A numerical and symbolical approximation of the Nonlinear Anderson Model

A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we obtain error estimates. This approach can be useful for the solution of other nonlinear differential equations of physical relevance.Comment: 21 pages and 7 figure

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

Echoes and revival echoes in systems of anharmonically confined atoms

We study echoes and what we call 'revival echoes' for a collection of atoms that are described by a single quantum wavefunction and are confined in a weakly anharmonic trap. The echoes and revival echoes are induced by applying two, successive temporally localized potential perturbations to the confining potential, one at time $t=0$, and a smaller one at time $t=\tau$. Pulse-like responses in the expectation value of position are predicted at $t \approx n\tau$ ($n=2,3,...$) and are particularly evident at $t \approx 2\tau$. A novel result of our study is the finding of 'revival echoes'. Revivals (but not echoes) occur even if the second perturbation is absent. In particular, in the absence of the second perturbation, the response to the first perturbation dies away, but then reassembles, producing a response at revival times $mT_x$ ($m=1,2,...$). Including the second perturbation at $t=\tau$, we find temporally localized responses, revival echoes, both before and after $t\approx mT_x$, e.g., at $t\approx m T_x-n \tau$ (pre-revival echoes) and at $t\approx mT_x+n\tau$, (post-revival echoes), where $m$ and $n$ are $1,2,...$ . Depending on the form of the perturbations, the 'principal' revival echoes at $t \approx T_x \pm \tau$ can be much larger than the echo at $t \approx 2\tau$. We develop a perturbative model for these phenomena, and compare its predictions to the numerical solutions of the time-dependent Schr\"odinger Equation. The scaling of the size of the various echoes and revival echoes as a function of the symmetry and size of the perturbations applied at $t=0$ and $t=\tau$ is investigated. We also study the presence of revivals and revival echoes in higher moments of position, , $p>1$, and the effect of atom-atom interactions on these phenomena.Comment: 33 pages, 13 figures, corrected typos and added reference

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

Invalidity of Classes of Approximated Hall Effect Calculations

In this comment, I point out a number of approximated derivations for the effective equation of motion, now been applied to d-wave superconductors by Kopnin and Volovik are invalid. The major error in those approximated derivations is the inappropriate use of the relaxation time approximation in force-force correlation functions, or in force balance equations, or in similar variations. This approximation is wrong and unnecessary.Comment: final version, minor changes, to appear in Phys. Rev. Let

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

Arnol'd Tongues and Quantum Accelerator Modes

The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in experiments with laser-cooled atoms. We show that their parametric dependence exhibits Arnol'd-like tongues and perform a perturbative analysis of such structures. We thus explain the arithmetical organisation of the accelerator modes and discuss experimental implications thereof.Comment: 20 pages, 6 encapsulated postscript figure

Knowledge Graph Completion to Predict Polypharmacy Side Effects

The polypharmacy side effect prediction problem considers cases in which two drugs taken individually do not result in a particular side effect; however, when the two drugs are taken in combination, the side effect manifests. In this work, we demonstrate that multi-relational knowledge graph completion achieves state-of-the-art results on the polypharmacy side effect prediction problem. Empirical results show that our approach is particularly effective when the protein targets of the drugs are well-characterized. In contrast to prior work, our approach provides more interpretable predictions and hypotheses for wet lab validation.Comment: 13th International Conference on Data Integration in the Life Sciences (DILS2018