Ergodic Theory of Inhomogeneous Quantum Processes

• URL: http://arxiv.org/abs/2506.12280v1
• Date: Sat, 14 Jun 2025 00:04:59 GMT
• Title: Ergodic Theory of Inhomogeneous Quantum Processes
• Authors: Abdessatar Souissi,
• Abstract summary: This work presents a rigorous framework for understanding ergodicity and mixing in time-inhomogeneous quantum systems.<n>A key contribution is the development of a quantum Markov-Dobrushin approach to characterize mixing behavior.<n>Results contribute to the mathematical foundations of quantum dynamics and support the broader goal of advancing quantum information science.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work presents a rigorous framework for understanding ergodicity and mixing in time-inhomogeneous quantum systems. By analyzing quantum processes driven by sequences of quantum channels, we distinguish between forward and backward dynamics and reveal their fundamental asymmetries. A key contribution is the development of a quantum Markov-Dobrushin approach to characterize mixing behavior, offering clear criteria for convergence and exponential stability. The framework not only generalizes classical and homogeneous quantum models but also applies to non-translation-invariant matrix product states, highlighting its relevance to real-world quantum systems. These results contribute to the mathematical foundations of quantum dynamics and support the broader goal of advancing quantum information science.

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