Quantum-Mechanical Lossy Transmission Lines-Analysis based on Damped Harmonic Oscillator GKSL Theory

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
L. Kumar ◽  
H. Parthasarathy
Keyword(s):  
Harmonic Oscillator ◽  
Transmission Lines ◽  
Quantum Mechanical ◽  
Damped Harmonic Oscillator ◽  
Lossy Transmission

scholarly journals Leapfrogging of electrical solitons in coupled nonlinear transmission lines: effect of an imperfect varactor

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Nkongho Achere Akem ◽  
Alain M. Dikandé ◽  
B. Z. Essimbi
Keyword(s):  
Harmonic Oscillator ◽  
Transmission Line ◽  
Numerical Simulations ◽  
Transmission Lines ◽  
Nonlinear Transmission Lines ◽  
Capacitively Coupled ◽  
Nonlinear Transmission ◽  
Damped Harmonic Oscillator ◽  
Initial Values ◽  
Soliton Pair

AbstractThe leapfrogging dynamics of a pair of electrical solitons is investigated, by considering two capacitively coupled nonlinear transmission lines with and without intraline resistances. We discuss two distinct transmission line set-ups: in the first, we assume two RLC ladder lines with intraline varactors and a coupling linear capacitor, and in the second, we consider two capacitively coupled lossless lines with a varactor carrying impurity (imperfect diode) in one of the two interacting transmission lines. In the first context, we find that the soliton-pair leapfrogging mimics the motion of a damped harmonic oscillator, the frequency and damping coefficient of which are obtained analytically. Numerical simulations predict leapfrogging of the soliton pair when the differences in the initial values of the amplitude and phase are reasonably small, and the resistance is not too large. In the second context, leapfrogging occurs when the impurity rate is small enough and the differences in the initial values of the amplitude as well as phase are also small. As the impurity rate increases, the soliton signal in the imperfect line gets accelerated upon approaching the defective diode, causing only this specific soliton signal to move faster than its counterpart, leading to the suppression of leapfrogging.

A concise quantum mechanical treatment of the forced damped harmonic oscillator

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Ti Li
Keyword(s):  
Harmonic Oscillator ◽  
Mechanical Treatment ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
External Influence ◽  
Classical Motion ◽  
Damped Harmonic Oscillator ◽  
Classical Energy ◽  
Quantum Mechanical Treatment ◽  
Generalized Coordinate

AbstractBy selecting a right generalized coordinate X, which contains the general solutions of the classical motion equation of a forced damped harmonic oscillator, we obtain a simple Hamiltonian which does not contain time for the oscillator such that Schrödinger equation and its solutions can be directly written out in X representation. The wave functin in x representation are also given with the help of the eigenfunctions of the operator $$ \hat X $$ in x representation. The evolution of $$ \left\langle {\hat x} \right\rangle $$ is the same as in the classical mechanics, and the uncertainty in position is independent of an external influence; one part of energy mean is quantized and attenuated, and the other is equal to the classical energy.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

Oscillations in Lossy Transmission Lines Terminated By Exponential R-Load

2012 ◽  
Vol 1 (4) ◽  
pp. 22-33
Author(s):  
Vasil Angelov ◽  
Dafinka Angelova
Keyword(s):  
Transmission Lines ◽  
Lossy Transmission

Path integral for the damped harmonic oscillator coupled to its dual

1994 ◽  
Vol 35 (3) ◽  
pp. 1185-1191 ◽  
Author(s):  
L. Chetouani ◽  
L. Guechi ◽  
T. F. Hammann ◽  
M. Letlout
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Damped Harmonic Oscillator
Sign in / Sign up

Export Citation Format

Share Document