Ergodic Properties of Quantum Markov Semigroups
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914179306225664 |
|---|---|
| author | Mousset, Nicolas Amini, Nina H. |
| author_facet | Mousset, Nicolas Amini, Nina H. |
| contents | In this paper, we study the ergodic theorem for infinite-dimensional quantum Markov semigroups, originally introduced by Frigerio and Verri in 1982, and its latest version developed by Carbone and Girotti in 2021. We provide a sufficient condition that ensures exponential convergence towards the positive recurrent subspace, a well-known result for irreducible quantum Markov semigroups in finite-dimensional Hilbert spaces. Several illustrative examples are presented to demonstrate the application of the ergodic theorem. Moreover, we show that the positive recurrent subspace plays a crucial role in the study of global asymptotic stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic Properties of Quantum Markov Semigroups Mousset, Nicolas Amini, Nina H. Quantum Physics Mathematical Physics Optimization and Control Probability In this paper, we study the ergodic theorem for infinite-dimensional quantum Markov semigroups, originally introduced by Frigerio and Verri in 1982, and its latest version developed by Carbone and Girotti in 2021. We provide a sufficient condition that ensures exponential convergence towards the positive recurrent subspace, a well-known result for irreducible quantum Markov semigroups in finite-dimensional Hilbert spaces. Several illustrative examples are presented to demonstrate the application of the ergodic theorem. Moreover, we show that the positive recurrent subspace plays a crucial role in the study of global asymptotic stability. |
| title | Ergodic Properties of Quantum Markov Semigroups |
| topic | Quantum Physics Mathematical Physics Optimization and Control Probability |
| url | https://arxiv.org/abs/2509.20133 |