ⅆ2yⅆt2+2⋅γdyⅆt+ω2y=0, with thedamping factorγ=c2m,and thenatural frequencyω=km.The solution to this differential equation can be expressed in one of three ways, depending on the sign ofγ−ω...
Simple harmonic and damped motions of dissipative solitons in two-dimensional complex Ginzburg-Landau equation supported by an external V-shaped potentialOptical solitonDissipative systemGinzburg-LandauSimple harmonic motionDamped motionDissipative solitons based on the complex Ginzburg-Landau (CGL) model show...
In the framework of the Lindblad theory for open quantum systems, a master equation for the quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived for the case when the interaction is based on deformed algebra. The equations of motion...
hi guys, doing damped and forced harmonic motion at college at the moment, but i don't do further maths...hence I'm a tad behind compared to those who do...
The mathematical essence ofdamped oscillationis researched with the qualitative theory of differential equation from the odd characters of the plane autonomous system. 用微分方程定性理论,从平面自治系统奇点的性态角度出发分析了阻尼振荡的数学本质。
Statistical mechanics of mean field Ehrenfest quantum/classical molecular dynamics: The damped harmonic oscillator Redfield master equation, and the deficiencies of the quantum/classical approach pointed out by analyzing the nature of energy/population relaxation and ... G Käb - 《Journal of Physical...
t be a physics course with the simple harmonic oscillator. Our point of departure is the general formof the lagrangian of a systemnear its position of stable equilibrium, from which we deduce the equation of motion. We will then consider both unforced and periodically forced motion before turn...
We analyze the new equation of motion for the damped oscillator. It differs from the standard one by a damping term which is nonlocal in time and hence it gives rise to a system with memory. Both classical and quantum analysis is performed. The characteristic feature of this nonlocal system...
Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation Quantum damping by coupling to a heat bath of harmonic oscillators is investigated theoretically, considering systems in which the system-bath interactions... CW Gardiner,MJ Collett - 《Physical...
The ODE for damped harmonic motion is: Solving this ODE yields: And from this general solution, we're able to easily derive the solutions for under-damped, critically-damped, and over-damped damped harmonic oscillation. The full proof can be foundin this PDFfromplanetmath.org. ...