Related papers: Harmonic oscillator with time-dependent effective-…
This paper presents a novel approach to understanding the role of harmonic dynamics and gaining a deeper appreciation for its impact within and outside of quantum mechanics. This includes consequences of harmonic dynamics and the…
The classical and quantum formalism for a p-adic and adelic harmonic oscillator with time-dependent frequency is developed, and general formulae for main theoretical quantities are obtained. In particular, the p-adic propagator is…
We treat quantum back-reaction in time dependent processes for quantum field theory in various simplified models. The first example is a harmonic oscillator whose frequency depends on a second quantum variable $x$. Beginning with a…
Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…
Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical…
Data from gravitational wave detectors are recorded as time series that include contributions from myriad noise sources in addition to any gravitational wave signals. When regularly sampled data are available, such as for ground based and…
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general…
We simulate the nonlinear hydrodynamical evolution of tidally-excited inertial waves in convective envelopes of rotating stars and giant planets modelled as spherical shells containing incompressible, viscous and adiabatically-stratified…
The interaction of a gravitational wave with a system made of an RLC circuit forming one end of a mechanical harmonic oscillator is investigated. We show that, in some configurations, the coherent interaction of the wave with both the…
The quantum quartic anharmonic oscillator with the Hamiltonian $H=\frac{1}{2}\left( p^{2}+x^{2}\right) +\lambda x^{4}$ is a classical and fundamental model that plays a key role in various branches of physics, including quantum mechanics,…
We investigate quantum mechanical Hamiltonians with explicit time dependence. We find a class of models in which an analogue of the time independent \S equation exists. Among the models in this class is a new exactly soluble model, the…
Gravitational waves at suitable frequencies can resonantly interact with a binary system, inducing changes to its orbit. A stochastic gravitational-wave background causes the orbital elements of the binary to execute a classic random walk,…
We provide a time-dependent Dyson map and metric for the two dimensional harmonic oscillator with a non-Hermitian $i xy$ coupling term. This particular time-independent model exhibits spontaneously broken $\mathcal{PT}$-symmetry and becomes…
Primordial gravitational waves generated from early universe are placed in the squeezed vacuum state and the resulting stochastic background is studied for various models of the expanding universe. The quantum effect on the stochastic…
Vibrations, electromagnetic oscillations and temperature drifts are among the main reasons for dephasing in matter-wave interferometry. Sophisticated interferometry experiments, e.g. with ions or heavy molecules, often require integration…
We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and…
Conventional techniques that measure rapid time variations are inefficient or inadequate to discover and observe rapidly pulsating astronomical sources. It is therefore conceivable that there exist some classes of objects pulsating with…
We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the…
A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not…
Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase-space, a credible possibility of their detection lies in the present day gravitational wave…