Non-Markovianity, Loschmidt echo and criticality: a unified picture
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.
Keywords
Cite
@article{arxiv.1202.2997,
title = {Non-Markovianity, Loschmidt echo and criticality: a unified picture},
author = {Pinja Haikka and John Goold and Suzanne McEndoo and Francesco Plastina and Sabrina Maniscalco},
journal= {arXiv preprint arXiv:1202.2997},
year = {2012}
}