Search results for "Linear"

Cross-Kerr nonlinearity: a stability analysis

2015

We analyse the combined effect of the radiation-pressure and cross-Kerr nonlinearity on the stationary solution of the dynamics of a nanomechanical resonator interacting with an electromagnetic cavity. Within this setup, we show how the optical bistability picture induced by the radiation-pressure force is modified by the presence of the cross-Kerr interaction term. More specifically, we show how the optically bistable region, characterising the pure radiation-pressure case, is reduced by the presence of a cross-Kerr coupling term. At the same time, the upper unstable branch is extended by the presence of a moderate cross-Kerr term, while it is reduced for larger values of the cross-Kerr co…

Spectroscopie Raman Anti-Stokes Cohérente femtoseconde (DRASC – fs) : expériences et modélisation dans le cas du mélange H2 – N2 à basse pression

2006

Dans l'objectif du diagnostic de la temperature dans les milieux en combustion, la Diffusion Raman Anti-Stokes Coherente resolue en temps (DRASC - fs) est utilisee pour sonder H 2 dans les melanges H 2 -N 2 a basse pression. Le dispositif DRASC mis en place est decrit en detail. Un nouveau modele de la reponse DRASC temporelle, prenant en compte tous les effets collisionnels specifiques a l'hydrogene (effets dits « de vitesse ») est presentee, ainsi que la comparaison avec l'experience, l'accord se revelant tres satisfaisant.

One-particle Green's function

2013

In this chapter we get acquainted with the one-particle Green's function G , or simply the Green's function. The chapter is divided in three parts. In the first part (Section 6.1) we illustrate what kind of physical information can be extracted from the different Keldysh components of G . The aim of this first part is to introduce some general concepts without being too formal. In the second part (Section 6.2) we calculate the noninteracting Green's function. Finally in the third part (Sections 6.3 and 6.4) we consider the interacting Green's function and derive several exact properties. We also discuss other physical (and measurable) quantities that can be calculated from G and that are re…

Model of compact 3D electromagnetic solitons

2019

Accurate Nonlinear Optical Properties for Small Molecules

2006

During the last decade it became possible to calculate by quantum chemical ab initio methods not only static but also frequency-dependent properties with high accuracy. Today, the most important tools for such calculations are coupled cluster response methods in combination with systematic hierarchies of correlation consistent basis sets. Coupled cluster response methods combine a computationally efficient treatment of electron correlation with a qualitatively correct pole structure and frequency dispersion of the response functions. Both are improved systematically within a hierarchy of coupled cluster models. The present contribution reviews recent advances in the highly accurate calculat…

Thermodynamic pressure in nonlinear nonequilibrium thermodynamics of dilute nonviscous gases.

2000

In this paper, using extended thermodynamics, we build up a nonlinear theory for a dilute nonviscous gas under heat flux. The fundamental fields are the density, the velocity, the internal energy density, and the heat flux. The constitutive theory is builtup without approximations. We single out the nonlinear complete expressions of the Gibbs equation and of the nonequilibrium pressure. In particular, we determine the complete expressions furnished by the theory for the nonequilibrium pressure tensor and thermodynamic pressure, i.e., the derivative of the nonequilibrium internal specific entropy with respect to the specific volume, times the nonequilibrium temperature. In a second-order app…

Stability of Relativistic Hydrodynamical Planar Jets: Linear and Nonlinear Evolution of Kelvin-Helmholtz Modes

2004

Some aspects about the stability of relativistic flows against Kelvin-Helmholtz (KH) perturbations are studied by means of relativistic, hydrodynamical simulations. In particular, we analyze the transition to the fully nonlinear regime and the long-term evolution of two jet models with different specific internal energies.

General measurement technique of the ratio between chromatic dispersion and the nonlinear coefficient

2021

Measuring the nonlinear coefficient γ of any guiding medium, regardless of the sign and magnitude of its group-velocity dispersion parameter β 2 , is challenging because of the lack of general solutions of the nonlinear Schrodinger equation (NLSE). Indeed, existing approaches typically need to disregard chromatic-dispersion effects to determine γ [1] . Here we propose an all-encompassing approach to measure the ratio β 2 /γ and prove our method in polarization-maintaining (PM) and single-mode (SM) fibers with positive and negative β 2 .

Systems of Linear Equations

2016

A linear equation in \(\mathbb {R}\) in the variables \(x_1,x_2,\ldots ,x_n\) is an equation of the kind:

Beyond the Runge–Gross Theorem

2012

The Runge–Gross theorem (Runge and Gross, Phys Rev Lett, 52:997–1000, 1984) states that for a given initial state the time-dependent density is a unique functional of the external potential. Let us elaborate a bit further on this point. Suppose we could solve the time-dependent Schrodinger equation for a given many-body system, i.e. we specify an initial state \(| \Uppsi_0 \rangle\) at \(t=t_0\) and evolve the wavefunction in time using the Hamiltonian \({\hat{H}} (t).\) Then, from the wave function, we can calculate the time-dependent density \(n (\user2{r},t).\) We can then ask the question whether exactly the same density \(n(\user2{r},t)\) can be reproduced by an external potential \(v^…