Related papers: Non-Hermitian Localization in Biological Networks
We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave…
The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: The probability to find two independent walkers at the same…
We consider the limiting location and limiting distribution of the largest eigenvalue in real symmetric ($\beta$ = 1), Hermitian ($\beta$ = 2), and Hermitian self-dual ($\beta$ = 4) random matrix models with rank 1 external source. They are…
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…
Non-Hermitian systems possess exotic localization phenomena beyond their Hermitian counterparts, exhibiting massive accumulation of eigenstates at the system boundaries with different scaling behaviors. In this study, we investigate two…
We study the phenomenon of "crowding" near the largest eigenvalue $\lambda_{\max}$ of random $N \times N$ matrices belonging to the Gaussian Unitary Ensemble (GUE) of random matrix theory. We focus on two distinct quantities: (i) the…
One of unique features of non-Hermitian systems is the extreme sensitive to their boundary conditions, e.g., the emergence of non-Hermitian skin effect (NHSE) under the open boundary conditions, where most of bulk states become localized at…
We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws…
In general, the energy spectrum of a non-Hermitian system turns out to be complex, which is not so satisfactory since the time evolution of eigenstates with complex eigenvalues is either exponentially growing or decaying. Here we provide a…
The non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems depicts the exponential localization of eigenstates at system's boundaries. It has led to a number of counter-intuitive phenomena and challenged our understanding of…
We study a one-dimensional system subjected to a linearly varying imaginary vector potential, which is described by the single-particle continuous Schr\"odinger equation and is analytically solved. The eigenenergy spectrum is found to be…
In disordered Hermitian systems, localization of energy eigenstates prohibits wave propagation. In non-Hermitian systems, however, wave propagation is possible even when the eigenstates of Hamiltonian are exponentially localized by…
Localization is a pervasive phenomenon across physics, shaping transport from electrons in solids to light and sound in engineered media. In traditional settings, disorder strongly impedes transport, resulting in dynamical localization or,…
We consider Hermitian random band matrices $H=(h_{xy})$ on the $d$-dimensional lattice $(\mathbb Z/L\mathbb Z)^d$. The entries $h_{xy}$ are independent (up to Hermitian conditions) centered complex Gaussian random variables with variances…
There has been much recent interest, initiated by work of the physicists Hatano and Nelson, in the eigenvalues of certain random non-Hermitian periodic tridiagonal matrices and their bidiagonal limits. These eigenvalues cluster along a…
Phase transitions in one-dimensional lattice systems are well established and have been extensively studied within both Hermitian and non-Hermitian frameworks. In this work, we extend this understanding to a more general setting by…
We prove a large deviation principle for the largest singular value of sparse non-Hermitian random matrices, or directed Erd\H{o}s-R\'enyi networks in the constant average degree regime $p =\frac{d}{n}$ where $d$ is fixed. Entries are…
We consider the asymptotic local behavior of the second correlation functions of the characteristic polynomials of a certain class of Gaussian $N\times N$ non-Hermitian random band matrices with a bandwidth $W$. Given $W,N\to\infty$, we…
A nearest-neighbor tight-binding model on a tree structure is investigated. The full energy spectrum of the normalized Hamiltonian can be expressed in terms of successively increasing number of contributions at any finite step of…
The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this…