A dynamical phase transition for a family of Hamiltonian mappings: A phenomenological investigation to obtain the critical exponents - Leonel, Edson D. [UNESP] (2015)
Abstract A dynamical phase transition from integrability to non-integrability for a family of 2-D Hamiltonian mappings whose angle, θ, diverges in the limit of vanishingly action, I, is characterised. The mappings are described by two parameters: (i) Ïμ, controlling the transition from integrable (Ïμ=0) to non-integrable (Ïμ≠0); and (ii) γ, denoting the power of the action in the equation which defines the angle. We prove the average action is scaling invariant with respect to either Ïμ or n and obtain a scaling law for the three critical exponents.