepts which also permit us to give representation of the set of all solutions to the systems. The results are further extended to mixed integer systems

Constraints on Lorentz Invariance Violation from Fermi-Large Area Telescope Observations of Gamma-Ray Bursts

We analyze the MeV/GeV emission from four bright Gamma-Ray Bursts (GRBs) observed by the Fermi-Large Area Telescope to produce robust, stringent constraints on a dependence of the speed of light in vacuo on the photon energy (vacuum dispersion), a form of Lorentz invariance violation (LIV) allowed by some Quantum Gravity (QG) theories. First, we use three different and complementary techniques to constrain the total degree of dispersion observed in the data. Additionally, using a maximally conservative set of assumptions on possible source-intrinsic spectral-evolution effects, we constrain any vacuum dispersion solely attributed to LIV. We then derive limits on the "QG energy scale" (the energy scale that LIV-inducing QG effects become important, E_QG) and the coefficients of the Standard Model Extension. For the subluminal case (where high energy photons propagate more slowly than lower energy photons) and without taking into account any source-intrinsic dispersion, our most stringent limits (at 95% CL) are obtained from GRB090510 and are E_{QG,1}>7.6 times the Planck energy (E_Pl) and E_{QG,2}>1.3 x 10^11 GeV for linear and quadratic leading order LIV-induced vacuum dispersion, respectively. These limits improve the latest constraints by Fermi and H.E.S.S. by a factor of ~2. Our results disfavor any class of models requiring E_{QG,1} \lesssim E_Pl.Comment: Accepted for publication by Physical Review

Anomalous coupling in radiation mediated shocks}

We summarize recent attempts to unravel the role of plasma kinetic effects in radiation mediated shocks. Such shocks form in all strong stellar explosions and are responsible for the early electromagnetic emission released from these events. A key issue that has been overlooked in all previous works is the nature of the coupling between the charged leptons, that mediate the radiation force, and the ions, which are the dominant carriers of the shock energy. Our preliminary investigation indicates that in the case of relativistic shocks, as well as Newtonian shocks in multi-ion plasma, this coupling is driven by either, transverse magnetic fields of a sufficiently magnetized upstream medium, or plasma micro-turbulence if strong enough magnetic fields are absent. We discuss the implications for the shock breakout signal, as well as abundance evolution and kilonova emission in binary neutron star mergers.Comment: 8 pages, 2 figures, to appear in Journal of Plasma Physic

VLBI Observations of SN 2008D

We report on two epochs of very-long-baseline interferometry (VLBI) observations of the Type Ib/c supernova SN 2008D, which was associated with the X-ray outburst XRF 080109. At our first epoch, at t = 30 days after the explosion, we observed at 22 and 8.4 GHz, and at our second, at t = 133 days, at 8.4 and 5.0 GHz. The VLBI observations allow us to accurately measure the source's size and position at each epoch, and thus constrain its expansion velocity and proper motion. We find the source at best marginally resolved at both epochs, allowing us to place a 3sigma upper limit of ~0.75c on the expansion velocity of a circular source. For an elongated source, our measurements are compatible with mildly relativistic expansion. However, our 3sigma upper limit on the proper motion is 4 micro-arcsec/day, corresponding to an apparent velocity of <0.6c, and is consistent with a stationary flux centroid. This limit rules out a relativistic jet such as an gamma-ray burst jet away from the line of sight, which would be expected to show apparent proper motion of >c. Taken together, our measurements argue against the presence of any long-lived relativistic outflow in SN 2008D. On the other hand, our measurements are consistent with the nonrelativistic expansion velocities of <30,000 km/s and small proper motions (<500 km/s) seen in typical supernovae.Comment: Accepted for publication in the Astrophysical Journal Letter

The origin of the late rebrightening in GRB 080503

GRB 080503, detected by Swift, belongs to the class of bursts whose prompt phase consists of an initial short spike followed by a longer soft tail. It did not show any transition to a regular afterglow at the end of the prompt emission but exhibited a surprising rebrightening after one day. We aim to explain this rebrightening with two different scenarios - refreshed shocks or a density clump in the circumburst medium - and two models for the origin of the afterglow, the standard one where it comes from the forward shock, and an alternative one where it results from a long-lived reverse shock. We computed afterglow light curves either using a single-zone approximation for the shocked region or a detailed multizone method that more accurately accounts for the compression of the material. We find that in several of the considered cases the detailed model must be used to obtain a reliable description of the shock dynamics. The density clump scenario is not favored. We confirm previous results that the presence of the clump has little effect on the forward shock emission, except if the microphysics parameters evolve when the shock enters the clump. Moreover, we find that the rebrightening from the reverse shock is also too weak when it is calculated with the multi-zone method. On the other hand, in the refreshed-shock scenario both the forward and reverse shock models provide satisfactory fits of the data under some additional conditions on the distribution of the Lorentz factor in the ejecta and the beaming angle of the relativistic outflow.Comment: 8 pages, 4 figures, accepted for publication in A&

Retinal metric: a stimulus distance measure derived from population neural responses

The ability of the organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded activity of 100 neurons in the salamander retina. In contrast to previously used measures of stimulus similarity, this "neural metric" tells us how distinguishable a pair of stimulus clips is to the retina, given the noise in the neural population response. We show that the retinal distance strongly deviates from Euclidean, or any static metric, yet has a simple structure: we identify the stimulus features that the neural population is jointly sensitive to, and show the SVM-like kernel function relating the stimulus and neural response spaces. We show that the non-Euclidean nature of the retinal distance has important consequences for neural decoding.Comment: 5 pages, 4 figures, to appear in Phys Rev Let

Statistical Properties of Gamma-Ray Burst Polarization

The emission mechanism and the origin and structure of magnetic fields in gamma-ray burst (GRB) jets are among the most important open questions concerning the nature of the central engine of GRBs. In spite of extensive observational efforts, these questions remain to be answered and are difficult or even impossible to infer with the spectral and lightcurve information currently collected. Polarization measurements will lead to unambiguous answers to several of these questions. Recent developments in X-ray and gamma-ray polarimetry techniques have demonstrated a significant increase in sensitivity enabling several new mission concepts, e.g. POET (Polarimeters for Energetic Transients), providing wide field of view and broadband polarimetry measurements. If launched, missions of this kind would finally provide definitive measurements of GRB polarizations. We perform Monte Carlo simulations to derive the distribution of GRB polarizations in three emission models; the synchrotron model with a globally ordered magnetic field (SO model), the synchrotron model with a locally random magnetic field (SR model), and the Compton drag model (CD model). The results show that POET, or other polarimeters with similar capabilities, can constrain the GRB emission models by using the statistical properties of GRB polarizations. In particular, the ratio of the number of GRBs for which the polarization degrees can be measured to the number of GRBs that are detected (N_m/N_d) and the distributions of the polarization degrees (Pi) can be used as the criteria. If N_m/N_d > 30% and Pi is clustered between 0.2 and 0.7, the SO model will be favored. If instead N_m/N_d < 15%, then the SR or CD model will be favored. If several events with Pi > 0.8 are observed, then the CD model will be favored.Comment: Replaced with accepted version in ApJ. A few minor changes done. References adde