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Simulating hyperbolic space on a circuit board

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 spec...

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Autores principales: Lenggenhager, Patrick M., Stegmaier, Alexander, Upreti, Lavi K., Hofmann, Tobias, Helbig, Tobias, Vollhardt, Achim, Greiter, Martin, Lee, Ching Hua, Imhof, Stefan, Brand, Hauke, Kießling, Tobias, Boettcher, Igor, Neupert, Titus, Thomale, Ronny, Bzdušek, Tomáš
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9334621/
https://www.ncbi.nlm.nih.gov/pubmed/35902574
http://dx.doi.org/10.1038/s41467-022-32042-4
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author Lenggenhager, Patrick M.
Stegmaier, Alexander
Upreti, Lavi K.
Hofmann, Tobias
Helbig, Tobias
Vollhardt, Achim
Greiter, Martin
Lee, Ching Hua
Imhof, Stefan
Brand, Hauke
Kießling, Tobias
Boettcher, Igor
Neupert, Titus
Thomale, Ronny
Bzdušek, Tomáš
author_facet Lenggenhager, Patrick M.
Stegmaier, Alexander
Upreti, Lavi K.
Hofmann, Tobias
Helbig, Tobias
Vollhardt, Achim
Greiter, Martin
Lee, Ching Hua
Imhof, Stefan
Brand, Hauke
Kießling, Tobias
Boettcher, Igor
Neupert, Titus
Thomale, Ronny
Bzdušek, Tomáš
author_sort Lenggenhager, Patrick M.
collection PubMed
description 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.
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spelling pubmed-93346212022-07-30 Simulating hyperbolic space on a circuit board Lenggenhager, Patrick M. Stegmaier, Alexander Upreti, Lavi K. Hofmann, Tobias Helbig, Tobias Vollhardt, Achim Greiter, Martin Lee, Ching Hua Imhof, Stefan Brand, Hauke Kießling, Tobias Boettcher, Igor Neupert, Titus Thomale, Ronny Bzdušek, Tomáš Nat Commun Article 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. Nature Publishing Group UK 2022-07-28 /pmc/articles/PMC9334621/ /pubmed/35902574 http://dx.doi.org/10.1038/s41467-022-32042-4 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Lenggenhager, Patrick M.
Stegmaier, Alexander
Upreti, Lavi K.
Hofmann, Tobias
Helbig, Tobias
Vollhardt, Achim
Greiter, Martin
Lee, Ching Hua
Imhof, Stefan
Brand, Hauke
Kießling, Tobias
Boettcher, Igor
Neupert, Titus
Thomale, Ronny
Bzdušek, Tomáš
Simulating hyperbolic space on a circuit board
title Simulating hyperbolic space on a circuit board
title_full Simulating hyperbolic space on a circuit board
title_fullStr Simulating hyperbolic space on a circuit board
title_full_unstemmed Simulating hyperbolic space on a circuit board
title_short Simulating hyperbolic space on a circuit board
title_sort simulating hyperbolic space on a circuit board
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9334621/
https://www.ncbi.nlm.nih.gov/pubmed/35902574
http://dx.doi.org/10.1038/s41467-022-32042-4
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