{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:20:53Z","timestamp":1760145653084,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T00:00:00Z","timestamp":1724025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"JSPS Grant-in-Aid","award":["21K03292"],"award-info":[{"award-number":["21K03292"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>It is a common postulate that spectral properties of operators describing physical systems are independent of the underlying reference frames. For the Laplace operator on topological crystals, we prove such a statement from a deeper analysis of the behavior of spectral properties with respect to arbitrary choices. In particular, we investigate the impact of the choice of a unit cell, and of the choice of a family of generators for the transformation group.<\/jats:p>","DOI":"10.3390\/sym16081073","type":"journal-article","created":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T01:38:45Z","timestamp":1724117925000},"page":"1073","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topological Crystals: Independence of Spectral Properties with Respect to Reference Systems"],"prefix":"10.3390","volume":"16","author":[{"given":"Koichi","family":"Kato","sequence":"first","affiliation":[{"name":"Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan"}]},{"given":"Serge","family":"Richard","sequence":"additional","affiliation":[{"name":"Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan"},{"name":"Institute for Liberal Arts and Sciences, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sunada, T. 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Spectral Invariants and Their Application on Spectral Characterization of Graphs. Axioms, 11.","DOI":"10.3390\/axioms11060260"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/978-3-319-16619-3_7","article-title":"Intrinsic metrics on graphs: A survey","volume":"128","author":"Keller","year":"2015","journal-title":"Math. Technol. Netw."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"397","DOI":"10.4171\/jst\/35","article-title":"Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions","volume":"2","author":"Haeseler","year":"2012","journal-title":"J. Spectr. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Folland, G.B. (2016). A Course in Abstract Harmonic Analysis, CRC Press. 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