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A semiclassical model is used to investigate oscillations of atomic fermions in a combined magnetic trap and one dimensional optical lattice potential following axial displacement of the trap. The oscillations are shown to have a…
We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting…
The classical dynamical system possessing a quantum spectrum of energy and "quantum" behavior is suggested and investigated. The proposed model can be considered as a dynamical variant of the old quantum theory for harmonic oscillator in…
Recent investigations have looked at the many-body spectra of random two-body interactions. In fermion systems, such as the interacting shell model, one finds pairing-like spectra, while in boson systems, such as IBM-1, one finds rotational…
The collective dynamics of a many-body system is described as a special case of low-energy quantum dynamics, occurring when the ground state breaks a continuous symmetry of the Hamiltonian. This approach is applied to the spontaneous…
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors ranging from thermal noise and frequency noise of the…
In this paper, we investigate a two dimensional isotropic harmonic oscillator on a time-dependent spherical background. The effect of the background can be represented as a minimally coupled field to the oscillator's Hamiltonian. For a…
In this work, concentration properties of quasimodes for perturbed semiclassical harmonic oscillators are studied. The starting point of this research comes from the fact that, in the presence of resonances between frequencies of the…
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
By using Supersymmetric Quantum Mechanics and Semiclassical Quantization, one may argue that the low-lying excited states of any quantum system can be modeled by a set of harmonic oscillators. In the present paper, we fit the experimental…
The properties of cyclic structures (toroidal oscillators) based on classical tripolar (colour) fields are discussed, in particular, of a cyclic structure formed of three colour-singlets spinning around a ring-closed axis. It is shown that…
A new quartic force field for the SO$_2$ $\tilde{\text{C}}$$^1$B$_2$ state has been derived, based on high resolution data from S$^{16}$O$_2$ and S$^{18}$O$_2$. Included are eight $b_2$ symmetry vibrational levels of S$^{16}$O$_2$ reported…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…
We study the collective dynamics of noise-driven excitable elements, so-called active rotators. Crucially here, the natural frequencies and the individual coupling strengths are drawn from some joint probability distribution. Combining a…
Via the application of parallel magnetic field, we induce a single-layer to bilayer transition in two-dimensional electron systems confined to wide GaAs quantum wells, and study the geometric resonance of composite fermions (CFs) with a…
Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with…
At the classical level anyons with harmonic confinement are known to exhibit two important properties namely partial separability and pseudo-integrability. These stem from the fact that this system is locally identical to isotropic…