相关论文: Dynamical scaling for critical states: is Chalker'…
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large…
Recently, based on heuristic arguments, it was conjectured that an intimate relation exists between any multifractal dimensions, $D_q$ and $D_{q'}$, of the eigenstates of critical random matrix ensembles: $D_{q'} \approx…
Fractal dimensions are tools for probing the structure of quantum states and identifying whether they are localized or delocalized in a given basis. These quantities are commonly extracted through finite-size scaling, which limits the…
The distribution of the correlation dimension in a power law band random matrix model having critical, i.e. multifractal, eigenstates is numerically investigated. It is shown that their probability distribution function has a fixed point as…
Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant,…
Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse…
We propose a new method to analyze fluctuations in the strength function phenomena in highly excited nuclei. Extending the method of multifractal analysis to the cases where the strength fluctuations do not obey power scaling laws, we…
We study the spectral statistics and wave-function properties of a one-dimensional quantum system subject to a Cantor-type fractal potential. By analyzing the nearest-neighbor level spacings, inverse participation ratio (IPR), and the…
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…
The growth of ballistic aggregates on deterministic fractal substrates is studied by means of numerical simulations. First, we attempt the description of the evolving interface of the aggregates by applying the well-established…
We present a random-matrix realization of a two-dimensional percolation model with the occupation probability $p$. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue…
We construct perturbation series for the q-th moment of eigenfunctions of various critical random matrix ensembles in the strong multifractality regime close to localization. Contrary to previous investigations, our results are valid in the…
Taylor's power law (or fluctuation scaling) states that on comparable populations, the variance of each sample is approximately proportional to a power of the mean of the population. It has been shown to hold by empirical observations in a…
We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
We study the intricate relationships between the dynamical scaling properties of electron wave packets and the multifractality of the eigenstates in quantum systems. Numerical simulations for the Harper model and the Fibonacci chain…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
Experimental data are presented on particle correlations and fluctuations in various high-energy multiparticle collisions, with special emphasis on evidence for scaling-law evolution in small phase-space domains. The notions of…