{"id":"https://openalex.org/W7128369840","doi":"https://doi.org/10.48550/arxiv.2602.06808","title":"Dynamical low-rank approximation for the semiclassical Schrodinger equation with uncertainties","display_name":"Dynamical low-rank approximation for the semiclassical Schrodinger equation with uncertainties","publication_year":2026,"publication_date":"2026-02-06","ids":{"openalex":"https://openalex.org/W7128369840","doi":"https://doi.org/10.48550/arxiv.2602.06808"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.06808","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125381062","display_name":"Liu Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125420997","display_name":"Limin Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Limin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125405784","display_name":"Zhenyi Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Zhenyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.2581000030040741,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.2581000030040741,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.13740000128746033,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.12630000710487366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/semiclassical-physics","display_name":"Semiclassical physics","score":0.9544000029563904},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5771999955177307},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5149000287055969},{"id":"https://openalex.org/keywords/randomness","display_name":"Randomness","score":0.48089998960494995},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4465999901294708},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4090999960899353},{"id":"https://openalex.org/keywords/quantum-decoherence","display_name":"Quantum decoherence","score":0.3700000047683716},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.3474999964237213}],"concepts":[{"id":"https://openalex.org/C535169671","wikidata":"https://www.wikidata.org/wiki/Q17080006","display_name":"Semiclassical physics","level":3,"score":0.9544000029563904},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5771999955177307},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5149000287055969},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.48089998960494995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4587000012397766},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4399999976158142},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4090999960899353},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3944000005722046},{"id":"https://openalex.org/C122527463","wikidata":"https://www.wikidata.org/wiki/Q578430","display_name":"Quantum decoherence","level":3,"score":0.3700000047683716},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.3474999964237213},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3449999988079071},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3249000012874603},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.29420000314712524},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2870999872684479},{"id":"https://openalex.org/C15184713","wikidata":"https://www.wikidata.org/wiki/Q7269042","display_name":"Quantum dynamics","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.27230000495910645},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.257999986410141},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2574000060558319}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.06808","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.06808","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.06808","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.06808","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,80,138],"propose":[4],"a":[5,73,105,130,148],"dynamical":[6],"low-rank":[7,74,131,193],"(DLR)":[8],"approximation":[9],"framework":[10],"for":[11,133,204],"solving":[12],"the":[13,25,29,31,36,40,44,56,60,65,70,83,92,100,117,122,134,141,158,167,172,179,184,192,209],"semiclassical":[14,37,66,159,210],"Schrodinger":[15],"equation":[16],"with":[17,147],"uncertainties.":[18,49],"The":[19],"primary":[20],"numerical":[21,78,151],"challenges":[22],"arise":[23],"from":[24],"dual":[26],"nature":[27],"of":[28,109,121,183,195],"oscillations:":[30],"spatial":[32],"oscillations":[33,42],"inherent":[34],"in":[35,43,129,208],"limit":[38],"and":[39,59,181,199],"high-frequency":[41],"random":[45],"space":[46],"induced":[47],"by":[48,178],"We":[50],"extend":[51],"two":[52],"robust":[53,155],"integrators":[54],"--":[55,63],"projector-splitting":[57],"integrator":[58,62],"unconventional":[61],"to":[64,68],"regime":[67],"evolve":[69],"solution":[71],"on":[72],"manifold.":[75],"Through":[76],"extensive":[77],"experiments,":[79],"demonstrate":[81],"that":[82,115,140,171],"DLR":[84,142],"method":[85,143],"is":[86,175],"significantly":[87],"more":[88],"computationally":[89],"efficient":[90,202],"than":[91],"standard":[93],"stochastic":[94],"Galerkin":[95],"method,":[96],"as":[97,157],"it":[98],"captures":[99],"essential":[101],"quantum":[102,197],"dynamics":[103],"using":[104],"much":[106],"smaller":[107],"number":[108],"basis":[110],"functions.":[111],"Our":[112],"findings":[113],"reveal":[114],"despite":[116],"complex":[118],"oscillatory":[119],"patterns":[120],"wave":[123],"function,":[124],"its":[125],"evolution":[126],"remains":[127,154],"concentrated":[128],"subspace":[132],"cases":[135],"investigated.":[136],"Specifically,":[137],"observe":[139],"achieves":[144],"high":[145],"fidelity":[146],"remarkably":[149],"small":[150],"rank,":[152],"which":[153],"even":[156],"parameter":[160],"$\\varepsilon$":[161],"decreases.":[162],"Within":[163],"our":[164],"problem":[165],"settings,":[166],"results":[168,187],"further":[169],"suggest":[170],"rank":[173],"growth":[174],"primarily":[176],"driven":[177],"randomness":[180],"regularity":[182],"potential.":[185],"These":[186],"provide":[188],"practical":[189],"insights":[190],"into":[191],"structure":[194],"uncertain":[196],"systems":[198],"offer":[200],"an":[201],"approach":[203],"high-dimensional":[205],"uncertainty":[206],"quantification":[207],"regime.":[211]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-02-10T00:00:00"}
