Related papers: Multifractality and quantum diffusion from self-co…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
We study the local regularity and multifractal nature of the sample paths of jump diffusion processes, which are solutions to a class of stochastic differential equations with jumps. This article extends the recent work of Barral {\it et…
The 1/[-i\omega + D(\omega, q)q^2] diffusion pole in the localized phase transfers to the 1/\omega Berezinskii-Gorkov singularity, which can be analyzed by the instanton method (M V. Sadovskii, 1982; J. L. Cardy, 1978). Straightforward use…
This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
We consider a self-similar phase space with specific fractal dimension $d$ being distributed with spectrum function $f(d)$. Related thermostatistics is shown to be governed by the Tsallis formalism of the non-extensive statistics, where the…
Wavefunction collapse models modify Schr\"odinger's equation so that it describes the collapse of a superposition of macroscopically distinguishable states as a dynamical process. This provides a basis for the resolution of the quantum…
Quantum diffusion is a major topic in condensed-matter physics, and the Caldeira-Leggett model has been one of the most successful approaches to study this phenomenon. Here, we generalize this model by coupling the bath to the system…
We study a simple model of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned space-dependent "attractiveness function", a situation frequently encountered in…
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…
We consider the set of monofractals within a multifractal related to the phase space being the support of a generalized thermostatistics. The statistical weight exponent $\tau(q)$ is shown to can be modeled by the hyperbolic tangent…
The phase diagram of the metal-insulator transition in a three dimensional quantum percolation problem is investigated numerically based on the multifractal analysis of the eigenstates. The large scale numerical simulation has been…
The harmonic measure (or diffusion field or electrostatic potential) near a percolation cluster in two dimensions is considered. Its moments, summed over the accessible external hull, exhibit a multifractal spectrum, which I calculate…
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 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…
We present a theoretical framework for understanding the wavefunctions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong…
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…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short…
This is a paper about multi-fractal scaling and dissipation in a shell model of turbulence, called the GOY model. This set of equations describes a one dimensional cascade of energy towards higher wave vectors. When the model is chaotic,…