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Séminaire de EDP - Physique Mathématique

Continuum limit for a discrete Hodge-Dirac operator on square lattices

Daniel Parra Vogel

( U. of Santiago (Chili) )

Salle de conférences

le 30 janvier 2024 à 11:00

We study the continuum limit for Dirac-Hodge operators defined on the nn-dimensional square lattice hZnh\mathbb{Z}^n as hh goes to 00. This result extends, to a first order discrete differential operator, the known convergence of discrete Schrödinger operators to their continuous counterpart.To establish this discrete analog, we introduce an alternative framework for higher-dimensional discrete differential calculus compared to the standard one defined on simplicial complexes. Subsequently, we express our operator as a differential operator acting on discrete forms, enabling us to demonstrate the convergence to the continuous Dirac-Hodge operator.