The geometry of the Double Gyroid wire network: Quantum and Classical
Ralph M. Kaufmann, Sergei Khlebnikov, Birgit Wehefritz-Kaufmann
TL;DR
This paper explores the geometric and algebraic properties of the Double Gyroid wire network, a novel nanomaterial, using advanced mathematical frameworks of commutative and non-commutative geometry.
Contribution
It introduces a detailed geometric description of the Double Gyroid wire network and links its non-commutative geometry to non-commutative 3-tori, advancing theoretical understanding.
Findings
Connection between the wire network's geometry and non-commutative 3-tori
Application of commutative and non-commutative geometry methods
New insights into the structure of Double Gyroid nanomaterials
Abstract
Quantum wire networks have recently become of great interest. Here we deal with a novel nano material structure of a Double Gyroid wire network. We use methods of commutative and non-commutative geometry to describe this wire network. Its non--commutative geometry is closely related to non-commutative 3-tori as we discuss in detail.
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