相关论文: Multifractality and intermediate statistics in qua…
We study numerically multifractal properties of two models of one-dimensional quantum maps, a map with pseudointegrable dynamics and intermediate spectral statistics, and a map with an Anderson-like transition recently implemented with cold…
We investigate numerically the statistics of wavefunction amplitudes $\psi({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|\psi|^2$ is log-normal,…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and…
The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $\Delta_q$ governing the scaling of…
Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the…
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide…
We investigate chaotic and multi-fractal properties of a two parameter map of the unit interval onto itself -- the Kim-Kong map. These results are compared with similar properties in well known one parameter maps of the unit interval onto…
We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on…
We present a one-parameter family of quantum maps whose spectral statistics are of the same intermediate type as observed in polygonal quantum billiards. Our central result is the evaluation of the spectral two-point correlation form factor…
We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
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…
Self-affine morphology of random interfaces governs their functionalities across tribological, geological, (opto-)electrical and biological applications. However, the knowledge of how energy carriers or generally classical/quantum waves…
The multifractal properties of the electronic spectrum of a general quasiperiodic chain are studied in first order in the quasiperiodic potential strength. Analytical expressions for the generalized dimensions are found and are in good…
We study the use of the quantum wavelet transform to extract efficiently information about the multifractal exponents for multifractal quantum states. We show that, combined with quantum simulation algorithms, it enables to build quantum…
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…
We analyze invariant measures of two coupled piecewise linear and everywhere expanding maps on the synchronization manifold. We observe that though the individual maps have simple and smooth functions as their stationary densities, they…