Effective Long-Range Interactions in Confined Curved Dimensions

Abstract

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 of equilibria of few-body chains with different symmetry character that are allowed to freely move. An outline concerning the implications on many-body helical chains is provided.

13 pages, 3 Figures

References in corpus (2)

• Controlling a magnetic Feshbach resonance with laser light
• Quantum Phase Transition between (Luttinger) Liquid and Gas of Cold Molecules

Cited by in corpus (16)

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• Bloch dynamics in lattices with long range hoppings
• Classical scattering of charged particles confined on an inhomogeneous helix
• Degeneracy and Inversion of Band Structure for Wigner Crystals on a Toroidal Helix
• Formation of classical crystals of dipolar particles in a helical geometry
• Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping
• Electrostatic bending response of a charged helix
• Quantum few-body bound states of dipolar particles in a helical geometry
• Pinned-to-sliding transition and structural crossovers for helically confined charges
• Local equilibria and state transfer of charged classical particles on a helix in an electric field
• Quantum single-particle properties in a one-dimensional curved space
• Tunable Order of Helically Confined Charges
• External field-induced dynamics of a charged particle on a closed helix
• Driven toroidal helix as a generalization of Kapitzas pendulum
• Formation and crossover of multiple helical dipole chains
• Long-Range Interacting Particles on a Helix: A Statistical and Correlation Analysis of Equilibrium Configurations