Thermal effect in the resonance fluorescence of a two-level system

1991 ◽  
Vol 69 (11) ◽  
pp. 1367-1372
Author(s):  
C. H. A. Fonseca ◽  
L. A. Amarante Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Normal Modes ◽  
Thermal Fluctuations ◽  
Harmonic Oscillators ◽  
Thermal Bath ◽  
Resonance Fluorescence ◽  
Level System ◽  
Near Resonance ◽  
Intensity Correlation Function ◽  
Heisenberg Equations

The damped two-level system, driven by a strong incident classical field near resonance frequency is subjected to the effect of thermal fluctuations. To simulate the thermal bath we introduce a large system of harmonic oscillators that represents the normal modes of the thermal radiation field. From the Heisenberg equations of motion we calculate the power spectrum of the scattered field and the intensity correlation function. The results show that the presence of the bath dramatically modifies the light scattered by the two-level system when compared with the case without a thermal bath.

scholarly journals Кулоновские плазмон-экситоны в планарных наноструктурах металл-полупроводник

2021 ◽  
Vol 63 (4) ◽  
pp. 527
Author(s):  
В.А. Кособукин
Keyword(s):  
Quantum Well ◽  
Surface Plasmons ◽  
Metal Film ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Coupled Harmonic Oscillators ◽  
Dipole Force ◽  
Two Peaks

A theory of Coulomb (non-radiative) plasmons-excitons in a semiconductor with adjacent quantum well and ultrathin metal film is presented. The equations of motion are formulated for the polarization waves of surface plasmons and quasi-two-dimensional excitons with taking account of Coulomb interaction between them. Within a model of coupled harmonic oscillators, solved are the problems of Coulomb plasmon, exciton and plasmon-exciton excitations in the presence of an external dipole force. The coupling contant is calculated for plasmon-excitons, their optical spectra are investigated, and the relative contributions of plasmons and excitons to the normal modes are found. It is concluded that near the resonance between plasmon and exciton the spectrum of plasmon-exciton excitations consists of two peaks whose behavior in passing through the resonance shows the signs of anti-crossing effect (repulsion of frequencies).

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

Model Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes

1999 ◽  
Author(s):  
E. Pesheck ◽  
C. Pierre ◽  
S. W. Shaw
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Single Equation ◽  
Rotating Beam ◽  
Model Size ◽  
Nonlinear Normal

Abstract Equations of motion are developed for a rotating beam which is constrained to deform in the transverse (flapping) and axial directions. This process results in two coupled nonlinear partial differential equations which govern the attendant dynamics. These equations may be discretized through utilization of the classical normal modes of the nonrotating system in both the transverse and extensional directions. The resultant system may then be diagonalized to linear order and truncated to N nonlinear ordinary differential equations. Several methods are used to determine the model size necessary to ensure accuracy. Once the model size (N degrees of freedom) has been determined, nonlinear normal mode (NNM) theory is applied to reduce the system to a single equation, or a small set of equations, which accurately represent the dynamics of a mode, or set of modes, of interest. Results are presented which detail the convergence of the discretized model and compare its dynamics with those of the NNM-reduced model, as well as other reduced models. The results indicate a considerable improvement over other common reduction techniques, enabling the capture of many salient response features with the simulation of very few degrees of freedom.

scholarly journals Nonlinear gas oscillations in pipes. Part 1. Theory

1973 ◽  
Vol 59 (1) ◽  
pp. 23-46 ◽  
Author(s):  
J. Jimenez
Keyword(s):  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Wave Form ◽  
Cube Root ◽  
Acoustic Oscillations ◽  
Open Mouth ◽  
Near Resonance ◽  
Reflexion Coefficient ◽  
Two Parameters

The problem of forced acoustic oscillations in a pipe is studied theoretically. The oscillations are produced by a moving piston in one end of the pipe, while a variety of boundary conditions ranging from a completely closed to a completely open mouth at the other end are considered. All these boundary conditions are modelled by two parameters: a length correction and a reflexion coefficient equivalent to the acoustic impedance.The linear theory predicts large amplitudes near resonance and nonlinear effects become crucially important. By expanding the equations of motion in a series in the Mach number, both the amplitude and wave form of the oscillation are predicted there.In both the open- and closed-end cases the need for shock waves in some range of parameters is found. The amplitude of the oscillation is different for the two cases, however, being proportional to the square root of the piston amplitude in the closed-end case and to the cube root for the open end.

scholarly journals Thermal Fluctuations in Electric Circuits and the Brownian Motion

2010 ◽  
Vol 61 (4) ◽  
pp. 252-256 ◽  
Author(s):  
Gabriela Vasziová ◽  
Jana Tóthová ◽  
Lukáš Glod ◽  
Vladimír Lisý
Keyword(s):  
Brownian Motion ◽  
Brownian Particle ◽  
Mean Square Displacement ◽  
Thermal Fluctuations ◽  
Stochastic Equations ◽  
Thermal Bath ◽  
Current Fluctuations ◽  
Electric Circuits ◽  
The Mean ◽  
Optically Trapped

Thermal Fluctuations in Electric Circuits and the Brownian MotionIn this work we explore the mathematical correspondence between the Langevin equation that describes the motion of a Brownian particle (BP) and the equations for the time evolution of the charge in electric circuits, which are in contact with the thermal bath. The mean quadrate of the fluctuating electric charge in simple circuits and the mean square displacement of the optically trapped BP are governed by the same equations. We solve these equations using an efficient approach that allows us converting the stochastic equations to ordinary differential equations. From the obtained solutions the autocorrelation function of the current and the spectral density of the current fluctuations are found. As distinct from previous works, the inertial and memory effects are taken into account.

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