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Entropy
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Quantum Chaos and Complexity
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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) | Viewed by 13521

Special Issue Editors

Prof. Dr. Olimpia Lombardi

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Guest Editor
Institute of Philosophy, CONICET and University of Buenos Aires, Buenos Aires 1406, Argentina
Interests: problem of the arrow of time; interpretation of quantum mechanics; nature of information; foundations of statistical mechanics; philosophy of chemistry
Special Issues, Collections and Topics in MDPI journals
Dr. Ignacio Gómez

E-Mail
Guest Editor
1. Instituto de Física, Universidade Federal da Bahia, Rua Barao de Jeremoabo, Salvador–BA 40170-115, Brazil
2. CONICET, Instituto de Física La Plata, Universidad Nacional de La Plata, La Plata B1900, Argentina
Interests: quantum chaos; classical limit; information geometry; dynamical systems; mathematical physics
Special Issues, Collections and Topics in MDPI journals
Dr. Federico Holik

E-Mail Website
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, Collections and Topics 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, Collections and Topics 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

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 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

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Published Papers (3 papers)

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21 pages, 3737 KiB  
Article
Signatures of Quantum Mechanics in Chaotic Systems
by Kevin M. Short and Matthew A. Morena
Entropy 2019, 21(6), 618; https://doi.org/10.3390/e21060618 - 22 Jun 2019
Cited by 8 | Viewed by 4411
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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13 pages, 890 KiB  
Article
Majorization and Dynamics of Continuous Distributions
by Ignacio S. Gomez, Bruno G. da Costa and Maike A. F. dos Santos
Entropy 2019, 21(6), 590; https://doi.org/10.3390/e21060590 - 14 Jun 2019
Cited by 3 | Viewed by 3177
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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43 pages, 5843 KiB  
Article
Quantum Chaos and Quantum Randomness—Paradigms of Entropy Production on the Smallest Scales
by Thomas Dittrich
Entropy 2019, 21(3), 286; https://doi.org/10.3390/e21030286 - 15 Mar 2019
Cited by 5 | Viewed by 5198
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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