Quantum strips on surfaces

Hardy Inequalities in Strips on Ruled Surfaces

Problems linking the geometry of two-dimensional manifolds and the spectrum of associated Laplacians have been considered for more than a century. While classical motivations come from theories of elasticity and electromagnetism, the same rather simple models can be also remarkably successful in describing even rather complicated phenomena in quantum heterostructures. Here, an enormous amount o...

Quantum Mechanics on Surfaces

Quantum Codes on Hurwitz Surfaces

Ever since the birth of the first quantum error correcting code, many error correcting techniques and formalism has been constructed so far. Among those, generating a quantum code on a locally planar geometry have lead to some interesting classes of codes. Main idea of this thesis stems from Kitaev's Toric code, which was the first surface code, yet it suffered from having a asymptotically vani...

Quantum Mechanics on Curves & Surfaces

In order to describe the quantum mechanics of a particle confined to a curve or a surface in R Schrödinger’s equation must be modified in two ways. The kinetic energy operator must be written in terms of the metric g induced on the surface from the flat space metric Gij = δij . The potential energy term must be modified by the inclusion of a geometric potential, necessary to constrain the parti...

Hyperbolic non-Euclidean elastic strips and almost minimal surfaces.

We study equilibrium configurations of thin and elongated non-Euclidean elastic strips with hyperbolic two-dimensional reference metrics ā which are invariant along the strip. In the vanishing thickness limit energy minima are obtained by minimizing the integral of the mean curvature squared among all isometric embeddings of ā. For narrow strips these minima are very close to minimal surfaces r...