Recent developments in perturbation theory

Rayleigh-Schroeder perturbation theory - degenerate and non-degenerate states - quantum chemistry - other perturbation equation

Comprehensive Spectral Analysis of Human EEG GENERATORS in Posterior Cerebral Regions

Human electroencephalogram generator spectral analysis in posterior cerebral region

The postulates of gravitational thermodynamics

The general principles and logical structure of a thermodynamic formalism that incorporates strongly self-gravitating systems are presented. This framework generalizes and simplifies the formulation of thermodynamics developed by Callen. The definition of extensive variables, the homogeneity properties of intensive parameters, and the fundamental problem of gravitational thermodynamics are discussed in detail. In particular, extensive parameters include quasilocal quantities and are naturally incorporated into a set of basic general postulates for thermodynamics. These include additivity of entropies (Massieu functions) and the generalized second law. Fundamental equations are no longer homogeneous first-order functions of their extensive variables. It is shown that the postulates lead to a formal resolution of the fundamental problem despite non-additivity of extensive parameters and thermodynamic potentials. Therefore, all the results of (gravitational) thermodynamics are an outgrowth of these postulates. The origin and nature of the differences with ordinary thermodynamics are analyzed. Consequences of the formalism include the (spatially) inhomogeneous character of thermodynamic equilibrium states, a reformulation of the Euler equation, and the absence of a Gibbs-Duhem relation.Comment: 28 pages, Revtex, no figures. An important sentence and several minor corrections included. To appear in Physical Review

Action Principle for the Generalized Harmonic Formulation of General Relativity

An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona--Casas and Palenzuela (BBP). The relationship between the generalized harmonic action and the BBP action is discussed in detail.Comment: This version is contains more thorough presentations and discussions of the key results. To be published in PRD. (8 pages, no figures

Microwave Power Transmission System Studies. Volume 1: Executive Summary

A study of microwave power generation, transmission, reception and control was conducted as a part of a program to demonstrate the feasibility of power transmission from geosynchronous orbit. A summary is presented of results concerning design approaches, estimated costs (ROM), critical technology, associated ground and orbital test programs with emphasis on dc to rf conversion, transmitting antenna, phase control, mechanical systems, flight operations, ground power receiving-rectifying antenna with systems analysis, and evaluation. Recommendations for early further in-depth studies complementing the technology program are included

Microwave power transmission system studies. Volume 2: Introduction, organization, environmental and spaceborne systems analyses

Introduction, organization, analyses, conclusions, and recommendations for each of the spaceborne subsystems are presented. Environmental effects - propagation analyses are presented with appendices covering radio wave diffraction by random ionospheric irregularities, self-focusing plasma instabilities and ohmic heating of the D-region. Analyses of dc to rf conversion subsystems and system considerations for both the amplitron and the klystron are included with appendices for the klystron covering cavity circuit calculations, output power of the solenoid-focused klystron, thermal control system, and confined flow focusing of a relativistic beam. The photovoltaic power source characteristics are discussed as they apply to interfacing with the power distribution flow paths, magnetic field interaction, dc to rf converter protection, power distribution including estimates for the power budget, weights, and costs. Analyses for the transmitting antenna consider the aperture illumination and size, with associated efficiencies and ground power distributions. Analyses of subarray types and dimensions, attitude error, flatness, phase error, subarray layout, frequency tolerance, attenuation, waveguide dimensional tolerances, mechanical including thermal considerations are included. Implications associated with transportation, assembly and packaging, attitude control and alignment are discussed. The phase front control subsystem, including both ground based pilot signal driven adaptive and ground command approaches with their associated phase errors, are analyzed

Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble

The thermodynamical properties of the Reissner-Nordstr\"om-anti-de Sitter black hole in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow us to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. Instantons with negative heat capacity are also found.Comment: 15 pages, 9 figures, Revtex. Published version. Changes: figures added to tex

Hamiltonian thermodynamics of the Reissner-Nordstr\"om-anti-de Sitter black hole

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric Einstein-Maxwell spacetimes with a negative cosmological constant. We impose boundary conditions that enforce every classical solution to be an exterior region of a Reissner-Nordstr\"om-anti-de Sitter black hole with a nondegenerate Killing horizon, with the spacelike hypersurfaces extending from the horizon bifurcation two-sphere to the asymptotically anti-de Sitter infinity. The constraints are simplified by a canonical transformation, which generalizes that given by Kucha\v{r} in the spherically symmetric vacuum Einstein theory, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the grand partition function of a thermodynamical grand canonical ensemble is obtained by analytically continuing the Lorentzian time evolution operator to imaginary time and taking the trace. A~similar analysis under slightly modified boundary conditions leads to the partition function of a thermodynamical canonical ensemble. The thermodynamics in each ensemble is analyzed, and the conditions that the (grand) partition function be dominated by a classical Euclidean black hole solution are found. When these conditions are satisfied, we recover in particular the Bekenstein-Hawking entropy. The limit of a vanishing cosmological constant is briefly discussed. (This paper is dedicated to Karel Kucha\v{r} on the occasion of his sixtieth birthday.)Comment: 34 pages, REVTeX v3.0. (Minor corrections and presentational revisions; added references.