We propose a new solvable class of multidimensional quantum harmonic oscillators for linear diffusive particle and quadratic energy absorbing well associated with semi-definite positive matrix force. Under natural easily checked controllability conditions, non necessarily reversible models possibly transient free diffusions, the ground state zero-point are explicitly computed in terms unique fi...

In linear dynamics, the set of solutions for unforced conservative systems exhibit a vector space structure. Any solution is a linear combination of particular periodic solutions known as modes. Such a strong result no longer holds in the framework of nonlinear dynamics. However, the dynamical behaviour can be captured in the vicinity of equilibrium points. Indeed, there exists two-dimensional ...

Image contrast enhancement is realised by using nonlinear oscillatory theory. Two different uncoupled networks based on nonlinear oscillators have been studied. Simulators for both networks are developed and tested with very low contrasted images. Results show a possible effective area of application of nonlinear oscillators for image processing tasks.

This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the covariance matrix for the invariant Gaussian state of such a system and the related purity functional subject to inaccuracies in the energy and coupling matr...

The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation for the distribution of phases which includes the diffusive effect of noise in the oscillator frequencies. The bifurcation from the phase-incoherent state is a...

The collective dynamics in populations of magnetic spin torque oscillators (STO) is an intensely studied topic in modern magnetism. Here, we show that arrays of STO coupled via dipolar fields can be modeled using a variant of the Kuramoto model, a well-known mathematical model in non-linear dynamics. By investigating the collective dynamics in arrays of STO we find that the synchronization in s...

We have fabricated several varieties of micro and nanomechanical resonators and have studied their phase response when driven at their natural frequency with and without parametric pumping. We found that micron-sized paddle oscillators with submicron-sized supports had resonant frequencies in the 3-10 MHz range for their translational mode. Due to the stretching of the support beams, the effect...