Nonstationary hierarchical equations of motion in complex time
Phys. Rev. A 114, 022213 – Published 19 August, 2026
DOI: https://doi.org/10.1103/jw66-2z61
Abstract
We present the formal derivation of a set of hierarchical equations of motion (HEOM) to compute system and environmental correlation functions in terms of a nonstationary underlying dynamics in complex time. This corresponds to partitioning the global validity of the HEOM spectral ansatz into local versions valid within a more limited time span. The non-Markovian indivisibility of the dynamics is recovered by gluing these HEOM patches to allow the propagation of degrees of freedom, whose purpose is to model how past system-bath dynamics affects the future. We illustrate the formalism to exemplify the regular dynamical case and the imaginary-time evolution.
