Discussing a transition from bounded to unbounded energy in a time-dependent billiard

Abstract

We revisit a time-dependent, oval-shaped billiard to investigate a phase transition from bounded to unbounded energy growth. In the static case, the phase space exhibits a mixed structure. The chaotic sea in the static scenario leads to average energy growth for a time-dependent boundary. However, inelastic collisions between the particle and the boundary limit this unbounded energy increase. This transition displays properties similar to continuous phase transitions in statistical mechanics, including scale invariance, interrelated critical exponents governed by scaling laws, and an order parameter/susceptibility approaching zero/infinity at the transition. Furthermore, the system exhibits an elementary excitation that promotes particle diffusion and lacks topological defects that provide modifications to the probability distribution function.

References in corpus (13)

• First order superconducting phase transition in CeCoIn${}_5$
• Quantum phase transitions in d-wave superconductors
• Tunable Fermi acceleration in the driven elliptical billiard
• Bose-Einstein condensation and Superfluidity of magnetoexcitons in Graphene
• Critical Exponents of the Superconducting Phase Transition
• Open circular billiards and the Riemann hypothesis
• Unusual thermodynamical and transport signatures of short coherence length superconductors: A BCS Bose-Einstein crossover approach
• Survival Probability for the Stadium Billiard
• Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas
• Exponential Fermi acceleration in general time-dependent billiards
• Thermodynamics of a time dependent and dissipative oval billiard: a heat transfer and billiard approach
• Aspects of diffusion in the stadium billiard
• Scaling Invariance in a Time-Dependent Elliptical Billiard