American Institute of Mathematical Sciences

Advanced
2003, 2003(Special): 596-603. doi: 10.3934/proc.2003.2003.596

Classical and quantum chaos in fundamental field theories

Harald Markum 1, and  Rainer Pullirsch 1,

1. 

Atominstitut der österreichischen Universitäten, Technische Universität Wien, Wiedner Haupstrabe 8-10, A-1040 Vienna, Austria, Austria

Received  September 2002 Published  April 2003

An investigation of classical chaos and quantum chaos in gauge fields and fermion fields, respectively, is presented for (quantum) electrodynamics. We analyze the leading Lyapunov exponents of U(1) gauge field configurations on a $12^3$ lattice which are initialized by Monte Carlo simulations. We find that configurations in the strong coupling phase are substantially more chaotic than in the deconfinement phase. Considering the quantum case, complete eigenvalue spectra of the Dirac operator in quenched $4d$ compact QED are studied on $8^3 \times 4$ and $8^3 \times 6$ lattices. We investigate the behavior of the nearest-neighbor spacing distribution $P(s)$ as a measure of the fluctuation properties of the eigenvalues in the strong coupling and the Coulomb phase. In both phases we find agreement with the Wigner surmise of the unitary ensemble of random-matrix theory indicating quantum chaos.
Keywords: quantum chaos., classical chaos, Gauge theories.
Mathematics Subject Classification: Primary: 70H05, 81T2.
Citation: Harald Markum, Rainer Pullirsch. Classical and quantum chaos in fundamental field theories. Conference Publications, 2003, 2003 (Special) : 596-603. doi: 10.3934/proc.2003.2003.596
[1]

Helmut Kröger. From quantum action to quantum chaos. Conference Publications, 2003, 2003 (Special) : 492-500. doi: 10.3934/proc.2003.2003.492
[2]

Yu. Dabaghian, R. V. Jensen, R. Blümel. Integrability in 1D quantum chaos. Conference Publications, 2003, 2003 (Special) : 206-212. doi: 10.3934/proc.2003.2003.206
[3]

John Erik Fornæss. Infinite dimensional complex dynamics: Quasiconjugacies, localization and quantum chaos. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 51-60. doi: 10.3934/dcds.2000.6.51
[4]

Marco Castrillón López, Mark J. Gotay. Covariantizing classical field theories. Journal of Geometric Mechanics, 2011, 3 (4) : 487-506. doi: 10.3934/jgm.2011.3.487
[5]

Emmanuel Hebey. Solitary waves in critical Abelian gauge theories. Discrete & Continuous Dynamical Systems - A, 2012, 32 (5) : 1747-1761. doi: 10.3934/dcds.2012.32.1747
[6]

Ryszard Rudnicki. An ergodic theory approach to chaos. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 757-770. doi: 10.3934/dcds.2015.35.757
[7]

Arsen R. Dzhanoev, Alexander Loskutov, Hongjun Cao, Miguel A.F. Sanjuán. A new mechanism of the chaos suppression. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 275-284. doi: 10.3934/dcdsb.2007.7.275
[8]

Eric A. Carlen, Maria C. Carvalho, Jonathan Le Roux, Michael Loss, Cédric Villani. Entropy and chaos in the Kac model. Kinetic & Related Models, 2010, 3 (1) : 85-122. doi: 10.3934/krm.2010.3.85
[9]

Vadim S. Anishchenko, Tatjana E. Vadivasova, Galina I. Strelkova, George A. Okrokvertskhov. Statistical properties of dynamical chaos. Mathematical Biosciences & Engineering, 2004, 1 (1) : 161-184. doi: 10.3934/mbe.2004.1.161
[10]

Y. Charles Li. Chaos phenotypes discovered in fluids. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1383-1398. doi: 10.3934/dcds.2010.26.1383
[11]

Kaijen Cheng, Kenneth Palmer. Chaos in a model for masting. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1917-1932. doi: 10.3934/dcdsb.2015.20.1917
[12]

Flaviano Battelli, Michal Fe?kan. Chaos in forced impact systems. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 861-890. doi: 10.3934/dcdss.2013.6.861
[13]

J. Alberto Conejero, Francisco Rodenas, Macarena Trujillo. Chaos for the Hyperbolic Bioheat Equation. Discrete & Continuous Dynamical Systems - A, 2015, 35 (2) : 653-668. doi: 10.3934/dcds.2015.35.653
[14]

Marat Akhmet, Ejaily Milad Alejaily. Abstract similarity, fractals and chaos. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020191
[15]

Kaijen Cheng, Kenneth Palmer, Yuh-Jenn Wu. Period 3 and chaos for unimodal maps. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1933-1949. doi: 10.3934/dcds.2014.34.1933
[16]

Piotr Oprocha. Specification properties and dense distributional chaos. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 821-833. doi: 10.3934/dcds.2007.17.821
[17]

Piotr Oprocha, Pawel Wilczynski. Distributional chaos via isolating segments. Discrete & Continuous Dynamical Systems - B, 2007, 8 (2) : 347-356. doi: 10.3934/dcdsb.2007.8.347
[18]

Jaroslav Smítal, Marta Štefánková. Omega-chaos almost everywhere. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1323-1327. doi: 10.3934/dcds.2003.9.1323
[19]

Xianwei Chen, Zhujun Jing, Xiangling Fu. Chaos control in a pendulum system with excitations. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 373-383. doi: 10.3934/dcdsb.2015.20.373
[20]

Lidong Wang, Xiang Wang, Fengchun Lei, Heng Liu. Mixing invariant extremal distributional chaos. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6533-6538. doi: 10.3934/dcds.2016082

 Impact Factor: 

Tools

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences