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A short review of phase transition in a chaotic system

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Abstract

The subject approached here is a dynamical phase transition observed in Hamiltonian systems, which is a transition from integrability to non-integrability. Using the dynamics defined by a discrete mapping on the variables action I and angle \(\theta \), we perform a description of the behaviour of the chaotic diffusion to particles in the chaotic sea using two methods. One is a phenomenological description obtaining the critical exponents via numerical simulation, and the other is an analytical result obtained by the solution of the diffusion equation. The scaling invariance is observed in the chaotic sea leading to an universal chaotic diffusion. This is a clear signature that the system is passing through a phase transition. We investigate a set of four questions that characterize a phase transition: (1) identify the broken symmetry; (2) define the order parameter; (3) identify what are the elementary excitations and; (4) detect the topological defects which impact on the transport of the particles.

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Acknowledgements

LKAM thanks FAPESP (2020/10602-1). CMK thanks to CAPES for support. YHH thanks CNPq. AKPF acknowledges FAPESP (2020/07219-1). JAO thanks FAPESP (Grant no. 2018/14685-9) and CNPq (Grant nos. 303242/2018-3, 421254/2016-5). EDL acknowledges support from CNPq (301318/2019-0) and FAPESP (2019/14038-6). CAPES, CNPq, and FAPESP are Brazilian agencies.

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Authors and Affiliations

  1. Departamento de Física, UNESP-Univ Estadual Paulista, Av.24A, 1515 Bela Vista, Rio Claro, SP, 13506-900, Brazil

    Lucas K. A. Miranda, Célia M. Kuwana, Yoná H. Huggler, Anne K. P. da Fonseca, Makoto Yoshida, Juliano A. de Oliveira & Edson D. Leonel

  2. UNESP-Univ Estadual Paulista, Câmpus de São João da Boa Vista, São João da Boa Vista, SP, Brazil

    Juliano A. de Oliveira

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  1. Lucas K. A. Miranda
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  2. Célia M. Kuwana
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  3. Yoná H. Huggler
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  4. Anne K. P. da Fonseca
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  5. Makoto Yoshida
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  6. Juliano A. de Oliveira
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  7. Edson D. Leonel
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Each author contributed equally to the paper.

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Correspondence to Lucas K. A. Miranda.

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Miranda, L.K.A., Kuwana, C.M., Huggler, Y.H. et al. A short review of phase transition in a chaotic system. Eur. Phys. J. Spec. Top. 231, 167–177 (2022). https://doi.org/10.1140/epjs/s11734-021-00415-3

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