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...
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...
Davidson,Russell - 《Journal of Mathematical Physics》 被引量: 67发表: 1970年 Solutions of the damped oscillator Fokker-Planck equation The quantum theory of damping is presented and illustrated by means of a driven damped harmonic oscillator. The theory is formulated in the coherent state ... ...
A damped oscillator is described by the equation m(x'') + b(x') + kx = 0, where the damping force is given by F = -b(x'). Show that the rate of change of...
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...
The eigenvectors of the damped system are the same as those of the corresponding undamped system. For the eigenvector {uk}, the characteristic equation is (11.18)λ2+ckλ+ωk2=0 which has two roots (11.19)λ±k=12(−ck±i4ωk2−ck2), i=−1 The damping ratio for ...
3.4a. The equation of motion for damped free vibration is given by the linear ODE Sign in to download full-size image FIGURE 3.4. Damped vibration response for various damping ratios: (a) system schematic and free-body diagram; (b) underdamped (ζ < 1); (c) critically damped (ζ ...
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。
Equation (1) represents a damped Duffing oscillator. In the case when ε = 0, we have an undamped Duffing oscillator which has an exact solution for any given arbitrary initial conditions. More precisely, the exact solution to the i.v.p. (2) is given by (3) where (4) The ...
Finally, a wave equation of the linearly damped oscillator is given. Nonequilibrium Thermodynamic and Quantum Model of a Damped Oscillator 41 http://dx.doi.org/10.5772/61010 2. Nonequilibrium thermodynamic theory of the linearly damped oscillator Meixner was the first to propose a nonequilibrium ...