Effective quantum dynamics on the Möbius strip

Abstract

The Laplace-Beltrami operator in the curved Möbius strip is investigated in the limit when the width of the strip tends to zero. By establishing a norm-resolvent convergence, it is shown that spectral properties of the operator are approximated well by an unconventional flat model whose spectrum can be computed explicitly in terms of Mathieu functions. Contrary to the traditional flat Möbius strip, our effective model contains a geometric potential. A comparison of the three models is made and analytical results are accompanied by numerical computations.

Electronic states in quantum wires on a Möbius strip

“…The properties of nonrelativistic quantum mechanics on the Möbius strip have been previously explored in other works, for instance, in the [26][27][28][29] where only the minimal coupling was considered. In other words, the contribution of the surface was considered only through the modification of the kinetic energy operator for curvilinear coordinates, and no geometric potential.…”