We study free particle motion on homogeneous kinematical spacetimes of galilean type. The three well-known cases Galilei and (A)dS–Galilei are included in our analysis, but focus will be the previously unexplored torsional spacetimes. show how well-chosen coordinates becomes equivalent to dynamics a damped harmonic oscillator, with damping set by torsion. realization symmetry algebra terms cons...

We study the dynamics of a damped harmonic oscillator in presence retarded potential with state-dependent time-delayed feedback. In limit small time-delays, we show that is equivalent to Li\'enard system. This allows us analytically predict value first Hopf bifurcation, unleashing self-oscillatory motion. compute bifurcation diagrams for several model parameter values and analyse multistable do...

In this paper, we propose a methodology for analyzing the near-field coupling between two surface mount device (SMD) inductors using 3-dimensional electromagnetic (3D-EM) model. To develop 3D-EM model, first constitute equivalent circuit of SMD inductor from measured impedance and derive loss tangent parameters. Secondly, damped harmonic oscillator model is introduced to extract effective perme...

The relaxation dynamics of a weathercock free-to-rotate, in the presence uniform flow, as it aligns with flow direction, is investigated experimentally wind-tunnel. observed to conveniently follow damped harmonic oscillator behavior. At first order, frequency set by aerodynamic coefficients. We show that quasi static approach fails precisely describe and non-stationary corrections are required ...

A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic os-cillator wave functions. Unlike the harmonic oscillator states, the new wave functions decay exponentially at large distances. Using the new basis, characteristics of w...

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a single harmonic oscillator is couple...

An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the method of linear invariants. It has been shown that such oscillator possesses cofluctuant states, different from widely studied Glauber’s coherent and ”ideal” s...

The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential features ofWigner’s little groups dictating the internal space-time symmetries of particles in the Lorentz-covariant world. The little groups are the ...

Adelic quantum mechanics is formulated. The corresponding model of the harmonic oscillator is considered. The adelic harmonic oscillator exhibits many interesting features. One of them is a softening of the uncertainty relation.