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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2024-11-01
|
| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-024-77484-6 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2045-2322 |