Related papers: Single parameter scaling in 1-D localized absorbin…
We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise…
We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the…
We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system…
We introduce a variant of the Banded Random Matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law.…
Wave localization is a ubiquitous phenomenon. It refers to situations that transmitted waves in scattering media are trapped in space and remain confined in the vicinity of the initial site until dissipated. Based on a scaling analysis, the…
By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling…
We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes…
We study scaling properties of the localized eigenstates of the random dimer model in which pairs of local site energies are assigned at random in a one dimensional disordered tight-binding model. We use both the transfer matrix method and…
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 investigate Anderson localization on various 1D structures having flat bands. The main focus is on the scaling laws obeyed by the localization length at weak disorder in the vicinity of flat-band energies. A careful distinction is made…
Scaling of the conductances and the finite-size localization lengths is generalized to anisotropic systems and tested in two dimensional systems. Scaling functions of isotropic systems are recovered once the dimension of the system in each…
We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
The influence of the initial fluctuations on the onset of scaling in the quench to zero temperature of a two dimensional system with conserved order parameter, is analyzed in detail with and without topological defects. We find that the…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and…
We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…