Related papers: Angular Normal Modes of a Circular Coulomb Cluster
Although time-reversal and inversion symmetry constrain the angular momentum of each phonon mode to vanish, we show that the vacuum state of crystals with such symmetries can nevertheless exhibit finite angular momentum fluctuations, which…
Zone-center phonon frequencies of polar lattices are calculated for uniaxial crystals from the symmetry arguments. Long-range Coulomb forces and crystal anisotropy are explicitly taken into account. Free-carrier contributions into a…
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures…
Using an expansion in order parameters, the equation of motion for the centroid of globally coupled oscillators with natural frequencies taken from a distribution is obtained for the case of high coupling, low dispersion of natural…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive…
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…
In this article, we study spatial Stark-Zeeman systems which describe the dynamics of a charged particle moving in three-dimensional space under the influence of a Coulomb potential, a magnetic field, and an electric field, possibly…
We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at second…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
The mutual compatibility of the dynamical equations and constraints describing a massive particle of arbitrary spin, though essential for consistency, is generically lost in the presence of interactions. The conventional Lagrangian approach…
The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions…
We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable…
In the frame of the Lindblad theory of open quantum systems, the system of three uncoupled harmonic oscillators with opening operators linear in the coordinates and momenta of the considered system is analyzed. The damping of the angular…
We present a new three-parameter family of self-consistent equilibrium models for quasi-relaxed stellar systems that are subject to the combined action of external tides and rigid internal rotation. These models provide an idealised…
The coherent quantum dynamics of a single bosonic spin variable, subject to a constraint derived from the quantum spherical model of a ferromagnet, and coupled to an external heat bath, is studied through the Lindblad equation for the…
In this paper we study cluster synchronization in networks of oscillators with heterogenous Kuramoto dynamics, where multiple groups of oscillators with identical phases coexist in a connected network. Cluster synchronization is at the…
We propose a mechanism to explain the fluctuations of the ground state energy in quantum dots in the Coulomb blockade regime. Employing the random matrix theory we show that shape deformations may change the adjacent peak spacing…
We study the fluctuations in the discrete spectrum of the hyperbolic Laplacian for the modular domain using smooth counting functions. We show that in a certain regime, these have Gaussian fluctuations.
We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with…