{"ID":2866598,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.20133","arxiv_id":"2509.20133","title":"Ergodic Properties of Quantum Markov Semigroups","abstract":"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.","short_abstract":"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 subs...","url_abs":"https://arxiv.org/abs/2509.20133","url_pdf":"https://arxiv.org/pdf/2509.20133v1","authors":"[\"Nicolas Mousset\",\"Nina H. Amini\"]","published":"2025-09-24T14:00:36Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"math-ph\",\"math.OC\",\"math.PR\"]","methods":"[]","has_code":false}