Abstract A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part a vibro-impact unit linear oscillator with an internally colliding small block. This block the secondary being damped oscillator. The mathematical model has been presented in non-dimensional form. analytical studies are restricted to case periodic steady-state motion sy...

The temperature dependence of the gapped triplet excitations (triplons) in the 2D Shastry-Sutherland quantum magnet SrCu(2)(BO(3))(2) is studied by means of inelastic neutron scattering. The excitation amplitude rapidly decreases as a function of temperature, while the integrated spectral weight can be explained by an isolated dimer model up to 10 K. Analyzing this anomalous spectral line shape...

Extracting a weak audio signal buried below a stronger one is a difficult task that may be encountered in forensic applications. Extraction of the background signal is made difficult by the signal-to-noise ratio that is clearly negative. Apart from this difficulty, the problem would look like the problem of separating different components from an audio signal. We investigate the possibility of ...

Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerf...

It is well known that in open quantum systems resonances can coalesce at an exceptional point, where both the energies and the wave functions coincide. In contrast to the usual behaviour of the scattering amplitude at one resonance, the coalescence of two resonances invokes a pole of second order in the Green’s function, in addition to the usual first order pole. We show that the interference d...

The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time-lapse recordings. Three applications are discussed: (i) The effects of finite sampling rate and time, de...

In this paper we study to what extent the canonical equivalence and the identity of the geometric phases of dissipative and conservative linear oscillators, established in a preceeding paper, can be generalized to nonlinear ones. Considering first the 1-D quartic generalized oscillator we determine, by means of a perturbative time dependent technic of reduction to normal forms, the canonical tr...

The Lagrange formalism is developed for Bateman oscillators, which include both damped and amplified systems, a novel method to derive the Caldirola-Kanai null Lagrangians presented. For Lagrangians, corresponding gauge functions are obtained. It shown that can be used convert undriven oscillators into driven ones. Applications of obtained results quantizatation briefly discussed.

Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples — the damped harmonic oscillator and a two-level atom with homodyne photodetection. Then, we consider how t...