Simulating hyperbolic space on a circuit board

Patrick M. Lenggenhager, Alexander Stegmaier, Lavi K. Upreti, Tobias Hofmann, Tobias Helbig, Achim Vollhardt, Martin Greiter, Ching Hua Lee, Stefan Imhof, Hauke Brand, Tobias Kießling, Igor Boettcher, Titus Neupert (), Ronny Thomale () and Tomáš Bzdušek ()
Additional contact information
Patrick M. Lenggenhager: Paul Scherrer Institute
Alexander Stegmaier: Institut für Theoretische Physik und Astrophysik, Universität Würzburg
Lavi K. Upreti: Institut für Theoretische Physik und Astrophysik, Universität Würzburg
Tobias Hofmann: Institut für Theoretische Physik und Astrophysik, Universität Würzburg
Tobias Helbig: Institut für Theoretische Physik und Astrophysik, Universität Würzburg
Achim Vollhardt: University of Zurich
Martin Greiter: Institut für Theoretische Physik und Astrophysik, Universität Würzburg
Ching Hua Lee: National University of Singapore
Stefan Imhof: Physikalisches Institut, Universität Würzburg
Hauke Brand: Physikalisches Institut, Universität Würzburg
Tobias Kießling: Physikalisches Institut, Universität Würzburg
Igor Boettcher: University of Alberta
Titus Neupert: University of Zurich
Ronny Thomale: Institut für Theoretische Physik und Astrophysik, Universität Würzburg
Tomáš Bzdušek: Paul Scherrer Institute

Nature Communications, 2022, vol. 13, issue 1, 1-8

Abstract: Abstract The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://www.nature.com/articles/s41467-022-32042-4 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32042-4

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-022-32042-4

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().