Effective quantum dynamics on the Möbius strip

Abstract: The Laplace-Beltrami operator in the curved M\"obius 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 M\"obius strip, our effective model contains a geometric potential. A comparison of the three models is made and analytical results are accompanied by numerical computations.