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Quantum Mechanics of a Rotating Billiard

Abstract

Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, =2E/2\lambda = 2E/\omega^{2} where E is the energy of the particle inside the billiard and \omega is the angular frequency of rotation of billiard. We study the system classically and quantum mechanically in view of obtaining a correspondence in the two descriptions. Classical phase space in Poincar\'{e} surface of section shows transition from regular to chaotic motion as the parameter \lambda is decreased. In the Quantum counterpart, the spectral statistics shows a transition from Poisson to Wigner distribution as the system turns chaotic with decrease in \lambda. The wavefunction statistics however show breakdown of time-reversal symmetry as \lambda decreases

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