arXiv subjects

Matic Orel

Publications and source records attributed to Matic Orel.

5 recordsLinked to original sources

arXiv2026

Perturbed quantum billiards on the hyperbolic plane

We study the emergence of generic quantum chaos from an arithmetic billiard in the hyperbolic plane. Starting from an arithmetic triangle, we introduce small area-preserving geometric perturbations and compute long consecutive sequences of eigenvalues and eigenstates. The spectral statistics show a perturbation-dependent crossover from Poisson-like arithmetic behaviour to the Gaussian orthogonal ensemble (GOE), with the crossover scale moving to higher wavenumbers as the perturbation decreases. To characterize the nearest-neighbour spacing distribution, we compare the data with Brody and generalized-gamma fits. The generalized-gamma form is used only as a two-parameter diagnostic, allowing the small- and intermediate-spacing structure to vary independently from the large-spacing tail, rather than as a universal crossover law. For the weakest perturbation, we also compare the data with an effective block-GOE model, which diagnoses residual block-like structure deep into the computed spectral range. We complement the spectral analysis with Poincar\'e-Husimi representations of the eigenstates and quantify phase-space localization using an entropy-based measure. Its distribution is well described by Beta distributions whose width decays as a power law in the wavenumber. Before the spectral crossover, the localization statistics retain memory of the near-arithmetic regime. After the GOE regime is reached, the localization-fluctuation widths collapse onto a common decay law, sigma(Beta) ~ k^{-eta}, with eta approximately 0.37--0.38. These results provide a combined spectral and eigenfunction-level picture of the arithmetic-to-GOE crossover in hyperbolic quantum billiards.

quant-ph↗

arXiv2026

Spectral statistics and localization properties of a $C_3$-symmetric billiard

We revisit the spectral statistics of the C$_3$--symmetric billiard introduced by Dembowski [Phys. Rev. E, R4516 (2000)], which exhibits both GOE and GUE statistics depending on the symmetry block. Using high--precision Beyn's contour--integral method for the nonlinear Fredholm eigenvalue problem with built-in separation of irreducible subspaces, we compute 2.8x10$^5$ eigenvalues in each symmetry subspace, enabling statistically meaningful comparisons with random matrix theory. The improved spectra reveal clear GOE--GUE correspondence and resolve previously observed deviations in long--range spectral correlations. Furthermore, we analyze phase--space eigenstate localization through the distribution of entropy localization measures, which, for chaotic states follow a Beta distribution whose standard deviation decays as a power--law with energy, consistent with the onset of quantum ergodicity as described by Schnirelman's theorem.

quant-ph↗

arXiv2025

Quantum chaos and semiclassical behavior in mushroom billiards II: Structure of quantum eigenstates and their phase space localization properties

We investigate eigenstate localization in the phase space of the Bunimovich mushroom billiard, a paradigmatic mixed-phase-space system whose piecewise-$C^{1}$ boundary yields a single clean separatrix between one regular and one chaotic region. By varying the stem half-width $w$, we continuously change the strength and extent of bouncing-ball stickiness in the stem, which for narrow stems gives rise to phase space localization of chaotic eigenstates. Using the Poincar\'e-Husimi (PH) representation of eigenstates we quantify localization via information entropies and inverse participation ratios of PH functions. For sufficiently wide stems the distribution of entropy localization measures converges to a two-parameter beta distribution, while entropy localization measures and inverse participation ratios across the chaotic ensemble exhibit an approximately linear relationship. Finally, the fraction of mixed (neither purely regular nor fully chaotic) eigenstates decays as a power-law in the effective semiclassical parameter, in precise agreement with the Principle of Uniform Semiclassical Condensation of Wigner functions (PUSC).

nlin.CD↗

arXiv2025

Correspondence principle, dissipation, and Ginibre ensemble

The correspondence between quantum and classical behavior has been essential since the advent of quantum mechanics. This principle serves as a cornerstone for understanding quantum chaos, which has garnered increased attention due to its strong impact in various theoretical and experimental fields. When dissipation is considered, quantum chaos takes concepts from isolated quantum chaos to link classical chaotic motion with spectral correlations of Ginibre ensembles. This correspondence was first identified in periodically kicked systems with damping, but it has been shown to break down in dissipative atom-photon systems [Phys. Rev. Lett. 133, 240404 (2024)]. In this contribution, we revisit the original kicked model and perform a systematic exploration across a broad parameter space, reaching a genuine semiclassical limit. Our results demonstrate that the correspondence principle, as defined through this spectral connection, fails even in this prototypical system. These findings provide conclusive evidence that Ginibre spectral correlations are neither a robust nor a universal diagnostic of dissipative quantum chaos.

quant-ph↗

arXiv2025

Quantum chaos and semiclassical behavior in mushroom billiards I: Spectral statistics

We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component, whose size depends on the width w of the stem, and has two limiting geometries, namely the circle (as the integrable system) and stadium (as the fully chaotic system). Therefore, this one-parameter system is ideal to study the semiclassical behavior of the quantum counterpart. Here, in paper I, we study the spectral statistics as a function of the geometry defined by w, and as a function of the semiclassical parameter k, which in this case is just the wavenumber k. We show that at sufficiently large k the level spacing distribution is excellently described by the Berry-Robnik (BR) distribution (without fitting). At lower k the small deviations from it can be well described by the Berry-Robnik-Brody (BRB) distribution, which captures the effects of weak dynamical localization of Poincar\'e-Husimi functions. We also employ the analytical theory of the level spacing ratios distribution P(r) for mixed-type systems, recently obtained by Yan (2025), which does not require a spectral unfolding procedure, and show excellent agreement with numerics in the semiclassical limit of large k. In paper II we shall analyze the eigenstates by means of Poincar\'e-Husimi functions.

quant-ph↗