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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

A short review of phase transition in a chaotic system

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Miranda, Lucas K. A. [1] ; Kuwana, Celia M. [1] ; Huggler, Yona H. [1] ; da Fonseca, Anne K. P. [1] ; Yoshida, Makoto [1] ; de Oliveira, Juliano A. [1, 2] ; Leonel, Edson D. [1]
Total Authors: 7
[1] Univ Estadual Paulista, UNESP, Dept Fis, Av 24A, 1515 Bela Vista, BR-13506900 Rio Claro, SP - Brazil
[2] Univ Estadual Paulista, UNESP, Campus Sao Joao da Boa Vista, Sao Joao Da Boa Vista, SP - Brazil
Total Affiliations: 2
Document type: Review article
Source: European Physical Journal-Special Topics; DEC 2021.
Web of Science Citations: 0

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. (AU)

FAPESP's process: 20/10602-1 - A study of phase transition in chaotic system
Grantee:Lucas Kenji Arima Miranda
Support Opportunities: Scholarships in Brazil - Scientific Initiation
FAPESP's process: 18/14685-9 - Transport properties and bifurcation analysis in nonlinear dynamical systems
Grantee:Juliano Antonio de Oliveira
Support Opportunities: Regular Research Grants
FAPESP's process: 19/14038-6 - Investigation of dynamical properties in nonlinear systems
Grantee:Edson Denis Leonel
Support Opportunities: Regular Research Grants
FAPESP's process: 20/07219-1 - Chaotic diffusion in time dependent billiards
Grantee:Anne Kétri Pasquinelli da Fonseca
Support Opportunities: Scholarships in Brazil - Scientific Initiation