Related papers: Hidden Symmetry in 1D Localization
One-dimensional disordered systems with a random potential of a small amplitude and short-range correlations are considered near the initial band edge. The evolution equation is obtained for the mutual ditribution P(\rho,\psi) of the…
We study the phase distribution of the complex reflection coefficient in different configurations as a disordered 1D system evolves in length, and its effect on the distribution of the 4-probe resistance $R_4$. The stationary ($L \to…
Localization of electrons in 1D disordered systems is usually described in the random phase approximation, when distributions of phases \varphi and \theta, entering the transfer matrix, are considered as uniform. In the general case, the…
Localization of electrons in 1D disordered systems is usually described in the random phase approximation, when distributions of phases \varphi and \theta, entering the transfer matrix, are considered as uniform. In the general case, the…
The propagation of light through a disordered layered system is studied. It is shown that distribution function of the transmission coefficient phase tends to stationary non-uniform distribution as the number of layers increases. The…
We discuss physical constructions, and the boundary properties of various symmetry protected topological phases that involve 1-form symmetries, from one spatial dimension (1d) to four spatial dimensions (4d). For example, the prototype 3d…
Open, non-equilibrium systems with balanced gain and loss, known as parity-time ($\mathcal{PT}$)-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the $\mathcal{PT}$-symmetry breaking…
We consider the mutual distribution of two linearly independent solutions y_1(x) and y_2(x) of the 1D Schroedinger equation with a random potential. Since individual distributions of $y_1$ and $y_2$ are log-normal, it is naturally to…
Spontaneous symmetry breaking generally circumvents one-dimensional systems with local interactions in thermal equilibrium. Here, we analyze a category of one-dimensional Hermitian models via local non-Hermitian constructions. Notably,…
The impact of local reflection symmetry on wave localization and transport within finite disordered chains is investigated. Local symmetries thereby play the role of a spatial correlation of variable range in the finite system. We find…
We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure…
Free fermions with a finite Fermi surface are known to exhibit an anomalously large entanglement entropy. The leading contribution to the entanglement entropy of a region of linear size $L$ in $d$ spatial dimensions is $S\sim L^{d-1}…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
We study the dynamics of phase ordering of a non-conserved, scalar order parameter in one dimension, with long-range interactions characterized by a power law $r^{-d-\sigma}$. In contrast to higher dimensional systems, the point nature of…
We study a Lindbladian generalization of the Anderson model of localization that describes disordered free fermions coupled to a disordered environment. From finite size scaling of both eigenvalue statistics and participation ratio, we…
Disordered systems have grown in importance in the past decades, with similar phenomena manifesting themselves in many different physical systems. Because of the difficulty of the topic, theoretical progress has mostly emerged from…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
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…
Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with…
Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…