Related papers: Dynamic Stability of The Time-averaged Orbiting Po…
Motivated by recent developments in ion trap design and fabrication, we investigate the stability of ion motion in asymmetrical, planar versions of the classic Paul trap. The equations of motion of an ion in such a trap are generally…
We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…
We study topological transport in the steady state of a quantum particle hopping on a one-dimensional lattice in the presence of dissipation. The model exhibits a rich phase structure, with the average particle velocity in the steady state…
Non-adiabatic motion of Bose-Einstein condensates of rubidium atoms arising from the dynamical nature of a time-orbiting-potential (TOP) trap was observed experimentally. The orbital micromotion of the condensate in velocity space at the…
We present two methods for characterization of motional-mode configurations that are generally applicable to the weak and strong-binding limit of single or multiple trapped atomic ions. Our methods are essential to realize control of the…
We study the stability of symmetric trajectories of a particle on the Lie group $SO(3)$ whose motion is governed by an $SO(3)\times SO(2)$ invariant metric and an $SO(2)\times SO(2)$ invariant potential. Our method is to reduce the number…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
There are various types of motion of a heavy symmetric top like regular precession, cusp like motion, rise of the top, etc. One of the tools used to understand that motion is effective potential. The effective potential for a spinning heavy…
The normal modes of a trapped ion crystal are derived using an approach based on the Hermitian properties of the systems dynamical matrix. This method is equivalent to the standard Bogoliubov method, but for classical systems it is arguably…
We theoretically and experimentally examine the effects of anharmonic terms in the trapping potential for linear chains of trapped ions. We concentrate on two different effects that become significant at different levels of anharmonicity.…
It is shown that in an anisotropic harmonic trap that rotates with the properly chosen rotation rate, the force of gravity leads to a resonant behavior. Full analysis of the dynamics in an anisotropic, rotating trap in 3D is presented and…
We consider a time dependent trap externally manipulated in such a way that one of its bound states is brought into an instant contact with the continuum threshold, and then down again. It is shown that, in the limit of slow evolution, the…
We discuss excited Bose-condensed states and find the criterion of dynamical stability of a kink-wise state, i.e., a standing matter wave with one nodal plane perpendicular to the axis of a cylindrical trap. The dynamical stability requires…
The motion of overdamped particles in a one-dimensional spatially-periodic potential is considered. The potential is also randomly-fluctuating in time, due to multiplicative colored noise terms, and has a deterministic tilt. Numerical…
The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. In the classical low-energy limit, the three characteristic eigenfrequencies of a charged particle trapped in this configuration do not…
We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes…
A one-dimensional run-and-tumble particle (RTP) switches randomly between a left and right moving state of constant speed $v$. This type of motion arises in a wide range of applications in cell biology, including the unbiased growth and…
We study the stability of circular orbits of the electromagnetic two-body problem in an electromagnetic setting that includes retarded and advanced interactions. We give a method to derive the equations of tangent dynamics about circular…
Rotation of atoms in a lattice is studied using a Hubbard model. It is found that the atoms are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in…