{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T22:37:49Z","timestamp":1788388669515,"version":"build-2803163510"},"reference-count":54,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Academic Research Fund of the Ministry of Education and Singapore","award":["A-0004592-00-00"],"award-info":[{"award-number":["A-0004592-00-00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present two diagrammatic Monte Carlo methods for quantum systems coupled with harmonic baths, whose dynamics are described by integro-differential equations. The first approach can be considered as a reformulation of the Dyson series, and the second one, called \u201cbold-thin-bold diagrammatic Monte Carlo,\u201d is based on resummation of the diagrams in the Dyson series to accelerate its convergence. The underlying mechanism of the governing equations associated with the two methods lies in the recurrence relation of the path integrals, which is the most costly part in the numerical methods. The proposed algorithms give an extension to the work of Cai, Lu, and Yang [ Comput. Phys. Commun. 278 (2022), 108417], where the algorithms are designed based on reusing the previous calculations of bath influence functionals. Compared with the algorithms therein, our methods further include the reuse of system-associated functionals and show better performance in terms of computational efficiency and memory cost. We demonstrate the two methods in the framework of spin-boson model, and numerical experiments are carried out to verify the validity of the methods.<\/jats:p>","DOI":"10.1137\/22m1499297","type":"journal-article","created":{"date-parts":[[2023,7,19]],"date-time":"2023-07-19T04:28:32Z","timestamp":1689740912000},"page":"A1812-A1843","source":"Crossref","is-referenced-by-count":10,"title":["The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7086-7983","authenticated-orcid":true,"given":"Zhenning","family":"Cai","sequence":"first","affiliation":[{"name":"Department of Mathematics, National University of Singapore, Singapore 119076."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7890-2758","authenticated-orcid":true,"given":"Geshuo","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, National University of Singapore, Singapore 119076."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6651-6224","authenticated-orcid":true,"given":"Siyao","family":"Yang","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Mathematics, National University of Singapore, Singapore 119076."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,19]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.95.085144"},{"key":"ref2","volume-title":"The Theory of Open Quantum Systems","author":"Breuer H.-P.","year":"2002"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.96.062122"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21888"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2022.108417"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3785"},{"key":"ref7","volume-title":"An Open Systems Approach to Quantum Optics: Lecture Notes in Physics","volume":"18","author":"Carmichael H.","year":"2009"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.110401"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1063\/1.4974328"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1063\/1.4974329"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.13.034045"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.266802"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.96.062103"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608389"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.75.486"},{"key":"ref16","volume-title":"From Special Relativity to Feynman Diagrams","author":"D\u2019Auria R.","year":"2011"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.124.206405"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4916(63)90068-X"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.82.075109"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.84.085134"},{"key":"ref21","first-page":"1018","volume":"20","author":"Keldysh L. 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