Multifractals Competing with Solitons on Fibonacci Optical Lattice

We study the stationary states for the nonlinear Schr\"odinger equation on the Fibonacci lattice which is expected to be realized by Bose-Einstein condensates loaded into an optical lattice. When the model does not have a nonlinear term, the wavefunctions and the spectrum are known to show fractal structures. Such wavefunctions are called critical. We present a phase diagram of the energy spectrum for varying the nonlinearity. It consists of three portions, a forbidden region, the spectrum of critical states, and the spectrum of stationary solitons. We show that the energy spectrum of critical states remains intact irrespective of the nonlinearity in the sea of a large number of stationary solitons.Comment: 5 pages, 4 figures, major revision, references adde

Particle Acceleration, Magnetic Field Generation, and Associated Emission in Collisionless Relativistic Jets

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., active galactic nuclei (AGNs), gamma-ray bursts (GRBs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations using injected relativistic electron-ion (electro-positron) jets show that acceleration occurs within the downstream jet. Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, other two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons has different properties than synchrotron radiation which assumes a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 4 pages, 3 figures, contributed talk at the workshop: High Energy Phenomena in Relativistic Outflows (HEPRO), Dublin, 24-28 September 2007. Fig. 3 is replaced by the correct versio

3-D GRMHD and GRPIC Simulations of Disk-Jet Coupling and Emission

We investigate jet formation in black-hole systems using 3-D General Relativistic Particle-In-Cell (GRPIC) and 3-D GRMHD simulations. GRPIC simulations, which allow charge separations in a collisionless plasma, do not need to invoke the frozen condition as in GRMHD simulations. 3-D GRPIC simulations show that jets are launched from Kerr black holes as in 3-D GRMHD simulations, but jet formation in the two cases may not be identical. Comparative study of black hole systems with GRPIC and GRMHD simulations with the inclusion of radiate transfer will further clarify the mechanisms that drive the evolution of disk-jet systems.Comment: 3 pages, 1 figure, Proceedings of the Eleventh Marcel Grossmann Meeting on General Relativity, edited by H. Kleinert, R.T. Jantzen and R. Ruffini, World Scientific, Singapore, 200

Relativistic Particle-In-Cell Simulation Studies of Prompt and Early Afterglows from GRBs

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks e.g. gamma-ray bursts (GRBs) active galactic nuclei (AGNs) and microquasars commonly exhibit power-law emission spectra. Recent PIC simulations of relativistic electron-ion (or electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In collisionless relativistic shocks particle (electron, positron and ion) acceleration is due to plasma waves and their associated instabilities (e.g. the Weibel (filamentation) instability) created in the shock region. The simulations show that the Weibel instability is responsible for generating and amplifying highly non-uniform small-scale magnetic fields. These fields contribute to the electron's transverse deflection behind the jet head. The resulting ``jitter'' radiation from deflected electrons has different properties compared to synchrotron radiation which assumes a uniform magnetic field. Jitter radiation may be important for understanding the complex time evolution and/or spectra in gamma-ray bursts, relativistic jets in general and supernova remnants.Comment: 19 pages,7 figures, contributed talk at Seventh European Workshop on Collisionless Shocks, Paris, 7- 9 November 2007. High resolution version can be obtained at http://gammaray.nsstc.nasa.gov/~nishikawa/shockws07.pd

Particle acceleration in electron-ion jets

Weibel instability created in collisionless shocks is responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-ion jet fronts propagating into an ambient plasma without initial magnetic fields with a longer simulation system in order to investigate nonlinear stage of the Weibel instability and its acceleration mechanism. The current channels generated by the Weibel instability induce the radial electric fields. The z component of the Poynting vector (E x B) become positive in the large region along the jet propagation direction. This leads to the acceleration of jet electrons along the jet. In particular the E x B drift with the large scale current channel generated by the ion Weibel instability accelerate electrons effectively in both parallel and perpendicular directions.Comment: 2 pages, 1 figure, Proceedings for Astrophysical Sources of High Energy Particles and Radiation, AIP proceeding Series, eds . T. Bulik, G. Madejski and B. Ruda

Deterministic Weak Localization in Periodic Structures

The weak localization is found for perfect periodic structures exhibiting deterministic classical diffusion. In particular, the velocity autocorrelation function develops a universal quantum power law decay at 4 times Ehrenfest time, following the classical stretched-exponential type decay. Such deterministic weak localization is robust against weak enough randomness (e.g., quantum impurities). In the 1D and 2D cases, we argue that at the quantum limit states localized in the Bravis cell are turned into Bloch states by quantum tunnelling.Comment: 5 pages, 2 figure

Radiation from relativistic jets

Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., gamma-ray bursts (GRBs), active galactic nuclei (AGNs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations of relativistic electron-ion (electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In the presence of relativistic jets, instabilities such as the Buneman instability, other two-streaming instability, and the Weibel (filamentation) instability create collisionless shocks, which are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons in small-scale magnetic fields has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation, a case of diffusive synchrotron radiation, may be important to understand the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 8 pages,3 figures, accepted for the Proceedings of Science of the Workshop on Blazar Variability across the Electromagnetic Spectrum, April 22 to 25, 200

Binary collisions of charged particles in a magnetic field

Binary collisions between charged particles in an external magnetic field are considered in second-order perturbation theory, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an improved binary collisions treatment which is valid for any strength of the magnetic field, where the second-order energy and velocity transfers are represented in Fourier space for arbitrary interaction potentials. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and non-singular at the origin, and which involves as limiting cases the Debye (i.e., screened) and Coulomb potential. Two distinct cases are considered in detail. (i) The collision of two identical (e.g., electron-electron) particles; (ii) and the collision between a magnetized electron and an uniformly moving heavy ion. The energy transfer involves all harmonics of the electron cyclotron motion. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte--Carlo calculations which also allows to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the non-perturbative numerical classical trajectory Monte--Carlo results agree excellently with the predictions of the perturbative treatment.Comment: submitted to Phys. Rev.

General Relativistic MHD Simulations of Jet Formation

We have performed 3-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations of jet formation from an accretion disk with/without initial perturbation around a rotating black hole. We input a sinusoidal perturbation (m = 5 mode) in the rotation velocity of the accretion disk. The simulation results show the formation of a relativistic jet from the accretion disk. Although the initial perturbation becomes weakened by the coupling among different modes, it survives and triggers lower modes. As a result, complex non-axisymmetric density structure develops in the disk and the jet. Newtonian MHD simulations of jet formation with a non-axisymmetric mode show the growth of the m = 2 mode but GRMHD simulations cannot see the clear growth of the m = 2 mode