Related papers: Fractal Weyl laws for chaotic open systems
We demonstrate both theoretically and experimentally that the distribution of the wavefunction inside a partially open chaotic timereversal symmetric system displays significant deviations from the Porter Thomas distribution. We give…
For two-dimensional quantum billiards we derive the partial Weyl law, i.e. the average density of states, for a subset of eigenstates concentrating on an invariant region $\Gamma$ of phase space. The leading term is proportional to the area…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
The distribution of eigenvalues of the wave equation in a bounded domain is known as Weyl's problem. We describe several computational projects related to the cumulative state number, defined as the number of states having wavenumber up to…
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on…
In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasi-bound states is…
We investigate the effects of classical stickiness (orbits temporarily confined to a region of the chaotic phase space) to the structures of the quantum states of an open system. We consider the standard map of the kicked rotor and verify…
The prediction of the response of a closed system to external perturbations is one of the central problems in quantum mechanics, and in this respect, the local density of states (LDOS) provides an in- depth description of such a response.…
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…
On a closed manifold $M$, we consider a smooth vector field $X$ that generates an Anosov flow. Let $V\in C^{\infty}\left(M;\mathbb{R}\right)$ be a smooth function called potential. It is known that for any $C>0$, there exists some…
In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system…
The electronic structure of a cubic $\mathcal{T}$-symmetric Weyl semimetal is analysed in the presence of atomic-sized vacancy defects. Isolated vacancies are shown to generate nodal bound states with $r^{{\scriptscriptstyle -2}}$…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of conductance vs. externally changed parameter, e.g. magnetic field, is a fractal with…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
In mesoscopic systems conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system with either fully chaotic or mixed phase space generically…
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter such as an applied…
We consider quantum interferences of ballistic electrons propagating inside fractal structures with nanometric size of their arms. We use a scaling argument to calculate the density of states of free electrons confined in a simple model…