Dynamics of nonlinear excitations of helically confined charges

Compression-induced crossovers for the ground state of classical dipole lattices on a Möbius strip

We explore the ground-state properties of a lattice of classical dipoles spanned on the surface of a Möbius strip. The dipole equilibrium configurations depend significantly on the geometrical parameters of the Möbius strip, as well as on the lattice dimensions. As a result of the variable dipole spacing on the curved surface of the Möbius strip, the ground state can consist of multiple domains with different dipole orientations which are separated by domain-wall-like boundaries. We analyze in particular the dependence of the ground-state dipole configuration on the width of the Möbius strip and highlight two crossovers in the ground state that can be correspondingly tuned. A first crossover changes the dipole lattice from a phase which resists compression to a phase that favors it. The second crossover leads to an exchange of the topological properties of the two involved domains. We conclude with a brief summary and an outlook on more complex topologically intricate surfaces.

Driven toroidal helix as a generalization of the Kapitza pendulum

We explore a model system consisting of a particle confined to move along a toroidal helix while being exposed to a static potential as well as a driving force due to a harmonically oscillating electric field. It is shown that in the limit of a vanishing helix radius, the governing equations of motion coincide with those of the well-known Kapitza pendulum-a classical pendulum with oscillating pivot-implying that the driven toroidal helix represents a corresponding generalization. It is shown that the two dominant static fixed points present in the Kapitza pendulum are also present for a finite helix radius. The dependence of the stability of these two fixed points on the helix radius, the driving amplitude, and the static potential are analyzed analytically. These analytical results are subsequently compared to results corresponding of numerical simulations. Additionally, the most prominent deviations of the driven helix from the Kapitza pendulum with respect to the resulting phase space are investigated and analyzed in some detail. These effects include an unusual transition to chaos and an effective directed transport due to the simultaneous presence of multiple chaotic phase space regions.

External-field-induced dynamics of a charged particle on a closed helix

We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split up of the chaotic part of the phase space, which prevents the particle from inverting its direction of motion. This allows for a nonzero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport. Within our chosen normalized units, the resulting average transport velocity is constant and does not change significantly with the driving amplitude. A very similar effect is found in case of the circularly polarized field and low driving amplitudes. Furthermore, when driving with a circularly polarized field, we unravel a second mechanism of the split up of the chaotic phase space region for very large driving amplitudes. There exists a wide range of parameter values for which trajectories may travel between the two chaotic regions by crossing a permeable cantorus. The limitations of these phenomena, as well as their implication on manipulating directed transport in helical geometries are discussed.

Tunable order of helically confined charges

We investigate a system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field. Due to the confinement, the particles experience an effective interaction that oscillates with the particle distance and allows for the existence of stable bound states, despite the purely repulsive character of the Coulomb interaction. We design an order parameter to classify these bound states and use it to identify a structural crossover of the particle order, occurring when the electric field strength is varied. Amorphous particle configurations for a vanishing electric field and crystalline order in the regime of a strong electric field are observed. We study the impact of parameter variations on the particle order and conclude that the crossover occurs for a wide range of parameter values and even holds for different helical systems.

Electrostatic bending response of a charged helix

We explore the electrostatic bending response of a chain of charged particles confined on a finite helical filament. We analyze how the energy difference ΔE between the bent and the unbent helical chain scales with the length of the helical segment and the radius of curvature and identify features that are not captured by the standard notion of the bending rigidity, normally used as a measure of bending tendency in the linear response regime. Using ΔE to characterize the bending response of the helical chain we identify two regimes with qualitatively different bending behaviors for the ground state configuration: the regime of small and the regime of large radius-to-pitch ratio, respectively. Within the former regime, ΔE changes smoothly with the variation of the system parameters. Of particular interest are its oscillations with the number of charged particles encountered for commensurate fillings which yield length-dependent oscillations in the preferred bending direction of the helical chain. We show that the origin of these oscillations is the nonuniformity of the charge distribution caused by the long-range character of the Coulomb interactions and the finite length of the helix. In the second regime of large values of the radius-to-pitch ratio, sudden changes in the ground state structure of the charges occur as the system parameters vary, leading to complex and discontinuous variations in the ground state bending response ΔE.

Spectroscopy and Directed Transport of Topological Solitons in Crystals of Trapped Ions

We study experimentally and theoretically discrete solitons in crystalline structures consisting of several tens of laser-cooled ions confined in a radio frequency trap. Resonantly exciting localized, spectrally gapped vibrational modes of the soliton, a nonlinear mechanism leads to a nonequilibrium steady state of the continuously cooled crystal. We find that the propagation and the escape of the soliton out of its quasi-one-dimensional channel can be described as a thermal activation mechanism. We control the effective temperature of the soliton's collective coordinate by the amplitude of the external excitation. Furthermore, the global trapping potential permits controlling the soliton dynamics and realizing directed transport depending on its topological charge.

Pinned-to-sliding transition and structural crossovers for helically confined charges

We explore the nonequilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective interactions between the charges induce a coupling of the center of mass to the relative motion which in turn gives rise to a pinned-to-sliding transition with increasing magnitude of the external force. In the sliding regime we observe an Ohmic behavior signified by a constant mobility. Within the same regime a structural transition of the helical particle chain takes place with increasing the helix radius leading to a global change of the crystalline arrangement. The resulting crystal is characterized by the existence of multiple defects whose number increases with the helix radius.

Local equilibria and state transfer of charged classical particles on a helix in an electric field

We explore the effects of a homogeneous external electric field on the static properties and dynamical behavior of two charged particles confined to a helix. In contrast to the field-free setup which provides a separation of the center-of-mass and relative motion, the existence of an external force perpendicular to the helix axis couples the center-of-mass to the relative degree of freedom leading to equilibria with a localized center of mass. By tuning the external field various fixed points are created and/or annihilated through different bifurcation scenarios. We provide a detailed analysis of these bifurcations based on which we demonstrate a robust state transfer between essentially arbitrary equilibrium configurations of the two charges that can be induced by making the external force time dependent.