Related papers: Distribution of resonances for open quantum maps
We discuss the statistical properties of lifetimes of electromagnetic eigenmodes in dielectric microresonators with fully chaotic ray dynamics. Using the example of a resonator of stadium geometry, we find that a recently proposed…
In this paper, we consider a sequence of open quantum graphs, with uniformly bounded data, and we are interested in the asymptotic distribution of their scattering resonances. Supposing that the number of leads in our quantum graphs is…
The statistics of scattering of waves inside single ray-chaotic enclosures have been successfully described by the Random Coupling Model (RCM). We expand the RCM to systems consisting of multiple complex ray-chaotic enclosures with variable…
In the context of dissipative systems, we show that for any quantum chaotic attractor a corre- sponding classical chaotic attractor can always be found. We provide with a general way to locate them, rooted in the structure of the parameter…
A generalization of the Weyl law to systems with a sharply divided mixed phase space is proposed. The ansatz is composed of the usual Weyl term which counts the number of states in regular islands and a term associated with sticky regions…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The…
Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as…
We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to…
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…
In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for…
We investigate the transport properties of open quantum chaotic systems in the semiclassical limit. We show how the transmission spectrum, the conductance fluctuations, and their correlations are influenced by the underlying chaotic…
Semiclassical behavior of Stark resonances is studied. The complex distortion outside a cone is introduced to study resonances in any energy region for the Stark Hamiltonians with non-globally analytic potentials. The non-trapping resolvent…
We study the signatures of a classical mixed phase space for open quantum systems. We find the scaling of the break time up to which quantum mechanics mimics the classical staying probability and derive the distribution of resonance widths.…
Discerning chaos in quantum systems is an important problem as the usual route of Lyapunov exponents in classical systems is not straightforward in quantum systems. A standard route is the comparison of statistics derived from model…
We study the spreading of a quantum-mechanical wavepacket in a one-dimensional tight-binding model with a noisy potential, and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
We consider compact Lie groups extensions of expanding maps of the circle, essentially restricting to U(1) and SU(2) extensions. The central object of the paper is the associated Ruelle transfer (or pull-back) operator $\hat{F}$. Harmonic…
We show that in clean chaotic cavities the power of shot noise takes a universal form. Our predictions go beyond previous results from random-matrix theory, in covering the experimentally relevant case of few channels. Following a…