A spin-less particle on a rotating curved surface in Minkowski space

Abstract

In Minkowski space  , we derive the effective Schrödinger equation describing a spin-less particle confined to a rotating curved surface  . Using the thin-layer quantization formalism to constrain the particle on  , we obtain the relativity-corrected geometric potential V g ′ , and a novel effective potential V ˜ g related to both the Gaussian curvature and the geodesic curvature of the rotating surface. The Coriolis effect and the centrifugal potential also appear in the equation. Subsequently, we apply the surface Schrödinger equation to a rotating cylinder, sphere and torus surfaces, in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.

Quantum dynamics within curved thin layers with deviation

“…It is straightforward to find that in the absence of the deviation (δ r θ = δ r y = 0), V gc = − h2 2m 1 4r 2 agrees with the previous results in Refs. [16,30]. To elaborately analyze the geometric effects resulting from deviations, in the following, we will take two cases into consideration.…”

“…[11][12][13][14][15] Specifically, the existence of V g results in the appearance of atomic-like bound states on the two-dimensional sheet rolled up into an Archimedean spiral, [5] and reconstructs electron level structures on corrugated nanotubes. [7,8] Moreover, the relativity-corrected geometric potential in Minkowski space [16,17] and the spin connection geometric potential acting on spin particles [17,18] are obtained, which contributes to modulating the transport prop-erties and spin-flip behavior of the particle. Importantly, the validity of this method was further verified by optical analogue realizations of the geometric potential in photonic crystal.…”