Classical scattering of charged particles confined on an inhomogeneous helix

Abstract

We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of mass and the relative motion is provided if and only if the confining manifold represents a homogeneous helix. In this case, bound states of repulsively Coulomb interacting particles occur. For an inhomogeneous helix, the coupling of the center of mass and relative motion induces an energy transfer between the collective and relative motion, leading to dissociation of initially bound states in a scattering process. Due to the time reversal symmetry, a binding of the particles out of the scattering continuum is thus equally possible. We identify the regimes of dissociation for different initial conditions and provide an analysis of the underlying phase space via Poincaré surfaces of section. Bound states inside the inhomogeneity as well as resonant states are identified.

Formation of classical crystals of dipolar particles in a helical geometry

“…In our work we will assume that the helical trap is rigid and no movement can occur away from the helix as done in some recent studies of the charged ions on a helix [34,35]. This effectively means that we assume a tight trapping potential and the cost of excitations in the transverse directions will thus be much larger than the interaction energies.…”

Degeneracy and inversion of band structure for Wigner crystals on a closed helix

“…Indeed, several works [5][6][7][8][9][10] have demonstrated unique novel features arising with respect to the structural and dynamical properties of charged (or dipolar) particles on a helix. First, one encounters that longrange interacting particles effectively experience forces of oscillatory character on the helix.…”

“…Rendering the helix locally inhomogeneous, the center of mass (c.m.) of the particles couples to their relative motions, allowing for dissociation of bound states or binding of particles out of the scattering continuum [9].In view of the structural complexity of helical long-range interacting many-particle systems the natural but intriguing question emerges of what is the dynamical response and, in particular, the vibrational structure of such systems. To address this question we explore the properties and dynamics of crystalline configurations formed by identical charged particles, so-called Wigner crystals [11], confined on a closed helix.…”

Dynamics of nonlinear excitations of helically confined charges

“…It is advantageous to do so in the arc length parametrization s so that the final Euler-Lagrange equations of motion and particularly the kinetic terms would assume the standard form [26]. To this purpose we calculate the matrices…”

“…(2) in both the interaction and the kinetic energy, due to the positiondependent factor |∂ u i r(u i )| 2 . If desired, the latter factor can be removed by transforming to arc-length parametrization s(u) = |∂ u r(u)|du, resulting in the familiar second time derivative terms in the Euler-Lagrange equations of motion for the s i (t) = s[u i (t)] [26], at the cost, however, of losing the explicit analytical form for the interaction energy. We choose dimensionless units by scaling all our physical quantities (e.g., position x, time t, and energy E) with λ, m 0 , and 2h/π as follows:…”