{"id":"https://openalex.org/W4412570037","doi":"https://doi.org/10.3390/sym17081173","title":"A Stochastic Schr\u00f6dinger Evolution System with Complex Potential Symmetry Using the Riemann\u2013Liouville Fractional Derivative: Qualitative Behavior and Trajectory Controllability","display_name":"A Stochastic Schr\u00f6dinger Evolution System with Complex Potential Symmetry Using the Riemann\u2013Liouville Fractional Derivative: Qualitative Behavior and Trajectory Controllability","publication_year":2025,"publication_date":"2025-07-22","ids":{"openalex":"https://openalex.org/W4412570037","doi":"https://doi.org/10.3390/sym17081173"},"language":"en","primary_location":{"id":"doi:10.3390/sym17081173","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17081173","pdf_url":"https://www.mdpi.com/2073-8994/17/8/1173/pdf?version=1753194715","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/8/1173/pdf?version=1753194715","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070501286","display_name":"Dimplekumar Chalishajar","orcid":"https://orcid.org/0000-0002-6146-5544"},"institutions":[{"id":"https://openalex.org/I185641255","display_name":"Virginia Military Institute","ror":"https://ror.org/01ngnm118","country_code":"US","type":"education","lineage":["https://openalex.org/I185641255"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dimplekumar Chalishajar","raw_affiliation_strings":["Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA"],"raw_orcid":"https://orcid.org/0000-0002-6146-5544","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Virginia Military Institute, Lexington, VA 24450, USA","institution_ids":["https://openalex.org/I185641255"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035722690","display_name":"Ravikumar Kasinathan","orcid":"https://orcid.org/0000-0002-5635-8517"},"institutions":[{"id":"https://openalex.org/I4210109528","display_name":"PSG INSTITUTE OF TECHNOLOGY AND APPLIED RESEARCH","ror":"https://ror.org/01sa9ng67","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210109528"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ravikumar Kasinathan","raw_affiliation_strings":["Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014, India","institution_ids":["https://openalex.org/I4210109528"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101753752","display_name":"Ramkumar Kasinathan","orcid":"https://orcid.org/0000-0002-3624-5363"},"institutions":[{"id":"https://openalex.org/I4210109528","display_name":"PSG INSTITUTE OF TECHNOLOGY AND APPLIED RESEARCH","ror":"https://ror.org/01sa9ng67","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210109528"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramkumar Kasinathan","raw_affiliation_strings":["Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014, India"],"raw_orcid":"https://orcid.org/0000-0002-3624-5363","affiliations":[{"raw_affiliation_string":"Department of Mathematics, PSG College of Arts and Science, Coimbatore 641014, India","institution_ids":["https://openalex.org/I4210109528"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098446047","display_name":"Dhanalakshmi Kasinathan","orcid":null},"institutions":[{"id":"https://openalex.org/I141431873","display_name":"Periyar University","ror":"https://ror.org/05crs8s98","country_code":"IN","type":"education","lineage":["https://openalex.org/I141431873"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Dhanalakshmi Kasinathan","raw_affiliation_strings":["Department of Mathematics, Periyar University, Salem 636011, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Periyar University, Salem 636011, India","institution_ids":["https://openalex.org/I141431873"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5119042893","display_name":"Himanshu Thaker","orcid":"https://orcid.org/0009-0005-0199-2026"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Himanshu Thaker","raw_affiliation_strings":["Engineering Institute of Technology, West Perth, WA 6005, Australia"],"raw_orcid":"https://orcid.org/0009-0005-0199-2026","affiliations":[{"raw_affiliation_string":"Engineering Institute of Technology, West Perth, WA 6005, Australia","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5070501286"],"corresponding_institution_ids":["https://openalex.org/I185641255"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23053703,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"8","first_page":"1173","last_page":"1173"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9847999811172485,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9847999811172485,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.979200005531311,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9580000042915344,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/controllability","display_name":"Controllability","score":0.7889376878738403},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.7106165289878845},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5895774364471436},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5707122087478638},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5458961725234985},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.49653488397598267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4652268588542938},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4173009395599365},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3880569338798523},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3829580247402191},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.20237421989440918},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09435805678367615}],"concepts":[{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7889376878738403},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.7106165289878845},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5895774364471436},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5707122087478638},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5458961725234985},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.49653488397598267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4652268588542938},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4173009395599365},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3880569338798523},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3829580247402191},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20237421989440918},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09435805678367615},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17081173","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17081173","pdf_url":"https://www.mdpi.com/2073-8994/17/8/1173/pdf?version=1753194715","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17081173","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17081173","pdf_url":"https://www.mdpi.com/2073-8994/17/8/1173/pdf?version=1753194715","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4412570037.pdf","grobid_xml":"https://content.openalex.org/works/W4412570037.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W588973965","https://openalex.org/W1527296550","https://openalex.org/W1965343298","https://openalex.org/W1977238873","https://openalex.org/W1977528171","https://openalex.org/W1993003487","https://openalex.org/W1999216164","https://openalex.org/W2012698396","https://openalex.org/W2013635057","https://openalex.org/W2033470589","https://openalex.org/W2041533189","https://openalex.org/W2043736482","https://openalex.org/W2080520637","https://openalex.org/W2082769641","https://openalex.org/W2099176558","https://openalex.org/W2161475106","https://openalex.org/W2555363413","https://openalex.org/W2773084900","https://openalex.org/W2802062783","https://openalex.org/W2901248047","https://openalex.org/W2909390028","https://openalex.org/W2946060714","https://openalex.org/W2993747424","https://openalex.org/W3044783665","https://openalex.org/W3047482235","https://openalex.org/W3164746976","https://openalex.org/W3207199240","https://openalex.org/W4206290559","https://openalex.org/W4309785125","https://openalex.org/W4313328495","https://openalex.org/W4379649223","https://openalex.org/W4386913907","https://openalex.org/W4388089890","https://openalex.org/W4388191138","https://openalex.org/W4392359013","https://openalex.org/W4401323460","https://openalex.org/W4403105519","https://openalex.org/W4409263782","https://openalex.org/W6664936963","https://openalex.org/W6712275900","https://openalex.org/W6730176618","https://openalex.org/W6864956973"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2140812588","https://openalex.org/W2411113819","https://openalex.org/W2072887367","https://openalex.org/W2332386680","https://openalex.org/W2561315646","https://openalex.org/W2089892488","https://openalex.org/W2416906960","https://openalex.org/W2050580331","https://openalex.org/W3049300385"],"abstract_inverted_index":{"This":[0],"work":[1],"investigates":[2],"fractional":[3],"stochastic":[4,27],"Schr\u00f6dinger":[5],"evolution":[6],"equations":[7],"in":[8],"a":[9],"Hilbert":[10],"space,":[11],"incorporating":[12],"complex":[13],"potential":[14],"symmetry":[15],"and":[16,31],"Poisson":[17],"jumps.":[18],"We":[19,46],"establish":[20],"the":[21,32,55,67],"existence":[22],"of":[23],"mild":[24],"solutions":[25],"via":[26],"analysis,":[28],"semigroup":[29],"theory,":[30],"M\u00f6nch":[33],"fixed-point":[34],"theorem.":[35],"Sufficient":[36],"conditions":[37,52],"for":[38,53],"exponential":[39],"stability":[40],"are":[41],"derived,":[42],"ensuring":[43],"asymptotic":[44],"decay.":[45],"further":[47],"explore":[48],"trajectory":[49],"controllability,":[50],"identifying":[51],"guiding":[54],"system":[56],"along":[57],"prescribed":[58],"paths.":[59],"A":[60],"numerical":[61],"example":[62],"is":[63],"provided":[64],"to":[65],"validate":[66],"theoretical":[68],"results.":[69]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
