Ideal quantum metrics from fractional Laplacians
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915141604343808 |
|---|---|
| author | Gerontogiannis, Dimitris Michail Mesland, Bram |
| author_facet | Gerontogiannis, Dimitris Michail Mesland, Bram |
| contents | We develop a novel framework for Monge--Kantorovič metrics using Schatten ideals and commutators of fractional Laplacians on Ahlfors regular spaces. Notably, for those metrics we derive closed formulas in terms of spectra of higher-order fractional Laplacians. For our proofs we develop new techniques in noncommutative geometry, in particular a Weyl law and Schatten-class commutators, yielding refined quantum metrics on the space of Borel probability measures. Lastly, our fractional analysis extends to dynamical systems. We showcase this in the setting of expansive algebraic $\mathbb Z^m$-actions and homoclinic $C^*$-algebras of certain hyperbolic dynamical systems. These findings illustrate the versatility of fractional analysis in fractal geometry, dynamical systems and noncommutative geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ideal quantum metrics from fractional Laplacians Gerontogiannis, Dimitris Michail Mesland, Bram Operator Algebras Dynamical Systems Functional Analysis Metric Geometry Spectral Theory 31C25, 30L99, 46L87, 46L30, 37A55 We develop a novel framework for Monge--Kantorovič metrics using Schatten ideals and commutators of fractional Laplacians on Ahlfors regular spaces. Notably, for those metrics we derive closed formulas in terms of spectra of higher-order fractional Laplacians. For our proofs we develop new techniques in noncommutative geometry, in particular a Weyl law and Schatten-class commutators, yielding refined quantum metrics on the space of Borel probability measures. Lastly, our fractional analysis extends to dynamical systems. We showcase this in the setting of expansive algebraic $\mathbb Z^m$-actions and homoclinic $C^*$-algebras of certain hyperbolic dynamical systems. These findings illustrate the versatility of fractional analysis in fractal geometry, dynamical systems and noncommutative geometry. |
| title | Ideal quantum metrics from fractional Laplacians |
| topic | Operator Algebras Dynamical Systems Functional Analysis Metric Geometry Spectral Theory 31C25, 30L99, 46L87, 46L30, 37A55 |
| url | https://arxiv.org/abs/2502.04187 |