Related papers: Non-Hermitian spectra and Anderson localization
Non-Hermitian systems with non-reciprocal hopping may display the non-Hermitian skin effect, where states under open boundary conditions localize exponentially at one edge of the system. This localization has been linked to spectral winding…
We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-su-persymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather…
Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of $N\times N$ real non-symmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if $|i-j|<b$…
This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…
We study non-Hermitian Aubry-Andr\'{e}-Harper models with p-wave pairing, where the non-Hermiticity is introduced by on-site complex quasiperiodic potentials. By analysing the $\mathcal{PT}$ symmetry breaking, winding numbers of energy…
We study a particular class of families of multi-dimensional lattice Schr\"o\-dinger operators with deterministic (including quasi-periodic) potentials generated by the "hull" given by an orthogonal series over the Haar wavelet basis on the…
In this paper, we study the properties of two-dimensional lattices in the presence of non-Hermitian disorder. In the context of coupled mode theory, we consider random gain-loss distributions on every waveguide channel (on site disorder).…
We introduce the one-dimensional quasireciprocal lattices where the forward hopping amplitudes between nearest neighboring sites $\{ t+t_{jR} \}$ are chosen to be a random permutation of the backward hopping $\{ t+t_{jL} \}$ or vice versa.…
The two main results of the article are concerned with Anderson Localization for one-dimensional lattice Schroedinger operators with quasi-periodic potentials with d frequencies. First, in the case d = 1 or 2, it is proved that the spectrum…
We studied numerically the distribution of the entanglement Hamiltonian eigenvalues in two one-dimensional free fermion models and the typical three-dimensional Anderson model. We showed numerically that this distribution depends on the…
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…
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear $\sigma$-model…
Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian…
The impact of disorder on wave transport has been extensively studied in Hermitian systems, where static randomness gives rise to Anderson localization. In non-Hermitian lattices, static disorder can lead to peculiar transport features,…
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a transition to a…
We establish exponential localization for a two-particle Anderson model in a Euclidean space ${\mathbb R}^{d}$, $d\ge 1$, in presence of a non-trivial short-range interaction and a random external potential of the alloy type. Specifically,…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary…
We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…
We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we…