# Effective long-range interactions in confined curved dimensions

@article{Schmelcher2011EffectiveLI, title={Effective long-range interactions in confined curved dimensions}, author={Peter Schmelcher}, journal={EPL (Europhysics Letters)}, year={2011}, volume={95}, pages={50005} }

We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience a force which is oscillating with the distance between the particles. This leads to stable equilibrium configurations and correspondingly induced bound states whose number is tunable with the parameters of the helix. We demonstrate the existence of a plethora…

## 13 Citations

### Tunable order of helically confined charges.

- PhysicsPhysical review. E
- 2020

A system of equally charged Coulomb-interacting particles confined to a toroidal helix in the presence of an external electric field is investigated and it is concluded that the crossover occurs for a wide range of parameter values and even holds for different helical systems.

### Quantum few-body bound states of dipolar particles in a helical geometry

- Physics
- 2015

We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this…

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

- PhysicsPhysical review. E
- 2017

The nonequilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix, characterized by the existence of multiple defects whose number increases with the helix radius, is explored.

### Classical scattering of charged particles confined on an inhomogeneous helix.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

The regimes of dissociation for different initial conditions and an analysis of the underlying phase space via Poincaré surfaces of section are identified and bound states inside the inhomogeneity as well as resonant states are identified.

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

- PhysicsPhysical review. E
- 2017

A robust state transfer is demonstrated between essentially arbitrary equilibrium configurations of the two charges that can be induced by making the external force time dependent by tuning the external field.

### Electrostatic bending response of a charged helix.

- PhysicsPhysical review. E
- 2018

This work analyzes 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 identifies features that are not captured by the standard notion of the bending rigidity.

### Formation of classical crystals of dipolar particles in a helical geometry

- Physics
- 2014

We consider crystal formation of particles with dipole–dipole interactions that are confined to move in a one-dimensional helical geometry with their dipole moments oriented along the symmetry axis…

### Quantum single-particle properties in a one-dimensional curved space

- Physics
- 2015

We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible Hamiltonians and…

### Formation and crossover of multiple helical dipole chains

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2022

It is demonstrated that all possible configurations form a self-similar bifurcation diagram which can be linked to the Stern–Brocot tree and the underlying Farey sequence.

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

- PhysicsPhysical review. E
- 2021

The dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field is investigated and a split up of the chaotic part of the phase space is found, which allows for a nonzero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport.

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