There is a one-to-one correspondence between HEOM and pseudomodes for exponential bath correlation functions, realized by N interacting Lindblad-damped pseudomodes and a non-unitary linear mirror transformation.
One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath correlation function (BCF) that can be written as a sum of $N$ exponential terms can be obtained from a physical model with $N$ 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.
fields
quant-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The Nakajima-Zwanzig memory kernel belongs to the operator-valued Hardy space and obeys Kramers-Kronig relations under a real-axis spectral hypothesis, while effective kernels can show upper-half-plane poles from uncancelled zeros in the state transform.
citing papers explorer
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One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics
There is a one-to-one correspondence between HEOM and pseudomodes for exponential bath correlation functions, realized by N interacting Lindblad-damped pseudomodes and a non-unitary linear mirror transformation.
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Kramers-Kronig Relations and Causality in Non-Markovian Open Quantum Dynamics: Kernel, State, and Effective Kernel
The Nakajima-Zwanzig memory kernel belongs to the operator-valued Hardy space and obeys Kramers-Kronig relations under a real-axis spectral hypothesis, while effective kernels can show upper-half-plane poles from uncancelled zeros in the state transform.