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

Pinja Haikka, John Goold, Suzanne McEdnoo, Francesco Plastina, Sabrina Maniscalco

Research output: Contribution to journalArticlepeer-review

94 Citations (Scopus)
44 Downloads (Pure)

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.
Original languageEnglish
Article number060101
Number of pages4
JournalPhysical Review A
Volume85
Issue number6
DOIs
Publication statusPublished - 14 Feb 2012

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