Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schr\"{o}dinger equations

Weak interactions of solitary waves in the generalized nonlinear Schr\"{o}dinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions and phases of interacting solitary waves. These dynamical equations contain a single parameter, which accounts for the different forms of nonlinearity. When this parameter is zero, these dynamical equations are integrable, and the exact analytical solutions are derived. When this parameter is non-zero, the dynamical equations exhibit fractal structures which match those in the original wave equations both qualitatively and quantitatively. Thus the universal nature of fractal structures in the weak interaction of solitary waves is analytically established. The origin of these fractal structures is also explored. It is shown that these structures bifurcate from the initial conditions where the solutions of the integrable dynamical equations develop finite-time singularities. Based on this observation, an analytical criterion for the existence and locations of fractal structures is obtained. Lastly, these analytical results are applied to the generalized nonlinear Schr\"{o}dinger equations with various nonlinearities such as the saturable nonlinearity, and predictions on their weak interactions of solitary waves are made.Comment: 22pages, 15 figure

The connection between the radio jet and the gamma-ray emission in the radio galaxy 3C 120

We present the analysis of the radio jet evolution of the radio galaxy 3C 120 during a period of prolonged gamma-ray activity detected by the Fermi satellite between December 2012 and October 2014. We find a clear connection between the gamma-ray and radio emission, such that every period of gamma-ray activity is accompanied by the flaring of the mm-VLBI core and subsequent ejection of a new superluminal component. However, not all ejections of components are associated with gamma-ray events detectable by Fermi. Clear gamma-ray detections are obtained only when components are moving in a direction closer to our line of sight.This suggests that the observed gamma-ray emission depends not only on the interaction of moving components with the mm-VLBI core, but also on their orientation with respect to the observer. Timing of the gamma-ray detections and ejection of superluminal components locate the gamma-ray production to within almost 0.13 pc from the mm-VLBI core, which was previously estimated to lie about 0.24 pc from the central black hole. This corresponds to about twice the estimated extension of the broad line region, limiting the external photon field and therefore suggesting synchrotron self Compton as the most probable mechanism for the production of the gamma-ray emission. Alternatively, the interaction of components with the jet sheath can provide the necessary photon field to produced the observed gamma-rays by Compton scattering.Comment: Already accepted for publication in The Astrophysical Journa

Induced ferroelectric phases in TbMn_2O_5

The magnetostructural transitions and magnetoelectric effects reported in TbMn2O5 are described theoretically and shown to correspond to two essentially different mechanisms for the induced ferroelectricity. The incommensurate and commensurate phases observed between 38 and 24 K exhibit a hybrid pseudoproper ferroelectric nature resulting from an effective bilinear coupling of the polarization with the antiferromagnetic order parameter. This explains the high sensitivity of the dielectric properties of the material under applied magnetic field. Below 24 K the incommensurate phase shows a standard improper ferroelectric character induced by the coupling of two distinct magnetic order parameters. The complex dielectric behavior observed in the material reflects the crossover from one to the other transition regime. The temperature dependences of the pertinent physical quantities are worked out, and previous theoretical models are discussed

Kubo formula for Floquet states and photoconductivity oscillations in a 2D electron gas

The recent discovery of the microwave induced vanishing resistance states in a two dimensional electron system (2DES) is an unexpected and surprising phenomena. In these experiments the magnetoresistance of a high mobility 2DES under the influence of microwave radiation of frequency $\omega$ at moderate values of the magnetic field, exhibits strong oscillations with zero-resistance states (ZRS) governed by the ratio $\omega /\omega_c$, where $\omega_c$ is the cyclotron frequency. In this work we present a model for the photoconductivity of a two dimensional electron system (2DES) subjected to a magnetic field. The model includes the microwave and Landau contributions in a non-perturbative exact way, impurity scattering effects are treated perturbatively. In our model, the Landau-Floquet states act coherently with respect to the oscillating field of the impurities, that in turn induces transitions between these levels. Based on this formalism, we provide a Kubo-like formula that takes into account the oscillatory Floquet structure of the problem. We study the effects of both short-range and long-range disorder on the photoconductivity. Our calculation yields a magnetoresistance oscillatory behavior with the correct period and phase. It is found that, in agreement with experiment, negative dissipation can only be induced in very high mobility samples. We analyze the dependence of the results on the microwave power and polarization. For high-intensity radiation multi-photon processes take place predicting new negative-resistance states centered at $\omega / \omega_c=1/2$, and $\omega / \omega_c= 3/2$.Comment: Final version, accepted for publication in Phys. Rev.

Quasisymmetric graphs and Zygmund functions

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class $\Lambda_*$. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.Comment: 21 pages, no figure

Disentanglement of the electronic and lattice parts of the order parameter in a 1D Charge Density Wave system probed by femtosecond spectroscopy

We report on the high resolution studies of the temperature (T) dependence of the q=0 phonon spectrum in the quasi one-dimensional charge density wave (CDW) compound K0.3MoO3 utilizing time-resolved optical spectroscopy. Numerous modes that appear below Tc show pronounced T-dependences of their amplitudes, frequencies and dampings. Utilizing the time-dependent Ginzburg-Landau theory we show that these modes result from linear coupling of the electronic part of the order parameter to the 2kF phonons, while the (electronic) CDW amplitude mode is overdamped.Comment: 4 pages, 3 figures + supplementary material, accepted for publication in Phys. Rev. Let

RadioAstron space VLBI imaging of polarized radio emission in the high-redshift quasar 0642+449 at 1.6 GHz

Polarization of radio emission in extragalactic jets at a sub-milliarcsecond angular resolution holds important clues for understanding the structure of the magnetic field in the inner regions of the jets and in close vicinity of the supermassive black holes in the centers of active galaxies. Space VLBI observations provide a unique tool for polarimetric imaging at a sub-milliarcsecond angular resolution and studying the properties of magnetic field in active galactic nuclei on scales of less than 10^4 gravitational radii. A space VLBI observation of high-redshift quasar TXS 0642+449 (OH 471), made at a wavelength of 18 cm (frequency of 1.6 GHz) as part of the Early Science Programme (ESP) of the RadioAstron} mission, is used here to test the polarimetric performance of the orbiting Space Radio Telescope (SRT) employed by the mission, to establish a methodology for making full Stokes polarimetry with space VLBI at 1.6 GHz, and to study the polarized emission in the target object on sub-milliarcsecond scales. Polarization leakage of the SRT at 18 cm is found to be within 9 percents in amplitude, demonstrating the feasibility of high fidelity polarization imaging with RadioAstron at this wavelength. A polarimetric image of 0642+449 with a resolution of 0.8 mas (signifying an ~4 times improvement over ground VLBI observations at the same wavelength) is obtained. The image shows a compact core-jet structure with low (~2%) polarization and predominantly transverse magnetic field in the nuclear region. The VLBI data also uncover a complex structure of the nuclear region, with two prominent features possibly corresponding to the jet base and a strong recollimation shock. The maximum brightness temperature at the jet base can be as high as 4*10^13 K.Comment: Accepted for publication in A&A, 10 pages, 6 figure

Spin Injection in Quantum Wells with Spatially Dependent Rashba Interaction

We consider Rashba spin-orbit effects on spin transport driven by an electric field in semiconductor quantum wells. We derive spin diffusion equations that are valid when the mean free path and the Rashba spin-orbit interaction vary on length scales larger than the mean free path in the weak spin-orbit coupling limit. From these general diffusion equations, we derive boundary conditions between regions of different spin-orbit couplings. We show that spin injection is feasible when the electric field is perpendicular to the boundary between two regions. When the electric field is parallel to the boundary, spin injection only occurs when the mean free path changes within the boundary, in agreement with the recent work by Tserkovnyak et al. [cond-mat/0610190].Comment: 7 pages, 1 figur

Microarcsecond VLBI pulsar astrometry with PSRπ\pi II. parallax distances for 57 pulsars

We present the results of PSR$\pi$, a large astrometric project targeting radio pulsars using the Very Long Baseline Array (VLBA). From our astrometric database of 60 pulsars, we have obtained parallax-based distance measurements for all but 3, with a parallax precision of typically 40 $\mu$as and approaching 10 $\mu$as in the best cases. Our full sample doubles the number of radio pulsars with a reliable ($\gtrsim$5$\sigma$) model-independent distance constraint. Importantly, many of the newly measured pulsars are well outside the solar neighbourhood, and so PSR$\pi$ brings a near-tenfold increase in the number of pulsars with a reliable model-independent distance at $d>2$ kpc. Using our sample along with previously published results, we show that even the most recent models of the Galactic electron density distribution model contain significant shortcomings, particularly at high Galactic latitudes. When comparing our results to pulsar timing, two of the four millisecond pulsars in our sample exhibit significant discrepancies in the estimates of proper motion obtained by at least one pulsar timing array. With additional VLBI observations to improve the absolute positional accuracy of our reference sources and an expansion of the number of millisecond pulsars, we will be able to extend the comparison of proper motion discrepancies to a larger sample of pulsar reference positions, which will provide a much more sensitive test of the applicability of the solar system ephemerides used for pulsar timing. Finally, we use our large sample to estimate the typical accuracy attainable for differential astrometry with the VLBA when observing pulsars, showing that for sufficiently bright targets observed 8 times over 18 months, a parallax uncertainty of 4 $\mu$as per arcminute of separation between the pulsar and calibrator can be expected.Comment: updated to version accepted by ApJ: 30 pages, 20 figures, 9 table