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arXiv · 2508.17813

Interfaces of discrete systems - spectral and index properties

Chris Bourne
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Abstract

We develop a general mathematical framework to study mixtures of different physical systems brought together on a discrete interface. Adapting work by M\u{a}ntoiu et al., we use an operator algebraic framework such that the bulk systems at infinity of the mixture are recovered via the spatial asymptotics of the operators on the interface. Fixing an asymptotics and interface algebra, we show how the essential spectrum and topological properties can be inferred from the bulk systems at infinity. By working with Hilbert $C^*$-modules, we can further refine these results with respect to an ambient algebra of observables.

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Chris Bourne. 2025-08-25. Interfaces of discrete systems - spectral and index properties. https://doi.org/10.1063/5.0301253

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