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arXiv · 1202.2997

Non-Markovianity, Loschmidt echo and criticality: a unified picture

Pinja Haikka·John Goold·Suzanne McEndoo·Francesco Plastina·Sabrina Maniscalco
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Abstract

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here.

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Pinja Haikka, John Goold, Suzanne McEndoo, Francesco Plastina, Sabrina Maniscalco. 2012-06-13. Non-Markovianity, Loschmidt echo and criticality: a unified picture. https://doi.org/10.1103/physreva.85.060101

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