Quantum repeated interactions and the chaos game

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Abstract

Inspired by the algorithm of Barnsley's chaos game, we construct an open quantum system model based on the repeated interaction process. We show that the quantum dynamics of the appropriate fermionic/bosonic system (in interaction with an environment) provides a physical model of the chaos game. When considering fermionic operators, we follow the system's evolution by focusing on its reduced density matrix. The system is shown to be in a Gaussian state (at all time t) and the average number of particles is shown to obey the chaos game equation. Considering bosonic operators, with a system initially prepared in coherent states, the evolution of the system can be tracked by investigating the dynamics of the eigenvalues of the annihilation operator. This quantity is governed by a chaos game-like equation from which different scenarios emerge.
Original languageEnglish
Article number395301
JournalJournal of Physics A: Mathematical and Theoretical
Volume51
Issue number39
Early online date12 Jul 2018
DOIs
Publication statusPublished - 28 Aug 2018

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games
Chaos theory
chaos
Chaos
Game
Interaction
operators
Operator
interactions
Open Quantum Systems
Evolution System
Quantum Dynamics
Density Matrix
Coherent States
Physical Model
Annihilation
eigenvalues
Model-based
Eigenvalue
Scenarios

Bibliographical note

This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the
manuscript or any version derived from it. The Version of Record is available online at 10.1088/1751-8121/aad304


Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • Chaos game
  • Coherent state

Cite this

Quantum repeated interactions and the chaos game. / Platini, Thierry; Low, Robert.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 51, No. 39, 395301, 28.08.2018.

Research output: Contribution to journalArticle

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