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Quantum renewal processes

Authors
  • Vacchini, Bassano1, 2
  • 1 Università degli Studi di Milano, Via Celoria 16, Milan, 20133, Italy , Milan (Italy)
  • 2 INFN, Sezione di Milano, Via Celoria 16, Milan, 20133, Italy , Milan (Italy)
Type
Published Article
Journal
Scientific Reports
Publisher
Springer Nature
Publication Date
Mar 27, 2020
Volume
10
Issue
1
Identifiers
DOI: 10.1038/s41598-020-62260-z
Source
Springer Nature
License
Green

Abstract

We introduce a general construction of master equations with memory kernel whose solutions are given by completely positive trace-preserving maps. These dynamics going beyond the Lindblad paradigm are obtained with reference to classical renewal processes, so that they are termed quantum renewal processes. They can be described by means of semigroup dynamics interrupted by jumps, separated by independently distributed time intervals, following suitable waiting time distributions. In this framework, one can further introduce modified processes, in which the first few events follow different distributions. A crucial role, marking an important difference with respect to the classical case, is played by operator ordering. Indeed, for the same choice of basic quantum transformations, different quantum dynamics arise. In particular, for the case of modified processes, it is natural to consider the time inverted operator ordering, in which the last few events are distributed differently.

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