Chaos and Gauge Field Theory

Bı́ró, Tamás; Matinyan, S.G.; Müller, Berndt

doi:10.1142/2584

Cited by 44 publications

(63 citation statements)

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“…In order to make the notion of "highly irregular" more precise, we calculate the Lyapunov exponents by integrating the equations of motion together with the respective variational systems [2]. Figure (2) shows the evolution of the function χ(t) -whose value for long times serves as an estimate of the Lyapunov exponent.…”

Section: Resultsmentioning

confidence: 99%

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Chaotic thermalization in classical gauge theories

Woitek¹,

Krein²

2013

AIP Conference Proceedings

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State-by-state assignment of the bending spectrum of acetylene at 15000 cm1: A case study of quantum-classical correspondence The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Though it works fine in some model systems, there exist a number of so-called pathological cases characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. Recently, we reported on how the reinjection probability density (RPD) can be generalized. Here, we extend this methodology and apply it to different dynamical systems exhibiting anomalous type-II and type-III intermittencies. Estimation of the universal RPD is based on fitting a linear function to experimental data and requires no a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets (dozens of points). Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. We show that the method copes well with dynamical systems exhibiting significantly different statistics reported in the literature. We also derive and classify characteristic relations between the mean laminar length and main controlling parameter in perfect agreement with data provided by numerical simulations. V C 2013 AIP Publishing LLC. Intermittency is a particular route to the deterministic chaos characterized by spontaneous transitions between laminar and chaotic dynamics. It is observed in a variety of different dynamical systems in Physics, Neuroscience, and Economics. Frequently, there is no feasible mathematical model for the process under study. Then reliable quantification of main characteristics of the intermittent process (e.g., the length of laminar phase) from experimental data is a challenging problem. The classical theory of intermittency has significant pitfalls. Though it works fine in some model systems, there exist a number of so-called pathological cases that deviate significantly from the classical predictions. In this work, we address the problem of unification of anomalous and standard intermittencies under single framework. The unified model can be fitted to experimental or numerical data. We note that to accomplish this step no a priori knowledge is required. We propose a procedure that can cope with reduced data sets consisting of several dozens of points. This makes our methodology useful for real-life applications. Using the experimentally obtained measures , we can classify intermittent processes into different theoretical types. We thoroughly test our method on two particular but canonical cases of intermittency.

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Section: Resultsmentioning

confidence: 99%

“…It has been shown for numerous particular cases that this feature may cause the systems to exhibit chaotic behavior [2]. In the present communication, we present results of an exploratory study on the connection between chaos and Statistical Mechanics (SM) and on its relevance to the problem of thermalization in gauge theories like QCD.…”

Section: Introductionmentioning

confidence: 91%

Chaotic thermalization in classical gauge theories

Woitek¹,

Krein²

2013

AIP Conference Proceedings

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“…Classical dynamical aspects of lattice gauge theories have recently attracted some interest [BMM95,GS88]. The classical limit of a lattice gauge theory is interesting both from the point of view of classical dynamical system theory and in the perspective of its quantum counterpart.…”

Section: Chaos In Physical Gauge Fieldsmentioning

confidence: 99%

“…From the point of view of the theory of classical dynamical systems, lattice gauge theories are highly non-trivial many DOF Hamiltonian systems which exhibit a rich and interesting phenomenology. The classical Hamiltonian dynamics of such systems is known to be chaotic [BMM95]; however, a precise characterization of the different chaotic regimes which may occur in these systems is still lacking.…”

Section: Chaos In Physical Gauge Fieldsmentioning

confidence: 99%

“…Many particular aspects of this general problem have been considered in the literature, concerning the properties of pure gauge theories and of theories coupled with matter (mainly Higgs fields), e.g., the systematic study of the Lyapunov spectra [BMM95], the study of thermalization processes [HHL97], and the relation between Lyapunov exponents and observable quantities like the plasmon damping rate [BMM95].…”

Section: Chaos In Physical Gauge Fieldsmentioning

confidence: 99%

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