Quantization of a damped harmonic oscillator leads to so called Bateman’s dual system. The corresponding Bateman’s Hamiltonian, being a self-adjoint operator, displays the discrete family of complex eigenvalues. We show that they correspond to the poles of energy eigenvectors and the corresponding resolvent operator when continued to the complex energy plane. Therefore, the corresponding genera...

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis–Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy related positive operators is determined for the oscillators under ...

PURPOSE To introduce a new model describing human in vivo corneal deswelling after hypoxic contact lens wear, based on a damped harmonic oscillator, which can describe an overshoot in corneal deswelling, to compare this new model with the currently used exponential model, and also to test whether a diurnal variation in baseline corneal thickness exists that would have to be taken into considera...

Duffing systems excited by harmonic excitations and subjected to noise additions are considered, it is examined whether the addition can be used steer response from one stable mode another. To help with this examination, authors propose a methodology for estimating probability that short duration Gaussian white generate or destroy modes of single nonlinear oscillator as well set coupled oscilla...

The Bertrand-Darboux integrability condition for a certain class of perturbed harmonic oscillators is studied from the viewpoint of the BirkhoffGustavson(BG)-normalization: In solving an inverse problem of the BGnormalization on computer algebra, it is shown that if the perturbed harmonic oscillators with a homogeneous cubic-polynomial potential and with a homogeneous quartic-polynomial potenti...

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...

This work proposes two novel simulation techniques that allow for fast and accurate predictions of phase noise in oscillators even adopting inexpensive software, such as PSpice. The traditional harmonic tone insertion is initially discussed, by applying it to a LC-tuned oscillator taken as benchmark. Then a first, much faster technique based on sensitivity analysis is proposed, which is suitabl...

Voltage-controlled oscillators are widely used circuit blocks, particularly in phase-locked loops. As CMOS is the technology of choice for many applications, CMOS oscillators with low phase noise and timing jitter are highly desired. CMOS ring oscillators with five different delay cell topologies have been designed, fabricated and evaluated for phase noise performance. Our results show that rin...