An efficient variational polaron master equation for non-Markovian spin-boson dynamics: Transformed initial states and general observables
Abstract
We investigate the effects of initial states on the dynamics of a quantum spin-boson model using an efficient variational polaron master equation approach. The transformation of a factorized system-environment initial state into the variational polaron frame introduces inhomogeneous terms in the master equation, essential for accurately describing non-Markovian dynamics beyond the weak coupling regime. To efficiently account for these effects, we formulate the dynamics in an extended auxiliary Liouville space, converting the resulting integro-differential equations into coupled ordinary differential equations. We further introduce a simplified variational polaron technique for computing the time evolution of expectation values of general observables, including those that do not commute with the polaron transformation, overcoming a major limitation of previous approaches and enabling the unified treatment of coherence and population dynamics. The effects of transformed initial states generated from arbitrary factorized initial states are systematically characterized through expectation values and trace-distance analysis, providing insight into the associated bath-relaxation dynamics over a broad range of tunneling amplitudes, temperatures, and coupling strengths. Comparison with the weak-coupling master equation reveals a delay phenomenon associated with multi-bath-quanta processes, pronounced at intermediate coupling strengths and tunneling amplitudes. We further show that coherent superposition initial states induce stronger nonequilibrium effects than localized states, with inhomogeneous terms playing a crucial role in the short-time dynamics. The proposed formalism applies to both undriven and resonantly driven spin-boson models, providing a computationally efficient framework for open quantum-system dynamics with arbitrary factorized initial states and general physical observables.
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BibTeX
@misc{chen2026efficient,
title = {{An efficient variational polaron master equation for non-Markovian spin-boson dynamics: Transformed initial states and general observables}},
author = {Chien-Chang Chen and Hsi-Sheng Goan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08953},
eprint = {2610.08953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08953},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An efficient variational polaron master equation for non-Markovian spin-boson dynamics: Transformed initial states and general observables
AU - Chien-Chang Chen
AU - Hsi-Sheng Goan
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08953
UR - https://arxiv.org/abs/2610.08953
AB - We investigate the effects of initial states on the dynamics of a quantum spin-boson model using an efficient variational polaron master equation approach. The transformation of a factorized system-environment initial state into the variational polaron frame introduces inhomogeneous terms in the master equation, essential for accurately describing non-Markovian dynamics beyond the weak coupling regime. To efficiently account for these effects, we formulate the dynamics in an extended auxiliary Liouville space, converting the resulting integro-differential equations into coupled ordinary differential equations. We further introduce a simplified variational polaron technique for computing the time evolution of expectation values of general observables, including those that do not commute with the polaron transformation, overcoming a major limitation of previous approaches and enabling the unified treatment of coherence and population dynamics. The effects of transformed initial states generated from arbitrary factorized initial states are systematically characterized through expectation values and trace-distance analysis, providing insight into the associated bath-relaxation dynamics over a broad range of tunneling amplitudes, temperatures, and coupling strengths. Comparison with the weak-coupling master equation reveals a delay phenomenon associated with multi-bath-quanta processes, pronounced at intermediate coupling strengths and tunneling amplitudes. We further show that coherent superposition initial states induce stronger nonequilibrium effects than localized states, with inhomogeneous terms playing a crucial role in the short-time dynamics. The proposed formalism applies to both undriven and resonantly driven spin-boson models, providing a computationally efficient framework for open quantum-system dynamics with arbitrary factorized initial states and general physical observables.
ER -