Search results for "classical"

Vortex-glass transition in three dimensions.

1991

We investigate the possibility of a vortex-glass transition in a disordered type-II superconductor in a magnetic field in three dimensions by numerical studies of a simplified model. Monte Carlo simulations at finite temperature and domain-wall renormalization-group calculations at {ital T}=0 indicate that {ital d}=3 is just above the lower critical dimension {ital d}{sub {ital l}}, though the possibility that {ital d}{sub {ital l}}=3 cannot be definitely ruled out. A comparison is made with {ital XY} and Ising spin glasses. The (effective) correlation-length exponent {nu} and dynamical exponent {ital z} are in fairly good agreement with experiment.

Hydrodynamic Equations of Anisotropic, Polarized, Turbulent Superfluids

2009

Relative velocities for radial motion in expanding Robertson-Walker spacetimes

2011

The expansion of space, and other geometric properties of cosmological models, can be studied using geometrically defined notions of relative velocity. In this paper, we consider test particles undergoing radial motion relative to comoving (geodesic) observers in Robertson-Walker cosmologies, whose scale factors are increasing functions of cosmological time. Analytical and numerical comparisons of the Fermi, kinematic, astrometric, and the spectroscopic relative velocities of test particles are given under general circumstances. Examples include recessional comoving test particles in the de Sitter universe, the radiation-dominated universe, and the matter-dominated universe. Three distinct …

Simple Microscopic Theory of Amontons' Laws for Static Friction

2001

A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons' laws. However the friction coefficient between bare surfaces vanishes as the area of individual contacts grows, except in the rare case of commensurate surfaces. An area independent friction coefficient is obtained for any surface geometry when an adsorbed layer of mobile atoms is introduced between the surfaces. The predictions from our simple analytic model are confirmed by atomistically detail…

Classical Geometric Phases: Foucault and Euler

2020

In the last chapter we saw how a quantum system can give rise to a Berry phase, by studying the adiabatic round trip of its quantum state on a certain parameter space. Rather than considering what happens to states in Hilbert space, we now turn to classical mechanics, where we are concerned instead with the evolution of the system in configuration space. As a first example, we are interested in the geometric phase of an oscillator that is constrained to a plane that is transported over some surface which moves along a certain path in three-dimensional space. Contrary to determining the Berry phase, there is no adiabatic approximation of the motion along the curve involved. The Foucault phas…

Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation

2011

Abstract. We construct a multi-parametric family of quasi-rational solutions to the focusing NLS equation, presenting a profile of multiple rogue waves. These solutions have also been used by us to construct a large family of smooth, real localized rational solutions of the KP-I equation quite different from the multi-lumps solutions first constructed in Bordag et al. (1977). The physical relevance of both equations is very large. From the point of view of geosciences,the focusing NLS equation is relevant to the description of surface waves in deep water, and the KP-I equation occurs in the description of capillary gravitational waves on a liquid surface, but also when one considers magneto…

Soliton-plasmon resonances as Maxwell nonlinear bound states

2012

We demonstrate that soliplasmons (soliton–plasmon bound states) appear naturally as eigenmodes of nonlinear Maxwell’s equations for a metal/Kerr interface. Conservative stability analysis is performed by means of finite element numerical modeling of the time-independent nonlinear Maxwell equations. Dynamical features are in agreement with the presented nonlinear oscillator model.

Near-field optics theories

1996

The development of near-field optics theory is reviewed. We first recall that near-field optics is not limited to near-field microscopy. Broadly speaking, it concerns phenomena involving evanescent electromagnetic waves. The importance of such waves was ignored for a long time in optical and surface physics until the emergence of scanning near-field optical microscopes. Taking evanescent waves into account prevents the use of any simple approximation in the set of Maxwell's equations. The various theoretical approaches of near-field optics are discussed from the point of view of their ability to assess evanescent electromagnetic waves. We discuss the main results of the application of the v…

General formulae for polarization observables in deuteron electrodisintegration and linear relations

1993

Formal expressions are derived for all possible polarization observables in deuteron electrodisintegration with longitudinally polarized incoming electrons, oriented deuteron targets and polarization analysis of outgoing nucleons. They are given in terms of general structure functions which can be determined experimentally. These structure functions are Hermitean forms of theT-matrix elements which, in principle, allow the determination of allT-matrix elements up to an arbitrary common phase. Since the set of structure functions is overcomplete, linear relations among various structure functions exist which are derived explicitly.

Focus on quantum Einstein gravity

2012

The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishin…