Continuum limit for a discrete Hodge-Dirac operator on square lattices
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912942805483520 |
|---|---|
| author | Miranda, Pablo Parra, Daniel |
| author_facet | Miranda, Pablo Parra, Daniel |
| contents | 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 Schrödinger 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Continuum limit for a discrete Hodge-Dirac operator on square lattices Miranda, Pablo Parra, Daniel Mathematical Physics Functional Analysis 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 Schrödinger 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. |
| title | Continuum limit for a discrete Hodge-Dirac operator on square lattices |
| topic | Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2304.00153 |