{"id":"https://openalex.org/W7221539149","doi":"https://doi.org/10.48550/arxiv.2610.13358","title":"Second quantization and compactness of induced Gaussian quantum Markov semigroups","display_name":"Second quantization and compactness of induced Gaussian quantum Markov semigroups","publication_year":2026,"publication_date":"2026-10-09","ids":{"openalex":"https://openalex.org/W7221539149","doi":"https://doi.org/10.48550/arxiv.2610.13358"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.13358","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13358","pdf_url":"https://arxiv.org/pdf/2610.13358","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.13358","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158461102","display_name":"Zheng Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li, Zheng","raw_affiliation_strings":["School of Mathematics and Statistics , Central South University Changsha 410083 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Central South University Changsha 410083 , China","institution_ids":["https://openalex.org/I139660479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5158461102"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9761000275611877,"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"}},"topics":[{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.9761000275611877,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.004900000058114529,"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/T10020","display_name":"Quantum Information and Cryptography","score":0.004000000189989805,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/second-quantization","display_name":"second quantization","score":0.7870000004768372},{"id":"https://openalex.org/keywords/compact-resolvent","display_name":"compact resolvent","score":0.7459999918937683},{"id":"https://openalex.org/keywords/drift-stability","display_name":"drift stability","score":0.8989999890327454},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.8769999742507935}],"concepts":[{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.9150999784469604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7562000155448914},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5213000178337097},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.5087000131607056},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4999000132083893},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.47909998893737793},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.47540000081062317},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.46709999442100525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45910000801086426},{"id":"https://openalex.org/C31498916","wikidata":"https://www.wikidata.org/wiki/Q583034","display_name":"Locally compact space","level":2,"score":0.45840001106262207},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4302000105381012},{"id":"https://openalex.org/C116827671","wikidata":"https://www.wikidata.org/wiki/Q5155316","display_name":"Compact quantum group","level":4,"score":0.40209999680519104},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.3962000012397766},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.39160001277923584},{"id":"https://openalex.org/C91229774","wikidata":"https://www.wikidata.org/wiki/Q193885","display_name":"Infinitesimal","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36890000104904175},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C109321718","wikidata":"https://www.wikidata.org/wiki/Q6059532","display_name":"Invariant subspace problem","level":5,"score":0.3255999982357025},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C131229623","wikidata":"https://www.wikidata.org/wiki/Q977297","display_name":"Trace class","level":3,"score":0.30979999899864197},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.3093999922275543},{"id":"https://openalex.org/C58450382","wikidata":"https://www.wikidata.org/wiki/Q2147620","display_name":"Locally compact group","level":3,"score":0.3050999939441681},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29750001430511475},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C52627884","wikidata":"https://www.wikidata.org/wiki/Q4424101","display_name":"Random compact set","level":4,"score":0.2646999955177307},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.25450000166893005}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.13358","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13358","pdf_url":"https://arxiv.org/pdf/2610.13358","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.13358","doi":"https://doi.org/10.48550/arxiv.2610.13358","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.13358","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.13358","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13358","pdf_url":"https://arxiv.org/pdf/2610.13358","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221539149.pdf","grobid_xml":"https://content.openalex.org/works/W7221539149.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1495294552","https://openalex.org/W1512127941","https://openalex.org/W1597741994","https://openalex.org/W1892380426","https://openalex.org/W1992390730","https://openalex.org/W2006559232","https://openalex.org/W2049561492","https://openalex.org/W2123720480","https://openalex.org/W2962686114","https://openalex.org/W4226478690","https://openalex.org/W4298194274","https://openalex.org/W4312382362","https://openalex.org/W4411958547","https://openalex.org/W4415291850","https://openalex.org/W4416054083","https://openalex.org/W7117711298","https://openalex.org/W7155564400","https://openalex.org/W7220700992"],"related_works":["https://openalex.org/W4397005187","https://openalex.org/W3198663297","https://openalex.org/W4303477806","https://openalex.org/W2952120086","https://openalex.org/W4300628503","https://openalex.org/W7220700992","https://openalex.org/W2082615644","https://openalex.org/W2035946693","https://openalex.org/W2220770537","https://openalex.org/W4285024695"],"abstract_inverted_index":{"We":[0,58],"characterize":[1],"compactness":[2,31,80,98],"of":[3,42,86],"the":[4,43,71,84,100],"Hilbert-Schmidt":[5,63],"semigroups":[6,13],"induced":[7],"by":[8],"finite-mode":[9],"Gaussian":[10],"quantum":[11],"Markov":[12],"with":[14,74],"a":[15,87,92],"faithful":[16],"normal":[17,44],"invariant":[18,45,101],"state.":[19],"A":[20],"unitary":[21],"second-quantization":[22],"representation":[23],"for":[24,55],"every":[25],"$":[26],"s":[27],"$-embedding":[28],"shows":[29],"that":[30,79,91],"at":[32],"one":[33],"positive":[34],"time,":[35],"compact":[36],"resolvent,":[37],"drift":[38],"stability,":[39],"and":[40,62,70,90],"uniqueness":[41],"state":[46,102],"are":[47],"equivalent.":[48],"These":[49],"conditions":[50],"imply":[51,97],"immediate":[52],"trace-class":[53],"membership":[54],"all":[56],"embeddings.":[57],"derive":[59],"exact":[60],"trace-norm":[61],"norm":[64],"formulas,":[65],"an":[66],"embedding-independent":[67],"trace":[68],"identity,":[69],"generator":[72],"spectrum":[73],"algebraic":[75],"multiplicities.":[76],"Examples":[77],"show":[78],"does":[81],"not":[82,96,104],"require":[83],"existence":[85],"spectral":[88,93],"gap":[89,94],"need":[95],"when":[99],"is":[103],"unique.":[105]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-13T00:00:00"}
