arXiv subjects

Barbara Dietz

Publications and source records attributed to Barbara Dietz.

At least 19 recordsLinked to original sources

arXiv2026

Lyapunov spectrum scaling transition for quasiperiodic nonlinear unitaries

We study the Lyapunov spectrum scaling of thermal weakly-nonlinear unitary maps in the presence of quasiperiodic potentials. We search for the crossover from long-range to short-range scaling as the localization length {\xi} decreases and compare the details to the case of uncorrelated Anderson disorder [Phys. Rev. Res. 6 L012064 (2024)]. A comparative statistical analysis of the eigenstates for the linear case shows that quasiperiodicity has a stronger localization impact at the same value of {\xi}. Therefore we expect that the scaling crossover should be enhanced as well. However, the numerical analysis shows that it is strongly delayed as compared to Anderson disorder, and is observed at anomalously small values of {\xi}. These findings hint at the potential impact of long range correlations of quasiperiodic localized eigenstates, which persist in the presence of interactions even in the case of integrability breaking and thermalization.

nlin.CD↗

arXiv2026

Relativistic Quantum Chaos in Neutrino Billiards

Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary conditions on the spinor components which were proposed in [Berry and Mondragon 1987, {\it Proc. R. Soc.} A {\bf 412} 53) . We review their general features and the properties of neutrino billiards with shapes of billiards with integrable dynamics. Furthermore, we review the features of two neutrino billiards with the shapes of billiards generating a chaotic dynamics, whose nonrelativistic counterpart exhibits particular properties. Finally we briefly discuss possible experimental realizations of relativistic quantium billiards based on graphene billiards, that is, finite size sheets of graphene.

nlin.CD↗

arXiv2026

Universality Emerging in a Universality: Derivation of the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation

At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached in which the cross section behaves like a random function. The scattering-matrix elements then follow a universal Gaussian distribution. For more than sixty years, the emergence of this robust additional universal behavior on top of the universal system stochasticity has awaited a concise analytical treatment. We derive the transition to the Ericson regime in the universal Heidelberg approach and prove the universal Gaussian distribution by a proper asymptotic expansion. We also obtain explicit formulae for the moments of the distributions. We compare with microwave experiments and numerical simulations.

cond-mat.stat-mech↗

arXiv2026

Experimental study of coupled quantum billiards with integrable and chaotic classical dynamics and test of a special Rosenzweig-Porter model

We report on the experimental study of the spectral properties of quantum systems consisting of two quantum billiards (QBs), one with chaotic, the other one with integrable classical dynamics, that are coupled to each other via an opening in a common wall. They are compared to those of a special case of the Rosenzweig-Porter model with random matrices composed of two diagonal blocks modeling the spectral properties of the QBs, that are coupled with a tunable parameter. We demonstrate that this model is suitable for the description of the experimental data and thus may be employed to determine the strength of the coupling. It results from the increasing overlap of eigenmodes in the QBs penetrating through the opening into the other one, leading to a mixing of their eigenstates, and the breaking of the symmetry present in the QB with integrable dynamics. This implicates deviations of the spectral properties from those of typical quantum systems with integrable and chaotic dynamics, respectively, and approaches those of a fully chaotic system for sufficiently large coupling strength. In contrast in previous studies the transition from integrable to chaotic dynamics was induced by introducing a random potential of increasing strength into such a QB and applicability of a variant of the Rosenzweig-Porter model was tested.

nlin.CD↗

arXiv2026

Nonrelativistic versus relativistic quantum scars in billiard systems

We study the features of scarred eigenstates of relativistic neutrino billiards (NBs), graphene billiards (GBs) and Haldane graphene billiards (HGBs) and recapitulate those for nonrelativistic quantum billiards (NRQBs) with the shapes of a full- and quarter-stadium billiard. Here, we restrict for the GBs and HGBs to the region of linear dispersion around the Fermi energy, where they are effectively described by the same Dirac equation for massless spin-1/2 particles as NBs. Scarred wave functions of the nonrelativistic billiards and spinor functions of the relativistic ones are localized along the same types of periodic orbits, the most prominent ones being bouncing-ball orbits. The objective is to demonstrate that the properties of the scarred eigenstates observed in the full- and quarter-stadium GB \emph{do not comply} with those of relativistic quantum systems. For this we apply the semiclassical approach associated with such non-generic contributions, which was developed for the spectral density of NRQBs and NBs. It provides semiclassical trace formulas in terms of the periodic orbits associated with a scarred wave function and a procedure to extract such contributions from the eigenvalue spectra. Furthermore, we analyze momentum distributions and Husimi functions of such scarred states and employ them to classify scarred wave functions according to the periodic orbits along which they are localized. We show that for the GB the semiclassical approach, the spectral properties, the symmetry properties and generally properties of the wave functions all comply with those of the NRQB, whereas for the HGB they agree well with those of the NB. Thus, even though around the Fermi energy GBs are described by the relativistic Dirac equation the quantum scars, or generally, the quantum scarred eigenstates observed in GBs do not exhibit those of relativistic ones.

nlin.CD↗

arXiv2025

Quartic level repulsion in a quantum chaotic three-body system without symplectic symmetry

Among the fundamental symmetry classes of quantum chaotic systems in Dyson's threefold way, the symplectic class is rarely observed in nature. Characterized by the strongest possible level repulsion in the energy spectrum, the symplectic symmetry class also implies a double (Kramers) degeneracy of levels. Studying the spectral statistics of three quantum particles (identical bosons or mass-imbalanced fermions) in a harmonic trap, we find numerical evidence for strong level repulsion in the regime of weak contact interactions. While the statistical indicators are consistent with quantum chaos in systems with symplectic symmetry, the absence of Kramers degeneracy rules out this symmetry. In the strongly-interacting unitary limit either Poissonian or stick statistics are observed (depending on commensurability of the mass ratio) indicating regular dynamics.

cond-mat.quant-gas↗

arXiv2025

Experimental study of the distributions of off-diagonal scattering-matrix elements of quantum graphs with symplectic symmetry

We report on experimental studies of the distribution of the off-diagonal elements of the scattering matrix of open microwave networks with symplectic symmetry and a chaotic wave dynamics. These consist of two geometrically identical subgraphs with unitary symmetry described by complex conjugate Hamiltonians, that are coupled by a pair of bonds. The results are compared to random-matrix theory predictions obtained on the basis of the Heidelberg approach for the scattering matrix of open quantum-chaotic systems. We demonstrate that deviations from random-matrix theory predictions observed in the distributions may be attributed to the fact that the subgraphs are not fully connected.

quant-ph↗

arXiv2025

Failure of the conformal-map method for relativistic quantum billiards

We demonstrate that the conformal-map method introduced by Robnik in 1984 for nonrelativistic quantum billiards is not applicable for the quantization of relativistic neutrino billiards (NBs) consisting of a massless non-interacting spin-1/2 particle confined to a two-dimensional domain. To be precise, we demonstrate in this work, that this method does not provide solutions of the associated Weyl (Dirac) equation, nor does it fulfill the boundary conditions imposed on the spinor eigenfunctions to ensure confinement of the particle to the domain of the billiard. We review in detail the wave equation, boundary conditions and quantization of NBs and derivation of relevant equations, to make the proof comprehensible for the general reader. Our results are corroborated with numerical results for non-relativistic and relativistic quantum billiards whose shapes depend on a parameter, which allows the study of the properties of their eigenstates as the classical dynamics experiences a transition from regular to chaotic dynamics.

nlin.CD↗

arXiv2025

Exact Results for the Ericson Transition in Stochastic Quantum Scattering and Experimental Validation

At lower energies, the resonances in scattering experiments are often isolated. The crucial parameter is the ratio of average resonance width and average mean level spacing. Towards larger energies, this parameter grows, because the resonances overlap. Eventually the cross-section becomes a random function and the scattering matrix elements follow a universal Gaussian distribution. For more than sixty years, this Ericson transition awaits a concise analytical treatment. We provide a complete solution within the Heidelberg approach which provides a full-fledged model of the scattering process. As a side result, we obtain explicit formulae for the moments of the distributions. We compare with microwave experiments.

cond-mat.stat-mech↗

arXiv2025

Decay Rates of Optical Modes Unveil the Island Structures in Mixed Phase Space

We explore the decay rates of optical modes in asymmetric microcavities with mixed phase space across a wide range of wavelengths that extend deep into the semiclassical, i.e., short-wavelength limit. Implementing an efficient numerical method, we computed 1000000 eigenmodes and discovered that certain decay rates form sequential separate branches with increasing wavenumber that eventually merge into smooth curves. The analysis of the localization properties and Husimi distributions reveals that each branch corresponds to a periodic orbit in the closed classical system. Our findings show that these decay rates gradually resolve the structure of the islands in mixed phase space as we approach the short-wavelength limit. We present an effective semiclassical model incorporating wavenumber-dependent localization, Fresnel reflection, and the Goos-Haenchen shift and demonstrate that these effects are crucial in accounting for the observed branches of decay rate curves.

physics.optics↗

arXiv2025

Observation of prethermalization in weakly nonintegrable unitary maps

We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $\Lambda(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for different initial conditions and compute the mean $\mu(t)$ and standard deviation $\sigma(t)$ of $\Lambda(t)$. Thermalization implies a temporal decay $\sigma \sim t^{-1/2}$ at a converged finite value of $\mu$. We report prethermalization plateaus that persist for long times where both $\mu$ and $\sigma$ appear to have converged to finite values, seemingly implying differing saturated Lyapunov exponent values for different trajectories. The lifetime of such plateaus furnishes a novel time scale characterizing the thermalization dynamics of many-body systems close to integrability. We also find that the plateaus converge to their respective thermal values for long enough times.

nlin.CD↗

arXiv2024

The Rosenzweig Porter model revisited for the three Wigner Dyson symmetry classes

We present numerical results for the Rosenzweig Porter model for all symmetry classes of the Dyson threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the spectral properties as measures to explore the transition from Poisson to Wigner Dyson WD statistics. Furthermore, we performed thorough studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback Leibler KL divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

cond-mat.stat-mech↗

arXiv2024

Haldane graphene billiards versus relativistic neutrino billiards

We study fluctuation properties in the energy spectra of finite-size honeycomb lattices, graphene billiards, subject to the Haldane-model onsite potential and next-nearest neighbor interaction at critical points, referred to as Haldane graphene billiards in the following. The billiards had the shapes of a rectangular billiard with integrable dynamics, one with chaotic dynamics, and one whose shape has, in addition, threefold rotational symmetry. It had been shown that the spectral properties of the graphene billiards coincide with those of the nonrelativistic quantum billiard with the corresponding shape, both at the band edges and in the region of low energy excitations around the Dirac points at zero energy. There, the dispersion relation is linear and, accordingly, the spectrum is described by the same relativistic Dirac equation for massless half-spin particles as relativistic neutrino billiards, whose spectral properties agree with those of nonrelativistic quantum billiards with violated time-reversal invariance. Deviations from the expected behavior are attributed to differing boundary conditions and backscattering at the boundary, which leads to a mixing of valley states corresponding to the two Dirac points, that are mapped into each other through time reversal. We employ a Haldane model to introduce a gap at one of the two Dirac points so that backscattering is suppressed in the energy region of the gap and demonstrate that there the correlations in the spectra comply with those of the neutrino billiard of the corresponding shape.

nlin.CD↗

arXiv2024

Closed and open superconducting microwave waveguide networks as a model for quantum graphs

We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds. The tetrahedral network comprises T junctions, while the honeycomb network exclusively consists of Y junctions, that join waveguides with relative angles 90 degree and 120 degree, respectively. We demonstrate that the vertex scattering matrix, which describes the propagation of the modes through the junctions strongly depends on frequency and is non-symmetric at a T junction and thus differs from that of a quantum graph with Neumann boundary conditions at the vertices. On the contrary, at a Y junction, similarity can be achieved in a certain frequeny range. We investigate the spectral properties of closed waveguide networks and fluctuation properties of the scattering matrix of open ones and find good agreement with random matrix theory predictions for the honeycomb waveguide graph.

cond-mat.mes-hall↗

arXiv2023

Thermalization Universality-Class Transition Induced by Anderson Localization

We study the disorder-induced crossover between the two recently discovered thermalization slowing-down universality classes -- characterized by long- and short-range coupling -- in classical unitary circuits maps close to integrability. We compute Lyapunov spectra, which display qualitatively distinct features depending on whether the proximity to the integrable limit is short or long ranged. For sufficiently small nonlinearity, translationally invariant systems fall into the long-range class. Adding disorder to such a system triggers a transition to the short-range class -- implying a breaking of this invariance -- and in the very limit of vanishing non-linearity Anderson localization emerges. The crossover from long- to short-range class is attained by tuning the localization length, $ξ$, from $ξ\approx N$ to $ξ\ll N$, where $N$ is the system size. As a consequence, the Lyapunov spectrum becomes exponentially suppressed, depending on how strongly its translational invariance is destroyed. We expect that this disorder-induced crossover will lead to prethermalized phases and, following quantization, to many-body localization.

nlin.CD↗

arXiv2023

Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics

We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T-invariance violation and chaoticity are induced by magnetizing a ferrite disk placed at its center, which above the cutoff frequency of the first transverse-electric mode acts as a random potential. We determine a complete sequence of approx. 1000 eigenfrequencies and find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model, which interpolates between Poisson statistics expected for typical integrable systems and Gaussian unitary ensemble statistics predicted for chaotic systems with violated T invariance. Furthermore, we combine the RP model and the Heidelberg approach for quantum-chaotic scattering to construct a random-matrix model for the scattering (S) matrix of the corresponding open quantum system and show that it perfectly reproduces the fluctuation properties of the measured S matrix of the microwave resonator.

quant-ph↗

arXiv2023

Machine learning wave functions to identify fractal phases

We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, non-ergodic extended (fractal) and localized phases in various systems: single-particle models, including random-matrix and random-graph models, and many-body quantum systems. The network can be successfully trained on a small data set of only 500 wave functions (images) per class for a single model. The trained network can then be used to classify phases in the other models and is thus very efficient. We discuss the strengths and limitations of the approach.

cond-mat.dis-nn↗

arXiv2023

Time-reversal Invariance Violation and Quantum Chaos Induced by Magnetization in Ferrite-Loaded Resonators

We investigate the fluctuation properties in the eigenfrequency spectra of flat cylindrical microwave cavities that are homogeneously filled with magnetized ferrite. These studies are motivated by experiments in which only small pieces of ferrite were embedded in the cavity and magnetized with an external static magnetic field to induce partial time-reversal (T ) invariance violation. We use two different shapes of the cavity, one exhibiting an integrable wave dynamics, the other one a chaotic one. We demonstrate that in the frequency region where only transverse-magnetic modes exist, the magnetization of the ferrites has no effect on the wave dynamics and does not induce T -invariance violation whereas it is fully violated above the cutoff frequency of the first transverse-electric mode. Above all, independently of the shape of the resonator, it induces a chaotic wave dynamics in that frequency range in the sense that for both resonator geometries the spectral properties coincide with those of quantum systems with a chaotic classical dynamics and same invariance properties under application of the generalized T operator associated with the resonator geometry.

nlin.CD↗