What is Markovian and non-Markovian in Quantum Mechanics: New Approaches and Viewpoints

By Francesco Ciccarello

Department of Physics, Duke University, Durham, NC

Published on


While in classical physics the notion of what is Markovian or not is well defined, this is not the case when it comes to open quantum systems. What makes a quantum dynamics Markovian or non-Markovian (NM)? Traditional answers to this question involve the celebrated Lindblad master equation (ME) and/or the ability of an open dynamics to be governed by a time-local ME. The last few years, yet, witnessed a thorough revision of such concepts with the aim to establish in a rigorous way exact criteria for assessing whether or not a dynamics is NM and even quantifying its degree of quantum “non-Markovianity”. This resulted in a number of “non-Markovianity measures” that have been put forward. Based on these and a number of theoretical advancements, the lack of a Lindblad ME or time-local ME turns out not to be a reliable criterion. For instance, there are Markovian dynamics that are not described by a Lindblad ME, while, on the other hand, many open dynamics that are strongly NM can be shown to effectively obey a time-local ME.

After reviewing these new concepts, in the last part of the talk I discuss a problem where they are used to tackle the question as to whether or not the dynamics of a qubit undergoing single-photon scattering in a waveguide is Markovian. It turns out that, in the infinite-waveguide case, the dynamics is NM when the photon-wavepacket width is comparable with the qubit-field coupling rate. In the semi-infinite waveguide case (mirror-like boundary condition), this source of non-Markovianity adds to that due to the photon delay time (owing to the finite qubit-mirror distance).

Cite this work

Researchers should cite this work as follows:

  • Francesco Ciccarello (2017), "What is Markovian and non-Markovian in Quantum Mechanics: New Approaches and Viewpoints," http://nanohub.org/resources/26547.

    BibTex | EndNote



Room 2001, Birck Nanotechnology Center, Purdue University, West Lafayette, IN