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Quantum chaos in triangular billiards
Črt Lozej, Giulio Casati, Tomaž Prosen, 2022, original scientific article

Abstract: We present an extensive numerical study of spectral statistics and eigenfunctions of quantized triangular billiards. We compute two million consecutive eigenvalues for six representative cases of triangular billiards, three with generic angles with irrational ratios with π, whose classical dynamics is presumably mixing, and three with exactly one angle rational with π, which are presumably only weakly mixing or even nonergodic in case of right triangles. We find excellent agreement of short- and long-range spectral statistics with the Gaussian orthogonal ensemble of random matrix theory for the most irrational generic triangle, while the other cases show small but significant deviations which are attributed either to a scarring or superscarring mechanism. This result, which extends the quantum chaos conjecture to systems with dynamical mixing in the absence of hard (Lyapunov) chaos, has been corroborated by analyzing distributions of phase-space localization measures of eigenstates and inspecting the structure of characteristic typical and atypical eigenfunctions.
Keywords: quantum physics, quantum chaos, quantum scars, wave chaos, billiards, chaos and nonlinear dynamics, ergodic theory
Published in DKUM: 12.10.2023; Views: 294; Downloads: 35
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Expanded boundary integral method and chaotic time-reversal in quatum billiards
Gregor Veble, Tomaž Prosen, Marko Robnik, 2007, original scientific article

Abstract: We present the expanded boundary integral method for solving the planar Helmholtz problem, which combines the ideas of the boundary integral method and the scaling method and is applicable to arbitrary shapes. We apply the method to a chaotic billiard with unidirectional transport, where we demonstrate the existence of doublets of chaotic eigenstates, which are quasi-degenerate due to time-reversal symmetry, and a very particular level spacing distribution that attains a chaotic Shnirelman peak at short energy ranges and exhibits Gaussian Unitary Ensemble (GUE) like statistics for large energy ranges. We show that, as a consequence of such particular level statistics or algebraic tunnelling between disjoint chaotic components connected by time-reversal operation, the system exhibits quantum current reversals.
Keywords: 2D Helmholtz equation, energy spectrum, quantum billiard
Published in DKUM: 03.07.2017; Views: 1811; Downloads: 203
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