title: Dynamical properties of the soft-wall elliptical billiard.
abstract: Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems.
authors.affiliation: Departamento Acadêmico de Física, Universidade Tecnológica Federal do Paraná-UTFPR Campus Pato Branco, Pato Branco 85503-390, PR, Brazil.|Departamento de Física, Universidade Federal do Paraná-UFPR, Curitiba 81531-990, PR, Brazil.
authors.forename: Tiago
authors.initials: T
authors.lastname: Kroetz
authors.affiliation: Departamento Acadêmico de Matemática, Universidade Tecnológica Federal do Paraná-UTFPR Campus Ponta Grossa, Ponta Grossa 84016-210, PR, Brazil.
authors.forename: Hércules A
authors.initials: HA
authors.lastname: Oliveira
authors.affiliation: Departamento Acadêmico de Física, Universidade Tecnológica Federal do Paraná-UTFPR Campus Pato Branco, Pato Branco 85503-390, PR, Brazil.
authors.forename: Jefferson S E
authors.initials: JS
authors.lastname: Portela
authors.affiliation: Departamento de Física, Universidade Federal do Paraná-UFPR, Curitiba 81531-990, PR, Brazil.
authors.forename: Ricardo L
authors.initials: RL
authors.lastname: Viana