Related papers: Periodic orbits in time-dependent planar Stark-Zee…
The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…
A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…
Spectral properties of the Hamiltonian function which characterizes a trapped ion are investigated. In order to study semiclassical dynamics of trapped ions, coherent state orbits are introduced as sub-manifolds of the quantum state space,…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
Particle trajectories in the form of a logarithmic spiral with specified angular time dependence, "ZK spirals," are shown to be analytic solutions for motion in non-central, but simple force power-laws. Each ZK spiral is a particular…
This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be…
This paper presents a combined sliding-mode control and subspace stabilization methodology for orbital stabilization of periodic trajectories in underactuated mechanical systems with one degree of underactuation. The approach starts with…
The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family…
We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on…
Spin-orbit coupling is a single-particle phenomenon known to generate topological order, and electron-electron interactions cause ordered many-body phases to exist. The rich interplay of these two mechanisms is present in a broad range of…
We reexamine the popular belief that a telluric planet or satellite on an eccentric orbit can, outside a spin-orbit resonance, be captured in a quasi-static tidal equilibrium called pseudosynchronous rotation. The existence of such…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…
Solar flares are explosive releases of magnetic energy stored in the solar corona, driven by magnetic reconnection. These events accelerate electrons, generating hard X-ray emissions and often display Quasi Periodic Pulsations (QPPs) across…
Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -- a prototypical system of 'quantum chaos' --…
The interplay between spin and orbital degrees of freedom gives rise to a variety of emergent phases in correlated 4d and 5d transition-metal systems. Strong spin-orbit coupling (SOC) significantly alters Jahn-Teller (JT) physics, often…
Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…
The influence of correlation effects on the orbital moments for transition metals and their alloys is studied by first-principle relativistic Density Functional Theory in combination with the Dynamical Mean-Field Theory. In contrast to the…
The rotation period of some planet-hosting stars appears to be in close commensurability with the orbital period of their close-by planets. A model is proposed to interpret such a phenomenon based on the excitation of resonant oscillations…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Understanding the dynamics around rotating black holes is imperative to the success of the future gravitational wave observatories. Although integrable in principle, test particle orbits in the Kerr spacetime can also be elaborate, and…