Dynamical Phase Transitions in Chaotic Systems

Edson Denis Leonel is a Professor of Physics at São Paulo State University, Rio Claro, Brazil. He has been dealing with scaling investigation since his Ph.D. in 2003, where the first scaling investigation in the chaotic sea for the Fermi-Ulam model was studied. His research group developed different approaches and formalisms to investigate and characterize the several scaling properties in a diversity types of systems ranging from one-dimensional mappings, passing to ordinary differential equations, cellular automata, meme propagations, and also in the time-dependent billiards. There are different types of transition we considered and discussed in these scaling investigations: (i) transition from integrability to non-integrability; (ii) transition from limited to unlimited diffusion; and (iii) production and suppression of Fermi acceleration. The latter approach involves the analytical solution of the diffusion equation. His group and he published more than 160 scientific papers in respected international journals, including three papers in Physical Review Letters. He is the Author of “Scaling Laws in Dynamical Systems” (2021) by Springer and Higher Education Press and two Portuguese books, one dealing with statistical mechanics (2015) and the other one dealing with nonlinear dynamics (2019), both edited by Blucher.

Posing the problems.- A Hamiltonian and a mapping.- A phenomenological description for chaotic diffusion.- A semi phenomenological description for chaotic diffusion.- A solution for the diffusion equation.- Characterization of a continuous phase transition in an area preserving map.- Scaling invariance for chaotic diffusion in a dissipative standard mapping.- Characterization of a transition from limited to unlimited diffusion.- Billiards with moving boundary.- Suppression of Fermi acceleration in oval billiard.- Suppressing the unlimited energy gain: evidences of a phase transition.