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

Abstract

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.

Electrostatic bending response of a charged helix

“…12 (l)) peaks in contrast to its low-f limit (f < f A ), where it is rather uniform, with all the ∆u i acquiring similar values. From such a profile we can conclude that the particles tend to fragment into smaller chains consisting of particles close to each other (small ∆u i ) which are separated by large ∆u i intervals similar to those observed for helically confined charges under a constant driving [28]. The extreme example of such a case, for very large f , would be the number of particles splitting into two approximately equal parts with half the particles occupying the first winding and the other half the last winding of the helix.…”

“…For values of f of order unity and beyond, the helical geometry is imprinted in the interaction potential, leading to the emergence of multiple potential wells which, combined with the hard wall boundary conditions studied here, yield a plethora of equilibrium states. Notably the number of such states is expected to increase very rapidly both with the number of particles N and with the ratio f [23,26,28], resulting in a high degree of complexity and making it particularly difficult to identify the GS of the system.…”

“…Identifying such a GS is a computationally hard task, becoming even intractable for large number of particles and large values of f due to the complexity of the potential energy landscape [23,26,28] and the long-range character of the interactions. A very brief taste of this fact can be given already by inspecting the number of equilibrium states (both stable and unstable) as a function of f for a very small system (N = 4, Fig.…”

Driven toroidal helix as a generalization of Kapitzas pendulum

“…Besides occurring in nature, helical systems of charged particles have recently been explored in the literature thereby demonstrating a number of intriguing effects emerging due to the geometry, such as interactions that oscillate with the (parametrized) distance along the helix [12]. These effects have been studied in lattice systems with long-range hopping [13,14], as well as in more fundamental models of classical charges moving on helices [15][16][17][18][19][20][21][22]. In such model systems, it has been demonstrated that based on the oscillating effective interactions already static setups become very complex since particles are able to localize into irregular lattice-like structures [16,20] exhibiting a plethora of possible equilibrium configurations [12,21].…”

“…In such model systems, it has been demonstrated that based on the oscillating effective interactions already static setups become very complex since particles are able to localize into irregular lattice-like structures [16,20] exhibiting a plethora of possible equilibrium configurations [12,21]. By varying the helix geometry it is possible to tune a variety of effects, such as scattering of bound states at local defects [15], band structure inversion and degeneracies [16,17] or unusual pinned to sliding transitions [18] in crystalline configurations on a toroidal helix.…”