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arXiv:2511.01358 · Physical Review Research

Non-Markovian dynamics in nonstationary Gaussian baths

Vladisalv Sukharnikov, Stasis Chuchurka, Frank Schlawin

quant-phSubmitted Nov 3, 2025• Announced Nov 4, 2025• 0 citations

v1 · Nov 3, 2025 v2 · Nov 24, 2025 v3 · Mar 12, 2026

Abstract

Building on the standard hierarchy of pure states (HOPS) approach, we construct a generalized formulation suitable for open quantum systems interacting with nonstationary Gaussian baths, potentially extending its applicability to nonequilibrium baths. This is achieved by extending the conventional exponential decomposition of bath correlation functions (BCF) to allow explicitly time-dependent forms. We demonstrate the method's performance on two examples of nonstationary squeezed reservoirs generated via uniform squeezing and degenerate parametric amplification. Benchmarking against the associated hierarchy of master equations shows that HOPS achieves superior efficiency under hierarchy truncation. In cases where each contribution in the BCF expansion can be associated with an independent physical bath, the formalism can be simplified in a pseudomode representation which is more efficient in a strongly non-Markovian regime. Our results highlight HOPS as a versatile and powerful tool for simulating open quantum systems in nonstationary baths, with potential applications ranging from squeezed light-matter interactions to driven quantum materials and dissipative phase transitions.

DOI: 10.1103/yt37-s9hz

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interacting pseudomodes which are damped in Lindblad form. Second, for every such BCF there exists a non-unitary, linear transformation which mirrors the evolution of the system-pseudomode state onto the HEOM hierarchy, and vice versa. Our proofs are constructive and we give explicit expressions for the mirror transformation as well as for the pseudomode Lindbladian corresponding to a given exponential BCF. This approach also gives insight and provides elegant derivations of the corresponding Hierarchy of stochastic Pure States (HOPS) method and its nearly-unitary version, nuHOPS. Our result opens several avenues for further optimization of non-Markovian open quantum system dynamics methods.

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