Related papers: Multifractal wave functions of simple quantum maps
We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin 2-D microwave cavities. Two, three, and four-disk scattering are investigated in detail. The experiments, which are able to probe the…
The computation of multifractal scaling properties associated with a critical field theory involves non-local operators and remains an open problem using conventional techniques of field theory. We propose a new description of Gaussian…
We consider a family of random matrix ensembles (RME) invariant under similarity transformations and described by the probability density $P({\bf H})= \exp[-{\rm Tr}V({\bf H})]$. Dyson's mean field theory (MFT) of the corresponding plasma…
The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on…
Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices.…
Complex systems are composed of mutually interacting components and the output values of these components are usually long-range cross-correlated. We propose a method to characterize the joint multifractal nature of such long-range cross…
In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…
We review the time evolution of wavepackets at the metal-insulator transition in two- and three-dimensional disordered systems. The importance of scale invariance and multifractal eigenfunction fluctuations is stressed. The implications of…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
Using low-temperature scanning tunneling spectroscopy, we map the local density of states (LDOS) of graphene quantum dots supported on Ir(111). Due to a band gap in the projected Ir band structure around the graphene K point, the electronic…
The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…
We consider the multifractal analysis of the pointwise dimension for Gibbs measures on countable Markov shifts. Our paper analyses the set of non-analytic points or phase transitions of the multifractal spectrum. By Sarig's thermodynamic…
We study (1+1)D transverse localization of electromagnetic radiation at microwave frequencies directly by two-dimensional spatial scans. Since the longitudinal direction can be mapped onto time, our experiments provide unique snapshots of…
Understanding the stochastic properties of conductance fluctuations in disordered mesoscopic systems is fundamental to quantum transport. In this work, we investigate the multifractal and ergodic properties of the fictitious time series of…
We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions subject to projective monitoring of local charge across the measurement-induced phase transition. Our observables are…
This paper gives the pointwise H\"older (or multifractal) spectrum of continuous functions on the interval $[0,1]$ whose graph is the attractor of an iterated function system consisting of $r\geq 2$ affine maps on $\mathbb{R}^2$. These…
Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike…
We introduce a new approach to the periodic Anderson model (PAM) that allows a detailed investigation of the magnetic properties in the Kondo as well as the intermediate valence regime. Our method is based on an exact mapping of the PAM…
A remarkable mathematical property -- somehow hidden and recently rediscovered -- allows obtaining the eigenvectors of a Hermitian matrix directly from their eigenvalues. That opens the possibility to get the wavefunctions from the…
We study hadronic wave functions using an instanton model for the QCD vacuum. The wave functions are defined in terms of gauge invariant Bethe Salpeter amplitudes which we have determined numerically using a Monte Carlo simulation of the…