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Understanding the dynamics of higher-dimensional quantum systems embedded ina complex environment remains a significant theoretical challenge. Whileseveral approaches yielding numerically converged solutions exist, these arecomputationally expensive and often provide only limited physical insight. Herewe address the question when more intuitive and simpler to computeweak-coupling approaches still provide adequate accuracy. We develop a simpleanalytical criterion and verify its validity for the case of the much-studiedFMO dynamics as well as the canonical spin-boson model.

When do weak-coupling approaches accurately capture the dynamics of complex quantum systems?