Related papers: Quantum chaos with graphs: a silicon photonics pla…
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…
Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of…
It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of…
To determine the regular or chaotic nature of the orbits in dynamical systems can be quite an issue. In this article, following Vozikis et al. (2000), we propose a new tool, namely, the Power Spectrum Indicator (PSI), $\psi^2$, that enables…
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the…
Chaotic systems that decompose into two cells connected only by a narrow channel exhibit characteristic deviations of their quantum spectral statistics from the canonical random-matrix ensembles. The equilibration between the cells…
We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the…
Whenever graphs admit equitable partitions, their quotient graphs highlight the structure evidenced by the partition. It is therefore very natural to ask what can be said about two graphs that have the same quotient according to certain…
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting…
The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of…
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
Chaotic maps are very important for establishing chaos-based image encryption systems. This paper introduces a coupling chaotic system based on a certain unit transform, which can combine any two 1D chaotic maps to generate a new one with…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
We give an estimate of the quantum variance for $d$-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum…
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…