Holographic Chern-Simons Defects

We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.Comment: 56 pages, 19 figures, v2: sign convention for CS level in terms of number of D7 branes switched, UV behavior of one and two point functions added in sec. 5.4.1 and 5.4.3, references added, typos correcte

Smoothing properties of evolution equations via canonical transforms and comparison principle

This paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L-2-boundedness properties are derived. This allows us to globally reduce general dispersive equations to normal forms in one or two dimensions. Then, a new comparison principle for evolution equations is introduced. In particular, it allows us to relate different smoothing estimates by comparing certain expressions involving their symbols. As a result, it is shown that the majority of smoothing estimates for different equations are equivalent to each other. Moreover, new estimates as well as several refinements of known results are obtained. The proofs are considerably simplified. A comprehensive analysis is presented for smoothing estimates for dispersive equations. Applications are given to the detailed description of smoothing properties of the Schrodinger, relativistic Schrodinger, wave, Klein-Gordon and other equations

Smoothing properties of evolution equations via canonical transforms and comparison principle

This paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L-2-boundedness properties are derived. This allows us to globally reduce general dispersive equations to normal forms in one or two dimensions. Then, a new comparison principle for evolution equations is introduced. In particular, it allows us to relate different smoothing estimates by comparing certain expressions involving their symbols. As a result, it is shown that the majority of smoothing estimates for different equations are equivalent to each other. Moreover, new estimates as well as several refinements of known results are obtained. The proofs are considerably simplified. A comprehensive analysis is presented for smoothing estimates for dispersive equations. Applications are given to the detailed description of smoothing properties of the Schrodinger, relativistic Schrodinger, wave, Klein-Gordon and other equations

Pre-suprenova evolution of rotating massive stars

The Geneva evolutionary code has been modified to study the advanced stages (Ne, O, Si burnings) of rotating massive stars. Here we present the results of four 20 solar mass stars at solar metallicity with initial rotational velocities of 0, 100, 200 and 300 km/s in order to show the crucial role of rotation in stellar evolution. As already known, rotation increases mass loss and core masses (Meynet and Maeder 2000). A fast rotating 20 solar mass star has the same central evolution as a non-rotating 26 solar mass star. Rotation also increases strongly net total metal yields. Furthermore, rotation changes the SN type so that more SNIb are predicted (see Meynet and Maeder 2003 and N. Prantzos and S. Boissier 2003). Finally, SN1987A-like supernovae progenitor colour can be explained in a single rotating star scenario.Comment: To appear in proceedings of IAU Colloquium 192, "Supernovae (10 years of 1993J)", Valencia, Spain 22-26 April 2003, eds. J.M. Marcaide, K.W. Weiler, 5 pages, 8 figure

Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets

A unified theory of the anomalous Hall effect (AHE) is presented for multi-band ferromagnetic metallic systems with dilute impurities. In the clean limit, the AHE is mostly due to the extrinsic skew-scattering. When the Fermi level is located around anti-crossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its non-perturbative nature, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit interaction energy.Comment: 5 pages including 4 figures, RevTex; minor changes, to appaer in Phys. Rev. Let

Discrimination with error margin between two states - Case of general occurrence probabilities -

We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence probabilities. The optimal measurements are classified into three types. One of the three types of measurement is optimal depending on parameters (occurrence probabilities and error margin). We determine the three domains in the parameter space and the optimal discrimination success probability in each domain in a fully analytic form. It is also shown that when the states to be discriminated are multipartite, the optimal success probability can be attained by local operations and classical communication. For discrimination of two mixed states, an upper bound of the optimal success probability is obtained.Comment: Final version, 9 pages, references added, presentation improve

Discrete element models of soil-geogrid interaction

Geogrids are the geosynthetics of choice for soil reinforcement applications. To evaluate the efficiency of geogrid reinforcement, several methods are used including field tests, laboratory tests and numerical modeling. Field studies consume long period of time and conducting these investigations may become highly expensive because of the need for real-size structures. Laboratory studies present also significant difficulties: large-size testing machines are required to accommodate realistic geogrid designs. The discrete element method (DEM) may be used as a complementary tool to extend physical testing databases at lower cost. Discrete element models do not require complex constitutive formulations and may be fed with particle scale data (size, strength, shape) thus reducing the number offree calibration parameters. Discrete element models also are well suited to problems in which large displacements are present, such as geogrid pullout. This paper reviews the different approaches followed to model soil-geogrid interaction in DEM and presents preliminary results from pull-out conditions.Peer ReviewedPostprint (author's final draft