{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T03:43:58Z","timestamp":1778989438128,"version":"3.51.4"},"reference-count":12,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,18]],"date-time":"2017-07-18T00:00:00Z","timestamp":1500336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We derive the quantum analogues of some recently discovered symmetry relations for time correlation functions in systems subject to a constant magnetic field. The symmetry relations deal with the effect of time reversal and do not require\u2014as in the formulations of Casimir and Kubo\u2014that the magnetic field be reversed. It has been anticipated that the same symmetry relations hold for quantum systems. Thus, here we explicitly construct the required symmetry transformations, acting upon the relevant quantum operators, which conserve the Hamiltonian of a system of many interacting spinless particles, under time reversal. Differently from the classical case, parity transformations always reverse the sign of both the coordinates and of the momenta, while time reversal only of the latter. By implementing time reversal in conjunction with ad hoc \u201cincomplete\u201d parity transformations (i.e., transformations that act upon only some of the spatial directions), it is nevertheless possible to achieve the construction of the quantum analogues of the classical maps. The proof that the mentioned symmetry relations apply straightforwardly to quantal time correlation functions is outlined.<\/jats:p>","DOI":"10.3390\/sym9070120","type":"journal-article","created":{"date-parts":[[2017,7,18]],"date-time":"2017-07-18T10:33:14Z","timestamp":1500373994000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Quantum Correlations under Time Reversal and Incomplete Parity Transformations in the Presence of a Constant Magnetic Field"],"prefix":"10.3390","volume":"9","author":[{"given":"Paolo","family":"Gregorio","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sara","family":"Bonella","sequence":"additional","affiliation":[{"name":"Centre Europ\u00e9en de Calcule Atomique et Mol\u00e9culaire (CECAM ), \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4223-6279","authenticated-orcid":false,"given":"Lamberto","family":"Rondoni","sequence":"additional","affiliation":[{"name":"Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy"},{"name":"Graphene@PoliTO Lab, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy"},{"name":"Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giura 1, I-10125 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1103\/RevModPhys.17.343","article-title":"On Onsager\u2019s Principle of Microscopic Reversibility","volume":"17","author":"Casimir","year":"1945","journal-title":"Rev. Mod. Phys."},{"key":"ref_2","unstructured":"Landau, L.D., and Lifshitz, E.M. (1980). Course of Theoretical Physics. Statistical Physics, Butterworth-Heinemann. [3rd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"115014","DOI":"10.1088\/1367-2630\/15\/11\/115014","article-title":"Multivariate fluctuation relations for currents","volume":"15","author":"Gaspard","year":"2013","journal-title":"New J. Phys."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"60004","DOI":"10.1209\/0295-5075\/108\/60004","article-title":"Time reversal symmetry in time-dependent correlation functions for systems in a constant magnetic field","volume":"108","author":"Bonella","year":"2014","journal-title":"EPL"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1143\/JPSJ.12.570","article-title":"Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems","volume":"12","author":"Kubo","year":"1957","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1088\/0034-4885\/29\/1\/306","article-title":"The fluctuation-dissipation theorem","volume":"29","author":"Kubo","year":"1966","journal-title":"Rep. Prog. Phys."},{"key":"ref_7","unstructured":"Brittin, W. (1959). Some aspects of the statistical-mechanical theory of irreversible processes. Lectures in Theoretical Physics, Interscience."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"P04021","DOI":"10.1088\/1742-5468\/2011\/04\/P04021","article-title":"Steady state fluctuation relations and time reversibility for non-smooth chaotic maps","volume":"2011","author":"Colangeli","year":"2011","journal-title":"J. Stat. Mech. Theory Exp."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Dal Cengio, S., and Rondoni, L. (2016). Broken versus Non-Broken Time Reversal Symmetry: Irreversibility and Response. Symmetry, 8.","DOI":"10.3390\/sym8080073"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bonella, S., Coretti, A., Rondoni, L., and Ciccotti, G. (2017). Time-reversal symmetry for systems in a constant external magnetic field. Phys. Rev. E, in press.","DOI":"10.1103\/PhysRevE.96.012160"},{"key":"ref_11","first-page":"546","article-title":"The operation of time reversal in quantum mechanics","volume":"32","author":"Wigner","year":"1932","journal-title":"Nachr. Ges. Wiss. G\u00f6ttingen Math-Physik K1"},{"key":"ref_12","unstructured":"Sachs, R.J. (1987). The Physics of Time Reversal, The University of Chicago Press."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/7\/120\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:04Z","timestamp":1760208184000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/7\/120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,18]]},"references-count":12,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2017,7]]}},"alternative-id":["sym9070120"],"URL":"https:\/\/doi.org\/10.3390\/sym9070120","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7,18]]}}}