Hawking Radiation as Quantum Tunneling in Rindler Coordinate

We substantiate the Hawking radiation as quantum tunneling of fields or particles crossing the horizon by using the Rindler coordinate. The thermal spectrum detected by an accelerated particle is interpreted as quantum tunneling in the Rindler spacetime. Representing the spacetime near the horizon locally as a Rindler spacetime, we find the emission rate by tunneling, which is expressed as a contour integral and gives the correct Boltzmann factor. We apply the method to non-extremal black holes such as a Schwarzschild black hole, a non-extremal Reissner-Nordstr\"{o}m black hole, a charged Kerr black hole, de Sitter space, and a Schwarzschild-anti de Sitter black hole.Comment: LaTex 19 pages, no figure; references added and replaced by the version accepted in JHE

Theories of Low-Energy Quasi-Particle States in Disordered d-Wave Superconductors

The physics of low-energy quasi-particle excitations in disordered d-wave superconductors is a subject of ongoing intensive research. Over the last decade, a variety of conceptually and methodologically different approaches to the problem have been developed. Unfortunately, many of these theories contradict each other, and the current literature displays a lack of consensus on even the most basic physical observables. Adopting a symmetry-oriented approach, the present paper attempts to identify the origin of the disagreement between various previous approaches, and to develop a coherent theoretical description of the different low-energy regimes realized in weakly disordered d-wave superconductors. We show that, depending on the presence or absence of time-reversal invariance and the microscopic nature of the impurities, the system falls into one of four different symmetry classes. By employing a field-theoretical formalism, we derive effective descriptions of these universal regimes as descendants of a common parent field theory of Wess-Zumino-Novikov-Witten type. As well as describing the properties of each universal regime, we analyse a number of physically relevant crossover scenarios, and discuss reasons for the disagreement between previous results. We also touch upon other aspects of the phenomenology of the d-wave superconductor such as quasi-particle localization properties, the spin quantum Hall effect, and the quasi-particle physics of the disordered vortex lattice.Comment: 42 Pages, 8 postscript figures, published version with updated reference

Implicit Differense Scheme for Solution of Maxwell's Equations

Abstract: The present paper is devoted to the description of numerical approach of solution problem Koshi for systems of Maxwell's equations in usual time. The implicit difference scheme used for approximation of Maxwell's equations with various boundary conditions is described. Mathematical algorithms of the decision of system of the equations arising at use the implicit scheme are considered.Note: Research direction:Mathematical problems and theory of numerical method