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Ferialdi, L. and Dürr, D. (2016): Effective non-Markovian description of a system interacting with a bath. In: Journal of Mathematical Physics, Vol. 57, No. 6, 62101

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We study a harmonic system coupled to a chain of first neighbor interacting oscillators. After deriving the exact dynamics of the system, we prove that one can effectively describe the exact dynamics by considering a suitable shorter chain. We provide the explicit expression for such an effective dynamics and we provide an upper bound on the error one makes considering it instead of the dynamics of the full chain. We eventually prove how error, time scale and number of modes in the truncated chain are related. Published by AIP Publishing.

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