Strong system-bath coupling induces a bright-dark structure in the effective coupling operator, producing a hierarchy of population relaxation timescales via spectral localization bounds on the Liouvillian in the reaction-coordinate polaron framework.
On truncations of hierarchical equations of motion for finite-dimensional systems
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abstract
We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges to that of the full HEOM as the truncation depth increases. We also prove that this approximation is free of spectral pollution: sufficiently deep truncations do not produce spurious unstable modes, provided the exact HEOM is stable. We illustrate the results for the spin-boson model.
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2026 1verdicts
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Hierarchical separation of relaxation timescales from spectral localization bounds
Strong system-bath coupling induces a bright-dark structure in the effective coupling operator, producing a hierarchy of population relaxation timescales via spectral localization bounds on the Liouvillian in the reaction-coordinate polaron framework.