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arXiv · 1712.05759

Response functions as quantifiers of non-Markovianity

Philipp Strasberg·Massimiliano Esposito
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Abstract

Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We here demonstrate that linear response theory also provides a way to derive dynamical maps, but for initially correlated (and in general entangled) states. Importantly, these maps are always time-translational invariant and allow for a much simpler quantification of non-Markovianity compared to previous approaches. We apply our theory to the Caldeira-Leggett model, for which our quantifier is valid beyond linear response and can be expressed analytically. We find that a classical Brownian particle coupled to an Ohmic bath can already exhibit non-Markovian behaviour, a phenomenon related to the initial state preparation procedure. Furthermore, for a peaked spectral density we demonstrate that there is no monotonic relation between our quantifier and the system-bath coupling strength, the sharpness of the peak or the resonance frequency in the bath.

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Philipp Strasberg, Massimiliano Esposito. 2018-07-25. Response functions as quantifiers of non-Markovianity. https://doi.org/10.1103/physrevlett.121.040601

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