Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:nlin/0111003

Heading towards chaos criterion for quantum field systems

В. И. Кувшинов, Kuzmin, A. V.

Published Nov 2, 2001• 1 citation
arXivHTMLPDF

Abstract

Chaos criterion for quantum field theory is proposed. Its accordance with classical chaos criterion is demonstrated in the semi-classical limit of quantum mechanics.
DOI
10.48550/arxiv.nlin/0111003

Related papers

THE DECOHERENCE CRITERION

Eleonora Alfinito, Rosario Gaetano Viglione, Giuseppe Vitiello

The decoherence mechanism signals the limits beyond which the system dynamics approaches the classical behavior. We show that in some cases decoherence may also signal the limits beyond which the system dynamics has to be described by quantum field theory, rather than by quantum mechanics.

arXiv:quant-ph/0007020•Modern Physics Letters B•Feb 28, 2001•19 citations

From Chaos & Strange Attractors to Quantum Theory

Ervin Goldfain

An open debate exists nowadays on how to properly connect chaos theory and strange attractors, on the one hand, to Quantum Field Theory (QFT) and Quantum Mechanics (QM) on the other. We post here a condensed flow-chart reflecting our personal view on this connection.

Prespacetime journal•Mar 1, 2020•0 citations

The Route from Chaotic Dynamics to Quantum Theory

Ervin Goldfain

An open debate exists nowadays on how to properly connect chaos theory and strange attractors, on the one hand, to Quantum Field Theory (QFT) and Quantum Mechanics (QM) on the other. We post here a condensed flow-chart reflecting our personal view on this topic.

•Feb 1, 2020•0 citations

Quantum Chaos and Semiclassical Mechanics

Robert W. Batterman

This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third theory of the asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the "classical counterpart to a quantum system" and a quantum system's "underlying classical motion". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave-functions. This significance of this association is discussed in some detail.

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1992•11 citations

Introduction

Giulio Casati, Boris Chirikov

The present collection of papers is devoted to a rather new and very controversial topic, the so-called “quantum chaos”. Some researchers see nothing essentially new at all in this phenomenon (apart from a number of various examples and models), and they have good reason to believe so. Indeed, the problems in this field all belong to the traditional, “old-fashion”, and rather “simple” quantum mechanics of finite-dimensional systems with a given interaction and no quantized fields. Nevertheless, many, including ourselves, consider quantum chaos to be a new discovery, though in an old field, of a great importance for fundamental physics. To understand this, the phenomenon of quantum chaos should be put into its proper perspective in recent developments in physics. The central point of this perspective is the conception of dynamical chaos (also a rather new topic) in classical mechanics (for a good review see, e.g., Refs.[l-3]). Thus before discussing the current understanding of quantum chaos we need briefly to describe classical dynamical chaos

Cambridge University Press eBooks•Apr 27, 1995•0 citations

Chaos in quantum mechanics

R. Blümel, William P. Reinhardt

Einstein (1917) appreciated early on that within the “old” pre-1925/26 quantum mechanics absence of integrability is a serious obstacle for the quantization of classical systems. Therefore, in retrospect not surprisingly, the quantization problem was not adequately solved until the advent of the “new” quantum mechanics by Heisenberg, Born, Jordan and Schrödinger. The new quantum mechanics did not rely at all on the notion of classical paths, and this way, unwittingly, sidestepped the chaos problem. Within the framework of the new theory, any classical system can be quantized, including classically chaotic systems. But while the quantization of integrable systems is straightforward, the quantization of classically chaotic systems, even today, presents a formidable technical challenge. This is especially true for quantization in the semiclassical regime, where the quantum numbers involved are large. In fact, efficient semiclassical quantization rules for chaotic systems were not known until Gutzwiller (1971, 1990) intoduced periodic orbit expansions. Gutzwiller's method is discussed in Section 4.1.3 below. It is important to emphasize here that the existence of chaos in certain classical systems in no way introduces conceptual problems into the framework of modern quantum theory, although, let it be emphasized again, chaos came back with a vengeance from the “old” days of quantum mechanics. Even given all the modern day computer power accessible to the “practitioner” of quantum mechanics, chaos is the ultimate reason for the slow progress in the numerical computation of even moderately excited states in such important, but chaotic problems as the helium atom.

Cambridge University Press eBooks•Jul 24, 1997•0 citations
This paper discusses the problem of finding and defining chaos in quantum mechanics. While chaotic time evolution appears to be ubiquitous in classical mechanics, it is apparently absent in quantum mechanics in part because for a bound, isolated quantum system, the evolution of its state is multiply periodic. This has led a number of investigators to search for semiclassical signatures of chaos. Here I am concerned with the status of semiclassical mechanics as a distinct third theory of the asymptotic domain between classical and quantum mechanics. I discuss in some detail the meaning of such crucial locutions as the "classical counterpart to a quantum system" and a quantum system's "underlying classical motion". A proper elucidation of these concepts requires a semiclassical association between phase space surfaces and wave-functions. This significance of this association is discussed in some detail.
The present collection of papers is devoted to a rather new and very controversial topic, the so-called “quantum chaos”. Some researchers see nothing essentially new at all in this phenomenon (apart from a number of various examples and models), and they have good reason to believe so. Indeed, the problems in this field all belong to the traditional, “old-fashion”, and rather “simple” quantum mechanics of finite-dimensional systems with a given interaction and no quantized fields. Nevertheless, many, including ourselves, consider quantum chaos to be a new discovery, though in an old field, of a great importance for fundamental physics. To understand this, the phenomenon of quantum chaos should be put into its proper perspective in recent developments in physics. The central point of this perspective is the conception of dynamical chaos (also a rather new topic) in classical mechanics (for a good review see, e.g., Refs.[l-3]). Thus before discussing the current understanding of quantum chaos we need briefly to describe classical dynamical chaos
Einstein (1917) appreciated early on that within the “old” pre-1925/26 quantum mechanics absence of integrability is a serious obstacle for the quantization of classical systems. Therefore, in retrospect not surprisingly, the quantization problem was not adequately solved until the advent of the “new” quantum mechanics by Heisenberg, Born, Jordan and Schrödinger. The new quantum mechanics did not rely at all on the notion of classical paths, and this way, unwittingly, sidestepped the chaos problem. Within the framework of the new theory, any classical system can be quantized, including classically chaotic systems. But while the quantization of integrable systems is straightforward, the quantization of classically chaotic systems, even today, presents a formidable technical challenge. This is especially true for quantization in the semiclassical regime, where the quantum numbers involved are large. In fact, efficient semiclassical quantization rules for chaotic systems were not known until Gutzwiller (1971, 1990) intoduced periodic orbit expansions. Gutzwiller's method is discussed in Section 4.1.3 below. It is important to emphasize here that the existence of chaos in certain classical systems in no way introduces conceptual problems into the framework of modern quantum theory, although, let it be emphasized again, chaos came back with a vengeance from the “old” days of quantum mechanics. Even given all the modern day computer power accessible to the “practitioner” of quantum mechanics, chaos is the ultimate reason for the slow progress in the numerical computation of even moderately excited states in such important, but chaotic problems as the helium atom.