{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:11:13Z","timestamp":1773249073222,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T00:00:00Z","timestamp":1738022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Jiangsu Provincial Higher Education Natural Science General Project","award":["24KJD610003"],"award-info":[{"award-number":["24KJD610003"]}]},{"name":"Jiangsu Provincial Higher Education Natural Science General Project","award":["GKYK\/2024\/2"],"award-info":[{"award-number":["GKYK\/2024\/2"]}]},{"name":"Natural Science Foundation of Jiangsu College of Engineering and Technology","award":["24KJD610003"],"award-info":[{"award-number":["24KJD610003"]}]},{"name":"Natural Science Foundation of Jiangsu College of Engineering and Technology","award":["GKYK\/2024\/2"],"award-info":[{"award-number":["GKYK\/2024\/2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We propose a versatile electronic dimer cooperatively coupled by means of mutual induction, capacitance, and resistance. In a lot of related works, the electronic dimer is inductively coupled, with one resonator characterized by positive resistance (dissipation) and the other by negative resistance (amplification). We go beyond this picture by considering capacitive and resistive coupling, and by exploring cases where both resistances are positive, as well as a case where the resonant frequencies of the individual resonators are different. Based on analytical derivation and numerical calculations, we obtain and observe the properties of parity-time (PT), quasi-PT (QPT) and quasi-anti-PT (QAPT) symmetry by adjusting the constitutive parameters of the system. This study provides a versatile and feasible platform for observing PT\/anti-PT (APT) symmetry-based phenomena and provides a foundation for further studies on finding PT\/APT symmetry in more sophisticated circuits.<\/jats:p>","DOI":"10.3390\/sym17020205","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T10:44:30Z","timestamp":1738061070000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Versatile Electronic Dimer Exhibiting PT and Anti-PT Symmetry"],"prefix":"10.3390","volume":"17","author":[{"given":"Ruiqi","family":"Li","sequence":"first","affiliation":[{"name":"School of Intelligent Manufacturing, Jiangsu College of Engineering and Technology, Nantong 226001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayang","family":"Gu","sequence":"additional","affiliation":[{"name":"School of Intelligent Manufacturing, Jiangsu College of Engineering and Technology, Nantong 226001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,28]]},"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. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2201","DOI":"10.1063\/1.532860","article-title":"PT-symmetric quantum mechanics","volume":"40","author":"Bender","year":"1999","journal-title":"J. Math. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2632","DOI":"10.1364\/OL.32.002632","article-title":"Theory of coupled optical PT-symmetric structures","volume":"32","author":"Makris","year":"2007","journal-title":"Opt. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1038\/nphys1515","article-title":"Observation of parity\u2013time symmetry in optics","volume":"6","author":"Makris","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1126\/science.1258480","article-title":"Parity-time symmetric microring lasers","volume":"346","author":"Hodaei","year":"2014","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1126\/science.1258479","article-title":"Single-mode laser by parity-time symmetry breaking","volume":"346","author":"Feng","year":"2014","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"213901","DOI":"10.1103\/PhysRevLett.106.213901","article-title":"Unidirectional Invisibility Induced by PT-Symmetric Periodic Structures","volume":"106","author":"Lin","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"043803","DOI":"10.1103\/PhysRevA.82.043803","article-title":"PT-symmetric optical structures","volume":"82","author":"Ramezani","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1038\/nature22404","article-title":"Robust wireless power transfer using a nonlinear parity\u2013time-symmetric circuit","volume":"546","author":"Assawaworrarit","year":"2017","journal-title":"Nature"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"053508","DOI":"10.1103\/PhysRevA.108.053508","article-title":"Guided modes in a PT-symmetric waveguide: Real dispersion curves","volume":"108","author":"Zhang","year":"2023","journal-title":"Phys. Rev. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"023820","DOI":"10.1103\/PhysRevA.96.023820","article-title":"Optical fluxes in coupled PT-symmetric photonic structures","volume":"96","author":"Ge","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"031801","DOI":"10.1103\/PhysRevA.82.031801","article-title":"PT-symmetric laser absorber","volume":"82","author":"Longhi","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1038\/nphoton.2016.216","article-title":"Lasing and anti-lasing in a single cavity","volume":"10","author":"Wong","year":"2016","journal-title":"Nat. Photon."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"De Carlo, M., De Leonardis, F., Soref, R.A., Colatorti, L., and Passaro, V.M.N. (2022). Non-Hermitian Sensing in Photonics and Electronics: A Review. Sensors, 22.","DOI":"10.3390\/s22113977"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1038\/s41563-019-0304-9","article-title":"Parity\u2013time symmetry and exceptional points in photonics","volume":"18","author":"Rotter","year":"2019","journal-title":"Nat. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1364\/OPTICA.6.000190","article-title":"Exceptional Surfaces in PT-Symmetric Non-Hermitian Photonic Systems","volume":"6","author":"Zhou","year":"2019","journal-title":"Optica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2182","DOI":"10.1038\/s41467-018-04690-y","article-title":"Observation of an anti-PT-symmetric exceptional point and energy-difference conserving dynamics in electrical circuit resonators","volume":"9","author":"Choi","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1139","DOI":"10.1038\/nphys3842","article-title":"Anti-parity\u2013time symmetry with flying atoms","volume":"12","author":"Peng","year":"2016","journal-title":"Nat. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"053810","DOI":"10.1103\/PhysRevA.88.053810","article-title":"Antisymmetric PT-photonic structures with balanced positive- and negative-index materials","volume":"88","author":"Ge","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"053845","DOI":"10.1103\/PhysRevA.96.053845","article-title":"Anti-PT symmetry in dissipatively coupled optical systems","volume":"96","author":"Yang","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_21","first-page":"444029","article-title":"PT-symmetric electronics","volume":"45","author":"Schindler","year":"2012","journal-title":"Phys. J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"040101","DOI":"10.1103\/PhysRevA.84.040101","article-title":"Experimental study of active LRC circuits with PT symmetries","volume":"84","author":"Schindler","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"033504","DOI":"10.1103\/PhysRevA.110.033504","article-title":"Experimental observation of coherent-perfect-absorber and laser points in anti-PT symmetry","volume":"110","author":"Yang","year":"2024","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s11082-019-2048-9","article-title":"Imaginary resistor based Parity-Time symmetry electronics dimers","volume":"51","author":"Tabeu","year":"2019","journal-title":"Opt. Quant. Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"045010","DOI":"10.1088\/2399-6528\/abf6a4","article-title":"Observation of the perturbed eigenvalues of PT-symmetric LC resonator systems","volume":"5","author":"Zhou","year":"2021","journal-title":"J. Phys. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1140\/epjd\/e2020-10131-7","article-title":"Observation of two PT transitions in an electric circuit with balanced gain and loss","volume":"74","author":"Wang","year":"2020","journal-title":"Eur. Phys. J. D"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"115101","DOI":"10.1088\/1572-9494\/acf285","article-title":"PT-symmetric electronic dimer without gain material","volume":"75","author":"Tagouegni","year":"2023","journal-title":"Commun. Theor. Phys."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1038\/s41565-021-01038-4","article-title":"Fully integrated parity\u2013time-symmetric electronics","volume":"17","author":"Cao","year":"2022","journal-title":"Nat. Nanotechnol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"3035","DOI":"10.1021\/acsphotonics.0c01053","article-title":"Antiparity-Time Symmetry in Passive Nanophotonics","volume":"7","author":"Fan","year":"2020","journal-title":"ACS Photonics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/205\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:37:56Z","timestamp":1759919876000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/2\/205"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,28]]},"references-count":29,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["sym17020205"],"URL":"https:\/\/doi.org\/10.3390\/sym17020205","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1,28]]}}}