{"id":"https://openalex.org/W2737287944","doi":"https://doi.org/10.1109/cdc.2017.8264475","title":"Lyapunov stability analysis for invariant states of quantum systems","display_name":"Lyapunov stability analysis for invariant states of quantum systems","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2737287944","doi":"https://doi.org/10.1109/cdc.2017.8264475","mag":"2737287944"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2017.8264475","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8264475","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.07372","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090608465","display_name":"Muhammad F. Emzir","orcid":"https://orcid.org/0000-0002-1855-2124"},"institutions":[{"id":"https://openalex.org/I40053085","display_name":"Australian Defence Force Academy","ror":"https://ror.org/02j5s7g39","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571","https://openalex.org/I40053085","https://openalex.org/I4394709116"]},{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Muhammad F. Emzir","raw_affiliation_strings":["School of Engineering and Information Technology, University of New South Wales, ADFA, Canberra, Australia","School of Engineering and Information Technology, University of New South Wales @ ADFA, Canberra ACT 2600, Australia"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Information Technology, University of New South Wales, ADFA, Canberra, Australia","institution_ids":["https://openalex.org/I40053085","https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Engineering and Information Technology, University of New South Wales @ ADFA, Canberra ACT 2600, Australia","institution_ids":["https://openalex.org/I40053085","https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011597574","display_name":"Ian R. Petersen","orcid":"https://orcid.org/0000-0003-4856-9450"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ian R. Petersen","raw_affiliation_strings":["ANU College of Engineering & Computer Science, The Australian National University, Canberra, Australia","[ANU College of Engineering and Computer Science, The Australian National University, Canberra, Australia]"],"affiliations":[{"raw_affiliation_string":"ANU College of Engineering & Computer Science, The Australian National University, Canberra, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"[ANU College of Engineering and Computer Science, The Australian National University, Canberra, Australia]","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103032262","display_name":"Matthew J. Woolley","orcid":"https://orcid.org/0000-0002-8716-3675"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]},{"id":"https://openalex.org/I40053085","display_name":"Australian Defence Force Academy","ror":"https://ror.org/02j5s7g39","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571","https://openalex.org/I40053085","https://openalex.org/I4394709116"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Matthew J. Woolley","raw_affiliation_strings":["School of Engineering and Information Technology, University of New South Wales, ADFA, Canberra, Australia","School of Engineering and Information Technology, University of New South Wales @ ADFA, Canberra ACT 2600, Australia"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Information Technology, University of New South Wales, ADFA, Canberra, Australia","institution_ids":["https://openalex.org/I40053085","https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Engineering and Information Technology, University of New South Wales @ ADFA, Canberra ACT 2600, Australia","institution_ids":["https://openalex.org/I40053085","https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090608465"],"corresponding_institution_ids":["https://openalex.org/I31746571","https://openalex.org/I40053085"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11155638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":null,"first_page":"5505","last_page":"5510"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9828000068664551,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6467851400375366},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6454206705093384},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6258955001831055},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4912874102592468},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.4726782441139221},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4623056948184967},{"id":"https://openalex.org/keywords/lyapunov-equation","display_name":"Lyapunov equation","score":0.4603644609451294},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45560163259506226},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4262714385986328},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3658595085144043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35148105025291443},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.12714362144470215},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.109063059091568},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10513272881507874},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06713694334030151}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6467851400375366},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6454206705093384},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6258955001831055},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4912874102592468},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.4726782441139221},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4623056948184967},{"id":"https://openalex.org/C25854792","wikidata":"https://www.wikidata.org/wiki/Q1028945","display_name":"Lyapunov equation","level":4,"score":0.4603644609451294},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45560163259506226},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4262714385986328},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3658595085144043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35148105025291443},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.12714362144470215},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.109063059091568},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10513272881507874},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06713694334030151},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/cdc.2017.8264475","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8264475","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1707.07372","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.07372","pdf_url":"https://arxiv.org/pdf/1707.07372","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":"","raw_type":"text"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/199974","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/199974","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017","raw_type":"Conference paper"},{"id":"doi:10.48550/arxiv.1707.07372","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1707.07372","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"},{"id":"mag:2737287944","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.07372","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.07372","pdf_url":"https://arxiv.org/pdf/1707.07372","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4974500837","display_name":null,"funder_award_id":"FL110100020","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2737287944.pdf","grobid_xml":"https://content.openalex.org/works/W2737287944.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1530682388","https://openalex.org/W1631356911","https://openalex.org/W1964281470","https://openalex.org/W1994439515","https://openalex.org/W2032085905","https://openalex.org/W2039540991","https://openalex.org/W2046936035","https://openalex.org/W2061260383","https://openalex.org/W2070389945","https://openalex.org/W2071818368","https://openalex.org/W2083520306","https://openalex.org/W2096501535","https://openalex.org/W2097876164","https://openalex.org/W2112046594","https://openalex.org/W2114626490","https://openalex.org/W2119389186","https://openalex.org/W2124714273","https://openalex.org/W2126953747","https://openalex.org/W2127981459","https://openalex.org/W2134403289","https://openalex.org/W2152430211","https://openalex.org/W2156888328","https://openalex.org/W2163872159","https://openalex.org/W2185709682","https://openalex.org/W2187891975","https://openalex.org/W2499754680","https://openalex.org/W2795696665","https://openalex.org/W2962777935","https://openalex.org/W2963942263","https://openalex.org/W2983536868","https://openalex.org/W3098532013","https://openalex.org/W3098587343","https://openalex.org/W3106524425","https://openalex.org/W6730594208"],"related_works":["https://openalex.org/W2902405931","https://openalex.org/W2983828834","https://openalex.org/W2292187384","https://openalex.org/W2604089502","https://openalex.org/W1988260983","https://openalex.org/W1976077083","https://openalex.org/W2786351342","https://openalex.org/W2780579194","https://openalex.org/W2337957759","https://openalex.org/W2005824792","https://openalex.org/W2344273278","https://openalex.org/W2596093749","https://openalex.org/W2043399761","https://openalex.org/W2536900284","https://openalex.org/W3126740471","https://openalex.org/W1677267862","https://openalex.org/W2004194090","https://openalex.org/W2992304969","https://openalex.org/W2965993008","https://openalex.org/W2040280226"],"abstract_inverted_index":{"In":[0,21],"this":[1,39,93],"article,":[2],"we":[3,41],"propose":[4],"a":[5,18,56,96],"Lyapunov":[6,98],"stability":[7,91],"approach":[8],"to":[9,23,88],"analyze":[10,42,89],"the":[11,14,43,50,62,75,90],"convergence":[12,27,44],"of":[13,17,45,52,64,77,92],"density":[15,32,46,53,66,82],"operator":[16],"quantum":[19],"system.":[20],"contrast":[22],"many":[24],"previously":[25],"studied":[26],"analysis":[28],"methods":[29],"for":[30],"invariant":[31,65,81],"operators":[33,47,54,67],"which":[34,73],"use":[35],"weak":[36],"convergence,":[37],"in":[38],"article":[40],"by":[48],"considering":[49],"set":[51,63,94],"as":[55],"Banach":[57],"space.":[58],"We":[59,84],"show":[60,86],"that":[61],"is":[68],"both":[69],"closed":[70],"and":[71],"convex,":[72],"implies":[74],"impossibility":[76],"having":[78],"multiple":[79],"isolated":[80],"operators.":[83],"then":[85],"how":[87],"via":[95],"candidate":[97],"operator.":[99]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}