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N-disk microwave billiards, which are representative of open quantum systems, are studied experimentally. The transmission spectrum yields the quantum resonances which are consistent with semiclassical calculations. The spectral…
It is shown that tunnelling splittings in ergodic double wells and resonant widths in ergodic metastable wells can be approximated as easily-calculated matrix elements involving the wavefunction in the neighbourhood of a certain real orbit.…
Non-universal correlations due to localization are observed in statistical properties of experimental eigenfunctions of quantum chaotic and disordered microwave cavities. Varying energy {E} and mean free path {l} enable us to experimentally…
In the framework of the semiclassical approach the universal spectral correlations in the Hamiltonian systems with classical chaotic dynamics can be attributed to the systematic correlations between actions of periodic orbits which (up to…
We study the scaling behavior of $M$-furcation $(M\!=\!2, 3, 4,\dots)$ sequences of $M^n$-period $(n=1,2,\dots)$ orbits in two coupled one-dimensional (1D) maps. Using a renormalization method, how the scaling behavior depends on $M$ is…
Semiclassical analysis of shell structures in realistic nuclear potentials are presented using periodic-orbit theory. We adopted r^alpha potential model and examined classical-quantum correspondence using Fourier transformation technique.…
Scrambling is the delocalization of quantum information over a many-body system and underlies all quantum-chaotic dynamics. We employ discrete quantum cellular automata as classically simulable toy models of scrambling. We observe that…
We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results…
Experiments performed on strongly interacting Rydberg atoms have revealed surprising persistent oscillations of local observables. These oscillations have been attributed to a special set of non-ergodic states, referred to as quantum…
Interfering electrons in a mesoscopic ring are irradiated with both classical and nonclassical microwaves. The average intensity of the charges is calculated as a function of time and it is found that it depends on the nature of the…
The semi-quantal dynamics is applied to investigate the influence of quantum fluctuations on problems in classical chaos through intermittency involving bifurcations. The results of the numerical calculations indicate that quantum effects…
In this work, we focus on an autocatalytic reaction-diffusion model and carry out multiple scale weakly nonlinear analysis. A cubic and a quadratic autocatalytic reaction system is analysed. We develop a framework to identify the critical…
Quantum trajectories defined in the de Broglie--Bohm theory provide a causal way to interpret physical phenomena. In this Letter, we use this formalism to analyze the short time dynamics induced by unstable periodic orbits in a classically…
The oscillation spectrum of pressure waves in stars can be determined by monitoring their luminosity. For rapidly rotating stars, the corresponding ray dynamics is mixed, with chaotic and regular zones in phase space. Our numerical…
Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical…
Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this…
We evaluate the variance of coefficients of the characteristic polynomial for binary quantum graphs using a dynamical approach. This is the first example where a spectral statistic can be evaluated in terms of periodic orbits for a system…
Protecting coherent quantum dynamics from chaotic environment is key to realizations of fragile many-body phenomena and their applications in quantum technology. We present a general construction that embeds a desired periodic orbit into a…
We show that electronic materials with disallowed rotational symmetries that enforce quasiperiodic order can exhibit quantum oscillations and that these are generically associated with exotic "spiral Fermi surfaces." These Fermi surfaces…
The spectrum of eigenenergies of a quantum integrable system whose hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the…