We propose a method to obtain the equilibrium distribution for positions and velocities of a one-dimensional particle via time-averaging and Laplace transformations. We apply it to the case of a damped harmonic oscillator in contact with a thermal bath. The present method allows us to treat, among other cases, a Gaussian noise function exponentially correlated in time, e.g., Gaussian colored no...

We propose a method to obtain the equilibrium distribution for positions and velocities of a one-dimensional particle via time-averaging and Laplace transformations. We apply it to the case of a damped harmonic oscillator in contact with a thermal bath. The present method allows us to treat, among other cases, a Gaussian noise function exponentially correlated in time, e.g., Gaussian colored no...

Finite pulse width effects in level crossing detectors and similar systems, such as neurons, can yield an output noise that is, in the low frequency limit, a monotonically increasing function of the frequency. The phenomenon can well be observed at excitations with strong noise when the firing frequency is high. Blue noise effects have been observed in stochastically driven dynamical systems li...

We consider the transient behavior of a large linear array of coupled linear damped harmonic oscillators following perturbation of a single element. Our work is motivated by modeling the behavior of flocks of autonomous vehicles. We first state a number of conjectures that allow us to derive an explicit characterization of the transients, within a certain parameter regime Ω. As corollaries we s...

The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The comparison of the a priori and a posteriori mean value of the optical quadrature operators and the photon number operator is given.

We analyze scattering cross sections at and near third-order exceptional points (EP3), i.e., points in physical parameter space where three energies and eigenfunctions coincide. At an EP3, the Green’s function contains a pole of third order, in addition to poles of second and first order. We show that the interference of the three pole terms produces a rich variety of line shapes at the excepti...

A new concept for quadrature coupling of oscillators is introduced and demonstrated on a 5-GHz CMOS voltagecontrolled oscillator (VCO). It uses the second harmonic of the outputs to couple the oscillators. The technique provides quadrature over a wide tuning range without introducing any increase in phase noise or power consumption. The VCO is tunable between 4.57 and 5.21 GHz and has a phase n...