ArticleNature communications2022
Simulating hyperbolic space on a circuit board.
Article in Nature communications, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
What it found
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
11 citing papers in PubMed.
- Topological non-Abelian gauge structures in Cayley-Schreier lattices.Nature communications · 2026Article
- Space and space-time topologies in a type-II hyperbolic lattice.Nature communications · 2026Article
- Topology in Thermal, Particle, and Plasma Diffusion Metamaterials.Chemical reviews · 2025Review
- Octupole topological insulating phase protected by a three-dimensional momentum-space nonsymmorphic group.National science review · 2025Article
- Hyperbolic Topological Quantum Sources.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Topolectrical space-time circuits.Nature communications · 2025Article
- Anomalous and Chern topological waves in hyperbolic networks.Nature communications · 2024Article
- Observation of a Higher-Order End Topological Insulator in a Real Projective Lattice.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2024Article
- Hyperbolic photonic topological insulators.Nature communications · 2024Article
- Hyperbolic band topology with non-trivial second Chern numbers.Nature communications · 2023Article
- Hyperbolic matter in electrical circuits with tunable complex phases.Nature communications · 2023Article
Corrections and comments
PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.
Authors and funding
15 authors.
Funding
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.
Identifiers
What OpenQuestion holds
Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.