{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:30:47Z","timestamp":1772253047079,"version":"3.50.1"},"reference-count":86,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T00:00:00Z","timestamp":1666656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council (ERC)","doi-asserted-by":"publisher","award":["742703"],"award-info":[{"award-number":["742703"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Inspired by recent developments in wave propagation and scattering experiments with parity-time (PT) symmetric materials, we discuss reciprocity and representation theorems for 3D inhomogeneous PT-symmetric materials and indicate some applications. We start with a unified matrix-vector wave equation which accounts for acoustic, quantum-mechanical, electromagnetic, elastodynamic, poroelastodynamic, piezoelectric and seismoelectric waves. Based on the symmetry properties of the operator matrix in this equation, we derive unified reciprocity theorems for wave fields in 3D arbitrary inhomogeneous media and 3D inhomogeneous media with PT-symmetry. These theorems form the basis for deriving unified wave field representations and relations between reflection and transmission responses in such media. Among the potential applications are interferometric Green\u2019s matrix retrieval and Marchenko-type Green\u2019s matrix retrieval in PT-symmetric materials.<\/jats:p>","DOI":"10.3390\/sym14112236","type":"journal-article","created":{"date-parts":[[2022,10,26]],"date-time":"2022-10-26T11:53:51Z","timestamp":1666785231000},"page":"2236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Reciprocity and Representations for Wave Fields in 3D Inhomogeneous Parity-Time Symmetric Materials"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1620-8282","authenticated-orcid":false,"given":"Kees","family":"Wapenaar","sequence":"first","affiliation":[{"name":"Department of Geoscience and Engineering, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4529-1134","authenticated-orcid":false,"given":"Evert","family":"Slob","sequence":"additional","affiliation":[{"name":"Department of Geoscience and Engineering, Delft University of Technology, Stevinweg 1, 2628 CN Delft, The Netherlands"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5243","DOI":"10.1103\/PhysRevLett.80.5243","article-title":"Real spectra in non-Hermitian Hamiltonians having PT symmetry","volume":"80","author":"Bender","year":"1998","journal-title":"Phys. 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