Holographic classification of Topological Insulators and its 8-fold periodicity

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the boundary states of topological insulators are Dirac fermions, we thereby holographically reproduce the Periodic Table of topological insulators found by Kitaev and Ryu. et. al, without using topological invariants nor K-theory. In addition we find candidate Z_2 topological insulators in classes AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table

On the role of a new type of correlated disorder in extended electronic states in the Thue-Morse lattice

A new type of correlated disorder is shown to be responsible for the appearance of extended electronic states in one-dimensional aperiodic systems like the Thue-Morse lattice. Our analysis leads to an understanding of the underlying reason for the extended states in this system, for which only numerical evidence is available in the literature so far. The present work also sheds light on the restrictive conditions under which the extended states are supported by this lattice.Comment: 11 pages, LaTeX V2.09, 1 figure (available on request), to appear in Physical Review Letter

Synthetic Observations of Simulated Radio Galaxies I: Radio and X-ray Analysis

We present an extensive synthetic observational analysis of numerically- simulated radio galaxies designed to explore the effectiveness of conventional observational analyses at recovering physical source properties. These are the first numerical simulations with sufficient physical detail to allow such a study. The present paper focuses on extraction of magnetic field properties from nonthermal intensity information. Synchrotron and inverse-Compton intensities provided meaningful information about distributions and strengths of magnetic fields, although considerable care was called for. Correlations between radio and X-ray surface brightness correctly revealed useful dynamical relationships between particles and fields. Magnetic field strength estimates derived from the ratio of X-ray to radio intensity were mostly within about a factor of two of the RMS field strength along a given line of sight. When emissions along a given line of sight were dominated by regions close to the minimum energy/equipartition condition, the field strengths derived from the standard power-law-spectrum minimum energy calculation were also reasonably close to actual field strengths, except when spectral aging was evident. Otherwise, biases in the minimum- energy magnetic field estimation mirrored actual differences from equipartition. The ratio of the inverse-Compton magnetic field to the minimum-energy magnetic field provided a rough measure of the actual total energy in particles and fields in most instances, within an order of magnitude. This may provide a practical limit to the accuracy with which one may be able to establish the internal energy density or pressure of optically thin synchrotron sources.Comment: 43 pages, 14 figures; accepted for publication in ApJ, v601 n2 February 1, 200

Cosmic Rays Accelerated at Cosmological Shock Waves

Based on hydrodynamic numerical simulations and diffusive shock acceleration model, we calculated the ratio of cosmic ray (CR) to thermal energy. We found that the CR fraction can be less than similar to 0.1 in the intracluster medium, while it would be of order unity in the warm-hot intergalactic mediumopen2

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Cosmological Shock Waves and Their Role in the Large Scale Structure of the Universe

We study the properties of cosmological shock waves identified in high-resolution, N-body/hydrodynamic simulations of a $\Lambda$CDM universe and their role on thermalization of gas and acceleration of nonthermal, cosmic ray (CR) particles. External shocks form around sheets, filaments and knots of mass distribution when the gas in void regions accretes onto them. Within those nonlinear structures, internal shocks are produced by infall of previously shocked gas to filaments and knots, and during subclump mergers, as well as by chaotic flow motions. Due to the low temperature of the accreting gas, the Mach number of external shocks is high, extending up to $M\sim 100$ or higher. In contrast, internal shocks have mostly low Mach numbers. For all shocks of $M\ge1.5$ the mean distance between shock surfaces over the entire computed volume is $\sim4 h^{-1}$ Mpc at present, or $\sim 1 h^{-1}$ Mpc for internal shocks within nonlinear structures. Identified external shocks are more extensive, with their surface area $\sim2$ times larger than that of identified internal shocks at present. However, especially because of higher preshock densities, but also due to higher shock speeds, internal shocks dissipate more energy. Hence, the internal shocks are mainly responsible for gas thermalization as well as CR acceleration. In fact, internal shocks with 2 \la M \la 4 contribute $\sim 1/2$ of the total dissipation. Using a nonlinear diffusive shock acceleration model for CR protons, we estimate the ratio of CR energy to gas thermal energy dissipated at cosmological shock waves to be $\sim1/2$ through the history of the universe. Our result supports scenarios in which the intracluster medium contains energetically significant populations of CRs.Comment: 25 pages, 8 figures including 1 in color. To appear in ApJ (v593 n2 August 20, 2003). Postscript file with full resolution ftp://canopus.chungnam.ac.kr/ryu/cosmoshock.p

Mutual information challenges entropy bounds

We consider some formulations of the entropy bounds at the semiclassical level. The entropy S(V) localized in a region V is divergent in quantum field theory (QFT). Instead of it we focus on the mutual information I(V,W)=S(V)+S(W)-S(V\cup W) between two different non-intersecting sets V and W. This is a low energy quantity, independent of the regularization scheme. In addition, the mutual information is bounded above by twice the entropy corresponding to the sets involved. Calculations of I(V,W) in QFT show that the entropy in empty space cannot be renormalized to zero, and must be actually very large. We find that this entropy due to the vacuum fluctuations violates the FMW bound in Minkowski space. The mutual information also gives a precise, cutoff independent meaning to the statement that the number of degrees of freedom increases with the volume in QFT. If the holographic bound holds, this points to the essential non locality of the physical cutoff. Violations of the Bousso bound would require conformal theories and large distances. We speculate that the presence of a small cosmological constant might prevent such a violation.Comment: 10 pages, 2 figures, minor change