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Transition from bounded to unbounded energy in a time-dependent billiard
Anne Kétri P da Fonseca1, Felipe Augusto O Silveira1, Célia M Kuwana1,2
1UNESP-Universidade Estadual Paulista, Departamento de Física, Avenida 24A, 1515, Bela Vista, Rio Claro, 13506-900 São Paulo, Brazil.
Physical Review. E
|June 19, 2025
Summary
This study explores energy growth in an oval billiard system, revealing a phase transition from bounded to unbounded growth. Inelastic collisions introduce a crossover, creating behaviors analogous to statistical mechanics phase transitions.
Area of Science:
- * Physics
- * Statistical Mechanics
- * Dynamical Systems
Background:
- * Investigates a time-dependent, oval-shaped billiard system.
- * Examines the transition from bounded to unbounded energy growth in particle dynamics.
Purpose of the Study:
- * To analyze the impact of inelastic collisions on energy growth dynamics.
- * To identify and characterize a phase transition in the system.
- * To establish a connection between critical exponents via scaling laws.
Main Methods:
- * Solved the diffusion equation using a probability distribution that satisfies boundary conditions.
- * Employed scaling hypotheses and generalized homogeneous functions to derive critical exponent relations.
- * Validated findings through numerical simulations and analytical methods.
Main Results:
- * Inelastic collisions limit unbounded energy growth observed in conservative dynamics.
- * A phase transition exhibiting properties of continuous phase transitions in statistical mechanics was identified.
- * Scale invariance, interrelated critical exponents, and an order parameter behavior were observed.
Conclusions:
- * The system demonstrates behaviors analogous to continuous phase transitions, including scale invariance.
- * A scaling law relating critical exponents was derived and validated.
- * Elementary excitations facilitate diffusion, and no topological defects were found.
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