{"id":"https://openalex.org/W4226297062","doi":"https://doi.org/10.1142/s1230161222500044","title":"Non-Hermitian Physics and Master Equations","display_name":"Non-Hermitian Physics and Master Equations","publication_year":2022,"publication_date":"2022-03-01","ids":{"openalex":"https://openalex.org/W4226297062","doi":"https://doi.org/10.1142/s1230161222500044"},"language":"en","primary_location":{"id":"doi:10.1142/s1230161222500044","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161222500044","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2201.05367","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049034373","display_name":"Federico Roccati","orcid":"https://orcid.org/0000-0002-6981-0613"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Federico Roccati","raw_affiliation_strings":["Universit\u00e0 degli Studi di Palermo, Dipartimento di Fisica e Chimica \u2013 Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Palermo, Dipartimento di Fisica e Chimica \u2013 Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067776424","display_name":"G. Massimo Palma","orcid":"https://orcid.org/0000-0001-7009-4573"},"institutions":[{"id":"https://openalex.org/I4210087815","display_name":"Istituto Nanoscienze","ror":"https://ror.org/0042e5975","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210087815","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Massimo Palma","raw_affiliation_strings":["NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, 56127 Pisa, Italy","Universit\u00e0 degli Studi di Palermo, Dipartimento di Fisica e Chimica \u2013 Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I4210087815"]},{"raw_affiliation_string":"Universit\u00e0 degli Studi di Palermo, Dipartimento di Fisica e Chimica \u2013 Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048485245","display_name":"Francesco Ciccarello","orcid":"https://orcid.org/0000-0002-6061-1255"},"institutions":[{"id":"https://openalex.org/I4210087815","display_name":"Istituto Nanoscienze","ror":"https://ror.org/0042e5975","country_code":"IT","type":"facility","lineage":["https://openalex.org/I4210087815","https://openalex.org/I4210155236"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Ciccarello","raw_affiliation_strings":["NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, 56127 Pisa, Italy","Universit\u00e0 degli Studi di Palermo, Dipartimento di Fisica e Chimica \u2013 Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NEST, Istituto Nanoscienze-CNR, Piazza S. Silvestro 12, 56127 Pisa, Italy","institution_ids":["https://openalex.org/I4210087815"]},{"raw_affiliation_string":"Universit\u00e0 degli Studi di Palermo, Dipartimento di Fisica e Chimica \u2013 Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043441302","display_name":"\u0424\u0430\u0431\u0438\u043e \u0411\u0430\u0433\u0430\u0440\u0435\u043b\u043b\u043e","orcid":"https://orcid.org/0000-0002-4454-091X"},"institutions":[{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fabio Bagarello","raw_affiliation_strings":["Universit\u00e0 degli Studi di Palermo, Dipartimento di Ingegneria, viale delle Scienze, I\u201390128 Palermo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e0 degli Studi di Palermo, Dipartimento di Ingegneria, viale delle Scienze, I\u201390128 Palermo, Italy","institution_ids":["https://openalex.org/I900890020"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5049034373"],"corresponding_institution_ids":["https://openalex.org/I900890020"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04564308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"01","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9399999976158142,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9399999976158142,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.009999999776482582,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.006399999838322401,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/master-equation","display_name":"Master equation","score":0.8714376091957092},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.8135030269622803},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6770285367965698},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5485672354698181},{"id":"https://openalex.org/keywords/lindblad-equation","display_name":"Lindblad equation","score":0.5468361973762512},{"id":"https://openalex.org/keywords/density-matrix","display_name":"Density matrix","score":0.5154739022254944},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.46430352330207825},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.457681804895401},{"id":"https://openalex.org/keywords/open-quantum-system","display_name":"Open quantum system","score":0.45501509308815},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.42653992772102356},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.42463916540145874},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.42163345217704773},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3600916564464569},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3463910222053528},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34238147735595703},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.0667104721069336}],"concepts":[{"id":"https://openalex.org/C128805008","wikidata":"https://www.wikidata.org/wiki/Q722878","display_name":"Master equation","level":3,"score":0.8714376091957092},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8135030269622803},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6770285367965698},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5485672354698181},{"id":"https://openalex.org/C201540876","wikidata":"https://www.wikidata.org/wiki/Q4476520","display_name":"Lindblad equation","level":4,"score":0.5468361973762512},{"id":"https://openalex.org/C56911000","wikidata":"https://www.wikidata.org/wiki/Q831774","display_name":"Density matrix","level":3,"score":0.5154739022254944},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.46430352330207825},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.457681804895401},{"id":"https://openalex.org/C190474826","wikidata":"https://www.wikidata.org/wiki/Q2495111","display_name":"Open quantum system","level":3,"score":0.45501509308815},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42653992772102356},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.42463916540145874},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.42163345217704773},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3600916564464569},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3463910222053528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34238147735595703},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0667104721069336},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s1230161222500044","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1230161222500044","pdf_url":null,"source":{"id":"https://openalex.org/S27332288","display_name":"Open Systems & Information Dynamics","issn_l":"1230-1612","issn":["1230-1612","1573-1324","1793-7191"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Systems & Information Dynamics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2201.05367","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.05367","pdf_url":"https://arxiv.org/pdf/2201.05367","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:iris.unipa.it:10447/583092","is_oa":false,"landing_page_url":"https://hdl.handle.net/10447/583092","pdf_url":null,"source":{"id":"https://openalex.org/S4306401065","display_name":"Nova Science Publishers (Nova Science Publishers, Inc.)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2201.05367","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2201.05367","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2201.05367","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.05367","pdf_url":"https://arxiv.org/pdf/2201.05367","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G344244721","display_name":null,"funder_award_id":"2017SRN-BRK QUSHIP","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W647986212","https://openalex.org/W1531935167","https://openalex.org/W1578322733","https://openalex.org/W1834921197","https://openalex.org/W1911969426","https://openalex.org/W1949069070","https://openalex.org/W1973828774","https://openalex.org/W1988877211","https://openalex.org/W1997323544","https://openalex.org/W2009626025","https://openalex.org/W2011317146","https://openalex.org/W2027807896","https://openalex.org/W2067123857","https://openalex.org/W2142869914","https://openalex.org/W2166080990","https://openalex.org/W2754319903","https://openalex.org/W2781491230","https://openalex.org/W2803613909","https://openalex.org/W2883094646","https://openalex.org/W2908266731","https://openalex.org/W2912642261","https://openalex.org/W2912742595","https://openalex.org/W2952385327","https://openalex.org/W2968252257","https://openalex.org/W2976994215","https://openalex.org/W2994665279","https://openalex.org/W3007798922","https://openalex.org/W3016299042","https://openalex.org/W3038300569","https://openalex.org/W3106269494","https://openalex.org/W3109565621","https://openalex.org/W3159544771","https://openalex.org/W3174787793","https://openalex.org/W4234011924","https://openalex.org/W4256298143"],"related_works":["https://openalex.org/W11966537","https://openalex.org/W36895355","https://openalex.org/W684975","https://openalex.org/W18873504","https://openalex.org/W37599226","https://openalex.org/W28577060","https://openalex.org/W44112049","https://openalex.org/W9105453","https://openalex.org/W20818496","https://openalex.org/W39508268"],"abstract_inverted_index":{"A":[0],"longstanding":[1],"tool":[2],"to":[3,43,70,82],"characterize":[4],"the":[5,13,38,51,88],"evolution":[6],"of":[7,46,53,62,78],"open":[8,22],"Markovian":[9],"quantum":[10,23],"systems":[11,24],"is":[12],"GKSL":[14,84],"(Gorini-Kossakowski-Sudarshan-Lindblad)":[15],"master":[16,85],"equation.":[17],"However,":[18],"in":[19,37,68],"some":[20],"cases,":[21],"can":[25],"be":[26],"effectively":[27],"described":[28],"with":[29],"non-Hermitian":[30,80],"Hamiltonians,":[31],"which":[32],"have":[33],"attracted":[34],"great":[35],"interest":[36],"last":[39],"twenty":[40],"years":[41],"due":[42],"a":[44,59,83],"number":[45],"unconventional":[47],"properties,":[48],"such":[49],"as":[50],"appearance":[52],"exceptional":[54],"points.":[55],"Here,":[56],"we":[57],"present":[58],"short":[60],"review":[61],"these":[63],"two":[64],"different":[65,76],"approaches":[66],"aiming":[67],"particular":[69],"highlight":[71],"their":[72],"relation":[73],"and":[74],"illustrate":[75],"ways":[77],"connecting":[79],"Hamiltonian":[81],"equation":[86],"for":[87],"full":[89],"density":[90],"matrix.":[91]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2022-05-05T00:00:00"}