Related papers: Probing Band-center Anomaly with the Kernel Polyno…
Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…
An exact solution is found for the problem of the center-of-band ($E=0$) anomaly in the one-dimensional (1D) Anderson model of localization. By deriving and solving an equation for the generating function $\Phi(u,\phi)$ we obtained an exact…
Anderson localization of $p$-polarized waves and the Brewster anomaly phenomenon, which is the delocalization of $p$-polarized waves at a special incident angle, in randomly-stratified anisotropic media are studied theoretically for two…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
The scaling of the Thouless time with system size is of fundamental importance to characterize dynamical properties in quantum systems. In this work, we study the scaling of the Thouless time in the Anderson model on random regular graphs…
Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at…
The Anderson model in one dimension is a quantum particle on a discrete chain of sites with nearest-neighbor hopping and random on-site potentials. It is a progenitor of many further models of disordered systems, and it has spurred numerous…
We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the…
The Kernel Polynomial Method (KPM) is a well-established scheme in quantum physics and quantum chemistry to determine the eigenvalue density and spectral properties of large sparse matrices. In this work we demonstrate the high optimization…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
The three-dimensional Anderson model with a rectangular distribution of site disorder displays two distinct localization-delocalization transitions, against varying disorder intensity, for a relatively narrow range of Fermi energies. Such…
We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
We study the three-dimensional two-band Anderson model of localization and compare our results to experimental results for amorphous metallic alloys (AMA). Using the transfer-matrix method, we identify and characterize the metal-insulator…
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states…
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted…
We rigorously analyse the correspondence between the one-dimensional standard Anderson model and a related classical system, the `kicked oscillator' with noisy frequency. We show that the Anderson localization corresponds to a parametric…
Anomalous change detection (ACD) is an important problem in remote sensing image processing. Detecting not only pervasive but also anomalous or extreme changes has many applications for which methodologies are available. This paper…