Can I read Continuum limit for a discrete Hodge-Dirac operator on square lattices on EtoBox?

Continuum limit for a discrete Hodge-Dirac operator on square lattices by Miranda, Pablo; Parra, Daniel is a scholarly article available to read on EtoBox.

What is Continuum limit for a discrete Hodge-Dirac operator on square lattices about?

We study the continuum limit for Dirac-Hodge operators defined on the $n$ dimensional square lattice $h\mathbb{Z}^n$ as $h$ goes to $0$. This result extends to a first order discrete differential operator the known convergence of discrete Schr\"odinger operators to their continuous counterpart. To be able to define such a discrete analog, we start by defining an alternative framework for a higher-dimensional discrete differential calculus. We believe that this framework, that generalize the standard one defined on simplicial complexes, could be of independent interest. We then express our operator as a differential operator acting on discrete forms to finally be able to show the limit to the continuous Dirac-Hodge operator.

Author

Miranda, Pablo; Parra, Daniel

Published

2023

Language

EN