Description
Open system dynamics, in continuous time, remains largely understood within the Born-Markov approximation where a closed form master equation can be obtained to describe the system dynamics. However, many-body systems arising in quantum optics and condensed matter physics often interact with environments that have memory and cannot be described by a Lindblad master equation. While both theoretical and algorithmic tools are available for understanding many-body Markovian open systems, their counterparts for non-Markovian systems remain less well understood.
In this talk I will present some of our attempts to develop a mathematically rigorous theory of non-Markovian open quantum systems with Gaussian environments. I will show that, for a broad class of environments which strictly generalize the Markovian environment, a system-environment unitary group can be rigorously defined and, in many cases, can also be shown to be strongly-continuous two-parameter group. I will then go onto consider many-body lattice models with non-Markovian environment and establish a Lieb-Robinson bounds for these models. Finally, I will describe our recent work on developing quantum algorithms for simulating the dynamics of these models with near-optimal scaling on the system size and evolution time.
References:
[1] R. T, arXiv:2204.0963 (2022).
[2] R. T, M. Rudner, arXiv:2410.15481 (2024).
[3] X. Yu et al R. T, arXiv:2509.02268 (2025).
