Simulations of Nonthermal Electron Transport in Multidimensional Flows: Application to Radio Galaxies

We have developed an economical, effective numerical scheme for cosmic-ray transport suitable for treatment of electrons up to a few hundreds of GeV in multidimensional simulations of radio galaxies. The method follows the electron population in sufficient detail to allow computation of synthetic radio and X-ray observations of the simulated sources, including spectral properties (see the companion paper by Tregillis et al. 1999). The cosmic-ray particle simulations can follow the effects of shock acceleration, second-order Fermi acceleration as well as radiative and adiabatic energy losses. We have applied this scheme to 2-D and 3-D MHD simulations of jet-driven flows and have begun to explore links between dynamics and the properties of high energy electron populations in radio lobes. The key initial discovery is the great importance to the high energy particle population of the very unsteady and inhomogeneous flows, especially near the end of the jet. Because of this, in particular, our simulations show that a large fraction of the particle population flowing from the jet into the cocoon never passes through strong shocks. The shock strengths encountered are not simply predicted by 1-D models, and are quite varied. Consequently, the emergent electron spectra are highly heterogeneous. Rates of synchrotron aging in "hot-spots" seem similarly to be very uneven, enhancing complexity in the spectral properties of electrons as they emerge into the lobes and making more difficult the task of comparing dynamical and radiative ages.Comment: 7 pages, 1 figure; to appear in Life Cycles of Radio Galaxies, ed. J. Biretta et al., New Astronomy Review

Zero-energy edge states and chiral symmetry breaking at edges of graphite sheets

Two-dimensional graphite sheets with a certain type of edges are known to support boundary states localized near the edges. Forming a flat band with a sharp peak in the density of states at the Fermi energy, they can trigger a magnetic instability or a distortion of the lattice in the presence of electron-electron or electron-phonon interactions. We shall discuss a relationship between chiral symmetry, which is the origin of the zero-energy edge states, and several types of induced orders such as spin density waves or lattice distortions. We also investigate electron correlation effects on the edge states for a wrapped quasi one-dimensional geometry, i.e., carbon nanotube, by means of the renormalization group and the open boundary bosonization.Comment: 4 pages, Proceedings of EP2DS1

Faraday Rotation Measure due to the Intergalactic Magnetic Field

Studying the nature and origin of the intergalactic magnetic field (IGMF) is an outstanding problem of cosmology. Measuring Faraday rotation would be a promising method to explore the IGMF in the large-scale structure (LSS) of the universe. We investigated the Faraday rotation measure (RM) due to the IGMF in filaments of galaxies using simulations for cosmological structure formation. We employed a model IGMF based on turbulence dynamo in the LSS of the universe; it has an average strength of $\sim 10$ nG and a coherence length of several $\times\ 100\ h^{-1}$ kpc in filaments. With the coherence length smaller than path length, the inducement of RM would be a random walk process, and we found that the resultant RM is dominantly contributed by the density peak along line of sight. The rms of RM through filaments at the present universe was predicted to be $\sim 1\ {\rm rad\ m^{-2}}$. In addition, we predicted that the probability distribution function of $|{\rm RM}|$ through filaments follows the log-normal distribution, and the power spectrum of RM in the local universe peaks at a scale of $\sim 1\ h^{-1}$ Mpc. Our prediction of RM could be tested with future instruments.Comment: To appear in ApJ. Pdf with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/ar.pd

Exactly Solvable Quantum Mechanics

A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.Comment: LaTeX 48 pages, 5 figures. arXiv admin note: text overlap with arXiv:1104.047

Zero-energy edge states and their origin in particle-hole symmetric systems: symmetry and topology

We propose a criterion to determine the existence of zero-energy edge states for a class of particle-hole symmetric systems. A loop is assigned for each system, and its topology and a symmetry play an essential role. Applications to d-wave superconductors are demonstrated.Comment: 2 pages, Proceedings of LT2

Cosmic Shock Waves on Large Scales of the Universe

In the standard theory of the large scale structure formation, matter accretes onto high density perturbations via gravitational instability. Collisionless dark matter forms caustics around such structures, while collisional baryonic matter forms accretion shocks which then halt and heat the infalling gas. Here, we discuss the characteristics, roles, and observational consequences of these accretion shocks.Comment: 3 pages with 1 figure, uses sprocl.sty, to appear in the Proceedings of the 18th Texas Symposium on Relativistic Astrophysics, ed. A. Olinto, J. Frieman and D. Schramm, also available upon request to [email protected]

Extensions of solvable potentials with finitely many discrete eigenstates

We address the problem of rational extensions of six examples of shape-invariant potentials having finitely many discrete eigenstates. The overshoot eigenfunctions are proposed as candidates unique in this group for the virtual state wavefunctions, which are an essential ingredient for multi-indexed and iso-spectral extensions of these potentials. They have exactly the same form as the eigenfunctions but their degrees are much higher than n_{max} so that their energies are lower than the groundstate energy.Comment: 22 pages, 3 figures. Typo corrected, comments and references added. To appear in J.Phys.A. arXiv admin note: text overlap with arXiv:1212.659