Geometry from the spectral point of view

In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.

This paper is dedicated to the memory of J. Schwinger     

On a heuristic point of view related to quantum nonequilibrium statistical mechanics

In this paper I propose a new way for counting the microstates of a system out of equilibrium. As, according to quantum mechanics, things happen as if a given particle can be found in more than one state at once, I extend this concept to propose the coherent access by a particle to the available states of a system. By coherent access I mean the possibility for the particle to act as if it is populating more than one microstate at once. This hypothesis has experimental implications, since the thermodynamical probability and, as a consequence, the Bose-Einstein distribution as well as the argument of the Boltzmann factor is modified.     

The statistical mechanics of topological polymers: a field theorist point of view

This is a self‐contained introduction to polymer physics and to the application of field theoretical techniques to the statistical mechanics of polymer systems. Of course, since polymer physics is a highly interdisciplinary subject, involving different disciplines like knot theory, field theory, statistical mechanics and some notions of bio‐chemistry and chemistry, it is not possible to cover all these topics in a single review. Particular emphasis is given here to the problem of describing the fluctuations of topologically linked polymers in a solution from a microscopical point of view. Some recent advances in this direction are presented. Another purpose of this work is to serve as a guide for whoever would like to apply the methods of field theory to polymers. To ease reading, technical terms have been quoted in boldface characters at the points in which their meaning is explained.     

Master-slave synchronization from the point of view of global dynamics

We present a mathematical framework for the theory of a synchronization phenomenon for dynamical systems discovered by Pecora and Carroll [Phys. Rev. Lett. 64, 821-824 (1990)]. From this perspective, we can synchronize, using a single coordinate, an open dense set of linear systems. We use our insights to synchronize nonlinear systems which were not previously recognized as being synchronizable. (c) 1995 American Institute of Physics.     

Holography: an interpretation from the phase-space point of view

The formation of holograms is interpreted as the consequence of the bilinearity of the ambiguity function. Reconstruction can then be regarded as the manipulation of the ambiguity function. Specifically, we show that in the case of in-line holography, the reconstruction can be regarded as phase tomography. In this way we provide a unified picture for the formulation of both noninterferometric and interferometric phase-retrieval techniques.     

Thin film substrates from the Raman spectroscopy point of view

We have investigated ten standard single crystal substrates of complex oxides on the account of their applicability in the Raman spectroscopy‐based thin film research. In this study, we suggest a spectra normalization procedure that utilizes a comparison of the substrate's Raman spectra to those of well‐established Raman reference materials. We demonstrate that MgO, LaGaO₃, (LaAlO₃)_0.3(Sr₂AlTaO₆)_0.7 (LSAT), DyScO₃, YAlO₃, and LaAlO₃ can be of potential use for Raman‐based thin film research. At the same time TiO₂ (rutile), NdGaO₃, SrLaAlO₄, and SrTiO₃ single crystals exhibit multiple phonon modes accompanied by strong Raman background that substantially hinder Raman‐based thin film experiments. Copyright © 2014 John Wiley & Sons, Ltd.     

Accelerator driven systems from the radiological safety point of view

In the proposed accelerator driven systems (ADS) the possible use of several milliamperes of protons of about 1 GeV incident on high mass targets like the molten lead-bismuth eutectic is anticipated to pose radiological problems that have so far not been encountered by the radiation protection community. Spallation reaction products like high energy gammas, neutrons, muons, pions and several radiotoxic nuclides including Po-210 complicate the situation. In the present paper, we discuss radiation safety measures like bulk shielding, containment of radiation leakage through ducts and penetration and induced activity in the structure to protect radiation workers as well as estimation of sky-shine, soil and ground water activation, release of toxic gases to the environment to protect public as per the stipulations of the regulatory authorities. We recommend the application of the probabilistic safety analysis technique by assessing the probability and criticality of different hazard-initiating events using HAZOP and FMECA.      

Amplification of light from an undulatory point of view

The traditional approach to light amplification is shown to be based on the idea that photons of the incoming beam act as independent particles. If atomic stimulation is instead attributed to the action of the wave, different photon statistics (but with the same average) is obtained in the final state.     

Heavy-ion dynamics from the point of view of classical mean-field theory

A simple classical force model, based on mean-field dynamics, is applied to fusion phenomena and other processes in heavy-ion collisions. We find reasonable agreement with trends in the fusion cross section going to heavy nuclei, including the barrier to fusion at high Z²/A. Collision times are calculated for a variety of reactions; recent evidence for non-equilibration of energy suggests that the equilibration time for energy is smaller than 300 fm/c and larger than 50 fm/c.     

Regularization in quantum field theory from the causal point of view

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973 [12]. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.     

Looking at the Haldane conjecture from a grouptheoretical point of view

Based on the Lieb-Schultz-Mattis construction we present a five parameter family of Spin-1 Hamiltonians with degenerate groundstate. Starting from the criticalSU (3) symmetric Hamiltonian, we look for those perturbations of theSU (3) symmetry, which leave the groundstate degenerate. We also discuss the spin-3/2SU (4)-case.     

A two-scale model from the point of view of the small-slope approximation

Abstract

General results for the scattering cross section following from the small-slope approximation (SSA) are applied to the case of two-scale surface roughness which can be represented as a superposition of small-scale and large-scale components. The purpose of the paper is to obtain analytically tractable results with obvious physical meaning which can be used for estimates prior to undertaking extensive numerical calculations according to exact unambiguous expressions of the SSA. The general case of vector (electromagnetic) or scalar (sound) waves is considered. The statistics of small-scale roughness is not assumed to be Gaussian (in any sense) or space-homogeneous, and the possible dependence of the statistics of small-scale roughness on a large-scale undulating surface is taken into account. As a result, a modified local spectrum of small-scale components of roughness enters into corresponding expressions for the scattering cross section. It is demonstrated that under appropriate conditions, the resulting formulae for the scattering cross section reduce to the conventional two-scale model.     

Revision of probability theory from the point of view of quantum statistics

Distributions for time series corresponding to problems related to Kolmogorov complexity are obtained. The notions of negative dimension and of quantization of spaces of positive and negative dimension are introduced. Applications of these notions to a broad spectrum of problems are considered, from linguistics to isotropic turbulence.     

Statistical thermodynamics from the point of view of statistical theory of estimation

An essentially statistical theory of thermodynamics is developed on the basis of additivity and conservation laws of fundamental entities of thermodynamics. The theory developed by Dutta (1953–59) stresses first the importance of the statistical theory of estimation in the statistical foundation of thermodynamics. The method of finding the distribution law is based on the principle similar to that of Bayes' rule in probability theory and the method of maximum-likelihood estimation of mathematical statistics. The model used is macroscopic in nature and the laws of microscopic distributions (M-B, B-E and F-D statistics) have been obtained by additional axiom regarding the constituents of the system. The object of the paper is to present an outline of the theory with some of its extensions to quantum macro-system and non-equilibrium thermodynamics.     

Generalized Veneziano model from the point of view of manifestly crossing-invariant parametrization

The construction of the Veneziano-typen-point function with manifestly crossing-invariant parametrization is reviewed in a heuristic way. Here, one meets a divergence problem, the solution of which is discussed in detail. Equivalence to previous works and its asymptotic behaviour are rederived with the help of affine group representation.     

Continuity of type-I intermittency from a measure-theoretical point of view

We study a simple dynamical system which displays a so-called type-I intermittency bifurcation. We determine the Bowen-Ruelle measure and prove that the expectation (g) of any continuous functiong and the Kolmogoroff-Sinai entropyh() are continuous functions of the bifurcation parameter. Therefore the transition is continuous from a measure-theoretical point of view. Those results could be generalized to any similar dynamical system.