相关论文: Mutifractal Analysis of Broadly Distributed Observ…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
We study percolation as a critical phenomenon on a multifractal support. The scaling exponents of the the infinite cluster size ($\beta$ exponent) and the fractal dimension of the percolation cluster ($d_f$) are quantities that seem do not…
We propose a generalization of multifractal analysis that is applicable to the critical regime of the Anderson localization-delocalization transition. The approach reveals that the behavior of the probability distribution of wavefunction…
We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a…
This work extends the analysis of the generalized multifractality of critical eigenstates at the spin quantum Hall transition in two-dimensional disordered superconductors [J. F. Karcher et al, Annals of Physics, 435, 168584 (2021)]. A…
This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness…
Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of…
We investigate numerically the localization-delocalization transition in quantum Hall systems with long-range disorder potential with respect to multifractal properties. Wavefunctions at the transition energy are obtained within the…
Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the…
Macroscopic systems often display phase transitions where certain physical quantities are singular or self-similar at different (spatial) scales. Such properties of systems are currently characterized by some order parameters and a few…
The critical dynamics of conformal field theories on random surfaces is investigated beyond the previously studied dynamics of the overall area and the genus. It is found that the evolution of the order parameter in physical time performs a…
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…
The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension $\xt$. We consider the case when the boundary…
Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases…
Many models and real complex systems possess critical thresholds at which the systems shift from one sate to another. The discovery of the early warnings of the systems in the vicinity of critical point are of great importance to estimate…
We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at…