Spectral origin of non-Markovian open-system dynamics: A finite harmonic model without approximations

Vasile, Ruggero; Galve, Fernando; Zambrini, Roberta
Physical Review A 89, 022109 (1-9) (2014)

Non-homogeneous chain environments (e.g. segmented ion traps) are
investigated through an exact diagonalization approach. Different
spectral densities, including band-gaps, can be engineered to
separately assess memory effects. Environment non-Markovianity is
quantified with recently introduced measures of information
flow-back and non-divisibility of the system dynamical map. By
sweeping the bath spectrum via tuning of the system frequency we
show strongest memory effect at band-gap edges and provide an
interpretation based on energy flow between system and environment.
A system weakly coupled to a stiff chain ensures a Markovian
dynamics, while the size of the environment as well as the local
density of modes are not substantial factors. We show an opposite
effect when increasing the temperature inside or outside the
spectral band-gap. Further, non-Markovianity arises for larger
(negative and positive) powers of algebraic spectral densities,
being the Ohmic case not always the most Markovian one.

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