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Chaos in the Diamond-Shaped Billiard with Rounded Crown

Acceso Abierto
ID Minciencias: ART-0000077224-12
Ranking: ART-GC_ART

Abstract:

We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $\xi$ which gradually change the shape of the billiard from a regular equilateral triangle ($\xi=1$) to a diamond ($\xi=0$) was used to control the transition between the regular and chaotic regimes. The classical behaviour is regular when the control parameter $\xi$ is one; in contrast, the system is chaotic when $\xi \neq 1$ even for values of $\xi$ close to one. The entropy grows fast as $\xi$ is decreased from 1 and the Lyapunov exponent remains positive for $\xi<1$. The Finite Difference Method was implemented in order to solve the quantum problem. The energy spectrum and eigenstates were numerically computed for different values of the control parameter. The nearest-neighbour spacing distribution is analysed as a function of $\xi$, finding a Poisson and a Gaussian Orthogonal Ensemble (GOE) distribution for regular and chaotic regimes respectively. Several scars and bouncing ball states are shown with their corresponding classical periodic orbits. Along the document the classical chaos identifiers are computed to show that system is chaotic. On the other hand, the quantum counterpart is in agreement with the Bohigas-Giannoni-Schmit conjecture and exhibits the standard features for chaotic billiard such as the scarring of the wavefunction. © Acad. Colomb. Cienc. Ex. Fis. Nat. 2015.

Tópico:

Quantum chaos and dynamical systems

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Citations: 2
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Información de la Fuente:

SCImago Journal & Country Rank
FuenteRevista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales
Cuartil año de publicaciónNo disponible
Volumen39
Issue51
Páginas152 - 152
pISSN0370-3908
ISSNNo disponible

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