Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1859668 | Physics Letters A | 2015 | 8 Pages |
•Scaling formalism to describe a transition from integrable to non-integrable;•Homogeneous function used to obtain critical exponents;•A break of symmetry of the probability function explains an additional scaling.
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) ϵ , controlling the transition from integrable (ϵ=0ϵ=0) to non-integrable (ϵ≠0ϵ≠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 ϵ or n and obtain a scaling law for the three critical exponents.