Quantum Mechanics of a Particle Confined to a Twisted Ring
Shuji Takagi, Tôru Tanzawa
We derive an effective Hamiltonian for a particle confined to a thin tube which is gently twisted and curved to form a closed loop. The Hamiltonian describes the effect of both the curvature and the torsion of the loop correctly to the second order. Applied to the case of a tube of circular cross section, it reveals complete analogy with the Aharonov-Bohm effect. We also discuss eigenmodes for Möbius-like rings formed by a tube of non-circular cross section.
Progress of Theoretical Physics•Mar 1, 1992•57 citations