2026/07/05 by Abdullah Guvendi, Hassan Hassanabadi, Semra Gurtas Dogan +1 · 1 voice
Physics and Astronomy · #physics.class-ph
We analyze the classical dynamics of a charged particle constrained to a helicoidally embedded Riemannian manifold in ℝ3 under a uniform magnetic field in the ambient space. The induced metric ds2=du2+(1+w2u2)dv2 and the pulled-back symmetric gauge yield an exact reduction to a one-dimensional nonlinear Hamiltonian system. The resulting effective potential couples geometry and magnetic field, producing transitions between bounded and unbounded motion and a reorganization of phase-space topology. In the asymptotic regime, the dynamics reduces to a harmonic oscillator with ωeff=ωc/2 and ℓ=√(2) ℓB. The system admits a Landau-type semiclassical spectrum and exhibits a geometry--magnetic control parameter Λ=qB+ℏ kv w governing a chirality transition.