Special Issue "Quantum Chaos and Complexity"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (15 September 2019).

Special Issue Editors

Prof. Dr. Olimpia Lombardi
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Guest Editor
CONICET - University of Buenos Aires, 3440 Crisólogo Larralde, 1430, Buenos Aires, Argentina
Interests: foundations of statistical mechanics; problem of the arrow of time; interpretation of quantum mechanics; nature of information; philosophy of chemistry
Special Issues and Collections in MDPI journals
Dr. Ignacio Gómez
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Guest Editor
1 INCT-SC (National Institute of Science for Complex Systems), Instituto de Física, Universidade Federal da Bahia, Brazil
2 CONICET, Instituto de Física La Plata, Universidad Nacional de La Plata, Argentina
Interests: quantum chaos; classical limit; information geometry; dynamical systems; mathematical physics
Dr. Federico Holik
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Guest Editor
Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, La Plata 1900, Argentina
Interests: foundations of quantum mechanics; quantum information theory; quantum probabilities; quantum logic
Special Issues and Collections in MDPI journals
Dr. Sebastian Fortin
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Guest Editor
CONICET, Universidad de Buenos Aires, Departamento de Física, Buenos Aires, Argentina
Interests: interpretation of quantum mechanics; quantum decoherence; classical limit of quantum mechanics; quantum information theory
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The research on quantum chaos finds its roots in the study of the spectrum of complex nuclei in the 1950s and the pioneering experiments in microwave billiards during the 1970s. This field is usually defined as the study of the connection between quantum mechanics and classical chaotic behavior, in order to understand how a well-defined characterization of the stationary and dynamical aspects of classical chaos emerges, both in the energy and in the time domains, respectively.

However, research on quantum chaos has certainly extended its scope during recent decades, due to the increasing discovery of connections with other disciplines in physics. It is nowadays an active field of research that has become of fundamental importance in the study of the properties, dynamics and control of complex quantum systems, and has found applications in a vast range of phenomena: nonlinear quantum dynamics, quantum complex networks, chaotic scattering in open systems, phase transitions in mixed quantum dynamics, Anderson localization, atoms in strong fields, etc.

Prof. Dr. Olimpia Lombardi
Dr. Ignacio Gómez
Dr. Federico Holik
Dr. Sebastian Fortin
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum chaos
  • Chaos and correspondence principle
  • Quantum chaos, decoherence and classical limit
  • Quantum ergodicity and mixing
  • Complex quantum systems
  • Quantum nonlinear systems
  • Quantum complex networks
  • Control of complex quantum systems
  • Information, disorder and complexity measures
  • Information theory and quantum chaos
  • Quantum statistical complexity
  • Random matrix theory
  • Characteristic time scales
  • Quantum billiards
  • Open chaotic systems
  • Quantum chaotic maps
  • Periodic orbit theory
  • Quantum expansion of trace formulas

Published Papers (3 papers)

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Research

Open AccessArticle
Signatures of Quantum Mechanics in Chaotic Systems
Entropy 2019, 21(6), 618; https://doi.org/10.3390/e21060618 - 22 Jun 2019
Abstract
We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable [...] Read more.
We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique. Full article
(This article belongs to the Special Issue Quantum Chaos and Complexity)
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Open AccessArticle
Majorization and Dynamics of Continuous Distributions
Entropy 2019, 21(6), 590; https://doi.org/10.3390/e21060590 - 14 Jun 2019
Abstract
In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide [...] Read more.
In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions ϕ for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker–Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements. Moreover, assuming a dynamics satisfying continuous majorization, the H-Boltzmann theorem is obtained as a special case for ϕ ( x ) = x ln x . Full article
(This article belongs to the Special Issue Quantum Chaos and Complexity)
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Open AccessArticle
Quantum Chaos and Quantum Randomness—Paradigms of Entropy Production on the Smallest Scales
Entropy 2019, 21(3), 286; https://doi.org/10.3390/e21030286 - 15 Mar 2019
Cited by 1
Abstract
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue that quantum chaos came [...] Read more.
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue that quantum chaos came as an indispensable rectification, removing inconsistencies related to entropy in classical chaos: bottom-up information currents require an inexhaustible entropy production and a diverging information density in phase-space, reminiscent of Gibbs’ paradox in statistical mechanics. It is shown how a mere discretization of the state space of classical models already entails phenomena similar to hallmarks of quantum chaos and how the unitary time evolution in a closed system directly implies the “quantum death” of classical chaos. As complementary evidence, I discuss quantum chaos under continuous measurement. Here, the two-way exchange of information with a macroscopic apparatus opens an inexhaustible source of entropy and lifts the limitations implied by unitary quantum dynamics in closed systems. The infiltration of fresh entropy restores permanent chaotic dynamics in observed quantum systems. Could other instances of stochasticity in quantum mechanics be interpreted in a similar guise? Where observed quantum systems generate randomness, could it result from an exchange of entropy with the macroscopic meter? This possibility is explored, presenting a model for spin measurement in a unitary setting and some preliminary analytical results based on it. Full article
(This article belongs to the Special Issue Quantum Chaos and Complexity)
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