Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises
Abstract Quantum Bernoulli noises are the family of annihilation and creation operators on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. The paper is devoted to the study of Quantum Exclusion Process driven by Brownian Motions in terms of Quantum Bernoulli...
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Nature Portfolio
2024-11-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-77484-6 |
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| author | Suling Ren Lixia Zhang |
| author_facet | Suling Ren Lixia Zhang |
| author_sort | Suling Ren |
| collection | DOAJ |
| description | Abstract Quantum Bernoulli noises are the family of annihilation and creation operators on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. The paper is devoted to the study of Quantum Exclusion Process driven by Brownian Motions in terms of Quantum Bernoulli Noises. We first study the existence and uniqueness of regular solutions to the classical Quantum Exclusion Process driven by Brownian Motions. We then provide an explicit representation formula by separating the action on off-diagonal and diagonal operators, on which they are reduced to the Quantum Exclusion Process of classical Markov chains. Finally, we prove that the existence of regular invariant measures for Quantum Exclusion Process driven by Brownian Motions in terms of Quantum Bernoulli Noises. |
| format | Article |
| id | doaj-art-fdec3740843e4e5e98fcaafc65a1a964 |
| institution | OA Journals |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-fdec3740843e4e5e98fcaafc65a1a9642025-08-20T02:18:27ZengNature PortfolioScientific Reports2045-23222024-11-0114111910.1038/s41598-024-77484-6Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noisesSuling Ren0Lixia Zhang1School of Statistics and Data Science, Lanzhou University of Finance and EconomicsSchool of Mathematics and Statistics, Northwest Normal UniversityAbstract Quantum Bernoulli noises are the family of annihilation and creation operators on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal time. The paper is devoted to the study of Quantum Exclusion Process driven by Brownian Motions in terms of Quantum Bernoulli Noises. We first study the existence and uniqueness of regular solutions to the classical Quantum Exclusion Process driven by Brownian Motions. We then provide an explicit representation formula by separating the action on off-diagonal and diagonal operators, on which they are reduced to the Quantum Exclusion Process of classical Markov chains. Finally, we prove that the existence of regular invariant measures for Quantum Exclusion Process driven by Brownian Motions in terms of Quantum Bernoulli Noises.https://doi.org/10.1038/s41598-024-77484-6 |
| spellingShingle | Suling Ren Lixia Zhang Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises Scientific Reports |
| title | Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises |
| title_full | Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises |
| title_fullStr | Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises |
| title_full_unstemmed | Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises |
| title_short | Quantum Exclusion Process driven by Brownian Motions in terms of quantum Bernoulli noises |
| title_sort | quantum exclusion process driven by brownian motions in terms of quantum bernoulli noises |
| url | https://doi.org/10.1038/s41598-024-77484-6 |
| work_keys_str_mv | AT sulingren quantumexclusionprocessdrivenbybrownianmotionsintermsofquantumbernoullinoises AT lixiazhang quantumexclusionprocessdrivenbybrownianmotionsintermsofquantumbernoullinoises |