Search results for "Damped"

A no-go result for the quantum damped harmonic oscillator

2019

Abstract In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons

2010

In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.

Non-stationary pre-envelope covariances of non-classically damped systems

1991

Abstract A new formulation is given to evaluate the stationary and non-stationary response of linear non-classically damped systems subjected to multi-correlated non-separable Gaussian input processes. This formulation is based on a new and more suitable definition of the impulse response function matrix for such systems. It is shown that, when using this definition, the stochastic response of non-classically damped systems involves the evaluation of quantities similar to those of classically damped ones. Furthermore, considerations about non-stationary cross-covariances, spectral moments and pre-envelope cross-covariances are presented for a monocorrelated input process.

Exact Results for Spectra of Overdamped Brownian Motion in Fixed and Randomly Switching Potentials

2004

The exact formulae for spectra of equilibrium diffusion in a fixed bistable piecewise linear potential and in a randomly flipping monostable potential are derived. Our results are valid for arbitrary intensity of driving white Gaussian noise and arbitrary parameters of potential profiles. We find: (i) an exponentially rapid narrowing of the spectrum with increasing height of the potential barrier, for fixed bistable potential; (ii) a nonlinear phenomenon, which manifests in the narrowing of the spectrum with increasing mean rate of flippings, and (iii) a nonmonotonic behaviour of the spectrum at zero frequency, as a function of the mean rate of switchings, for randomly switching potential. …

Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under sto…

2022

[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.

Exact 3D solution for static and damped harmonic response of simply supported general laminates

2014

International audience; The state-space method is adapted to obtain three dimensional exact solutions for the static and damped dynamic behaviors of simply supported general laminates. The state-space method is written in a general form that permits to handle both cross-ply and antisymmetric angle-ply laminates. This general form also permits to obtain exact solutions for general laminates, albeit with some constraints. For the general case and for the static behavior, either an additive term is added to the load to simulate simply supported boundary conditions, or the plate bends in a particular way. For the dynamic behavior, the general case leads to pairs of natural frequencies for each …

A fractionally-damped duffing oscillator driven by stochastic agencies

2012

On an approximate solution of fractionally damped dynamical systems

2011

Stochastic seismic analysis of MDOF structures with viscous damper devices

2009

Fluid damper devices in civil structures such as buildings or bridges are commonly used as energy absorbers for seismic protection. The problem in the response analysis of structures with filled dampers mainly consists in the fact that, due to the strongly nonlinear behavior of such equipments, the response spectrum technique fails. In this paper by using the concept of power spectral density function compatible with the elastic response spectrum and the stochastic linearization technique, the equivalent damping ratio is obtained. It is shown that once the system is linearized results obtained by Monte Carlo simulation and those obtained by stochastic analysis are in good agreement. Respons…