{"id":"https://openalex.org/W7213495841","doi":"https://doi.org/10.48550/arxiv.2609.17563","title":"The Global Geometry of the Gaussian Bures Manifold: Admissible Domain, Spectral Boundary, and Asymptotic Classicality","display_name":"The Global Geometry of the Gaussian Bures Manifold: Admissible Domain, Spectral Boundary, and Asymptotic Classicality","publication_year":2026,"publication_date":"2026-07-22","ids":{"openalex":"https://openalex.org/W7213495841","doi":"https://doi.org/10.48550/arxiv.2609.17563"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17563","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17563","pdf_url":"https://arxiv.org/pdf/2609.17563","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.17563","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5096736595","display_name":"Christian Kerskens","orcid":"https://orcid.org/0000-0003-0823-4648","observed_orcids":["https://orcid.org/0000-0003-0823-4648"]},"institutions":[{"id":"https://openalex.org/I205274468","display_name":"Trinity College Dublin","ror":"https://ror.org/02tyrky19","country_code":"IE","type":"education","lineage":["https://openalex.org/I205274468"]}],"countries":["IE"],"is_corresponding":true,"raw_author_name":"Kerskens, Christian","raw_affiliation_strings":["Trinity College Institute of Neuroscience , Trinity College Dublin , Dublin , Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Trinity College Institute of Neuroscience , Trinity College Dublin , Dublin , Ireland","institution_ids":["https://openalex.org/I205274468"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5096736595"],"corresponding_institution_ids":["https://openalex.org/I205274468"],"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.7529000043869019,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.7529000043869019,"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":0.11429999768733978,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.01590000092983246,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/gaussian-states","display_name":"Gaussian states","score":0.7149999737739563},{"id":"https://openalex.org/keywords/bures-distance","display_name":"Bures distance","score":0.6959999799728394},{"id":"https://openalex.org/keywords/squeezed-states","display_name":"squeezed states","score":0.5849999785423279},{"id":"https://openalex.org/keywords/thermal-states","display_name":"thermal states","score":0.6650000214576721},{"id":"https://openalex.org/keywords/classical-limit","display_name":"classical limit","score":0.5360000133514404},{"id":"https://openalex.org/keywords/quantum-to-classical-transition","display_name":"quantum-to-classical transition","score":0.5059999823570251}],"concepts":[{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6158999800682068},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6111000180244446},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6039000153541565},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.5443000197410583},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4790000021457672},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.40799999237060547},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3944000005722046},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.38510000705718994},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.35100001096725464},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34279999136924744},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.31200000643730164},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3107999861240387},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.3070000112056732},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C183212220","wikidata":"https://www.wikidata.org/wiki/Q3345669","display_name":"Heat kernel","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.25220000743865967},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17563","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17563","pdf_url":"https://arxiv.org/pdf/2609.17563","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.2609.17563","doi":"https://doi.org/10.48550/arxiv.2609.17563","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17563","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.17563","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17563","pdf_url":"https://arxiv.org/pdf/2609.17563","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213495841.pdf","grobid_xml":"https://content.openalex.org/works/W7213495841.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7169858804","https://openalex.org/W7172015831","https://openalex.org/W7143347404","https://openalex.org/W2091646725","https://openalex.org/W6948215467","https://openalex.org/W2975878735","https://openalex.org/W1970091017","https://openalex.org/W4405173611","https://openalex.org/W7213518923","https://openalex.org/W2396710644"],"abstract_inverted_index":{"We":[0,70],"construct":[1],"the":[2,12,22,26,41,48,62,72,93,109,124,160,165],"covariance-sector":[3],"Bures":[4,68,161,172],"geometry":[5,28],"of":[6],"centered":[7],"bosonic":[8],"Gaussian":[9,13,43],"states":[10],"from":[11,108],"symmetric-logarithmic-derivative":[14],"equation":[15],"and":[16,37,82,128,147],"determine":[17],"its":[18,148],"quantum-admissible":[19],"domain.":[20],"At":[21,89,153],"Williamson":[23],"uncertainty":[24],"floor,":[25],"boundary":[27,63],"is":[29,97,145,151],"anisotropic:":[30],"spectrum-changing":[31],"radial":[32,67,176],"coefficients":[33],"diverge,":[34],"whereas":[35],"squeezing":[36],"rotation":[38],"directions":[39],"along":[40],"pure":[42],"orbit":[44],"remain":[45],"finite.":[46],"Dually,":[47],"covariance":[49,80,100],"cometric":[50],"acquires":[51],"an":[52,134],"exact":[53,135],"\\(m^2\\)-dimensional":[54],"kernel":[55],"when":[56],"\\(m\\)":[57],"modes":[58],"become":[59],"pure,":[60],"yet":[61],"remains":[64,168],"at":[65,138],"finite":[66,156],"distance.":[69],"derive":[71],"potential":[73],"\\[":[74,139],"\u03a6=-\\tfrac12\\sum_k\\log(\u03bd_k^2-\\tfrac14),":[75],"\\]":[76,142],"which":[77],"generates":[78],"fixed-frame":[79],"dilation":[81],"equals":[83],"\\(\u03b2F\\)":[84],"on":[85],"fixed-Hamiltonian":[86],"thermal":[87],"families.":[88],"large":[90],"symplectic":[91],"eigenvalue,":[92],"relative":[94],"quantum":[95],"correction":[96],"\\(O(\\hbar^2/\u03bd^2)\\),":[98],"recovering":[99],"Fisher--Rao":[101],"geometry.":[102],"This":[103,143],"intrinsic":[104],"classical":[105,113],"regime":[106],"differs":[107],"pure-state":[110],"boundary,":[111],"where":[112],"statistics":[114],"require":[115],"a":[116,121,154,170],"specified":[117],"measurement":[118],"channel.":[119],"As":[120],"secondary":[122],"comparison,":[123],"normalized":[125],"Bures,":[126],"Fisher--Rao,":[127],"action-matched":[129],"Bures--Wasserstein":[130,166],"determinant":[131],"densities":[132],"possess":[133],"one-mode":[136],"junction":[137,144],"(x,\u03b7)=(\\sqrt\u03c6,\\sqrt\u03c6),\\qquad":[140],"x=2\u03bd/\\hbar.":[141],"kinematic,":[146],"branch":[149],"interpretation":[150],"conditional.":[152],"prescribed":[155],"nonzero":[157],"compression":[158],"rate,":[159],"action":[162],"diverges":[163],"while":[164],"cost":[167],"finite;":[169],"bounded":[171],"budget":[173],"instead":[174],"enforces":[175],"deceleration.":[177]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-09-18T00:00:00"}
