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Within the framework of non-Hermitian photonics, we investigate the spectral and dynamical properties of one- and two-dimensional non-Hermitian off-diagonal disordered optical lattices, where randomness is applied to the couplings rather…
We investigate the effects of stealthy hyperuniform bond distributions on the electronic and magnetic properties of the Hubbard model on the honeycomb lattice. Hyperuniform structures, distinct from random and quasiperiodic ones, have…
Quasiperiodic systems are neither randomly disordered nor translationally invariant in the absence of periodic length scales. Based on their incommensurate order, novel physical properties such as critical states and self-similar…
Hyperuniform disorder is a type of correlated disorder characterized by vanishing spectral density at small wavevectors, making the configuration effectively homogeneous on long length scales. In photonics, hyperuniform disorder is…
Absence of level repulsion between extended states in random non-Hermitian systems is demonstrated. As a result, the general Wigner-Dyson distributions of level spacing of diffusive metals in the usual Hermitian systems is replaced by the…
Wave turbulence describes the long-time statistical behavior of out-of-equilibrium systems composed of weakly interacting waves. Non-Hermitian media ranging from open quantum systems to active materials can sustain wave propagation in…
Strong disorder often has drastic consequences for quantum dynamics. This is best illustrated by the phenomenon of Anderson localization in non-interacting systems, where destructive quantum wave interference leads to the complete absence…
The single-parameter scaling hypothesis predicts the absence of delocalized states for noninteracting quasiparticles in low-dimensional disordered systems. We show analytically and numerically that extended states may occur in the one- and…
We develop a theoretical scheme to perform a read-out of the properties of a quasi-periodic system by coupling it to one or two qubits. We show that the decoherence dynamics of a single qubit coupled via a pure dephasing type term to a 1D…
Non-Gaussian shapes, despite a linear form of the mean-squared displacement, have been observed for the displacement distribution in a large range of diffusive systems. Stochastic models for such "Brownian yet non-Gaussian" diffusion will…
We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…
Unitary and dissipative models of quantum dynamics are linear maps on the space of states or density matrices. This linearity encodes the superposition principle, a key feature of quantum theory. However, this principle can break down in…
Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be…
Recent research has made significant progress in understanding localization transitions and mobility edges (MEs) that separate extended and localized states in non-Hermitian (NH) quasicrystals. Here we focus on studying critical states and…
A non-unitary transformation leading to a Hatano-Nelson problem is performed on an array of equally-spaced optical waveguides. Such transformation produces a non-reciprocal system of waveguides, as the corresponding Hamiltonian becomes…
We study the correlated Haldane-Hubbard model with single-particle gain and loss, focusing on its non-Hermitian phase diagram and the ensuing non-unitary dynamic properties. The interplay of interactions and non-hermiticity results in…
In this paper, we present a unifying analytical framework for identifying conditions for transport effects such as reflectionless and transparent transport, lasing, and coherent perfect absorption in non-Hermitian nonreciprocal systems…
From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…
We analyze the propagation of coherent states through general systems of pseudodifferential form associated with Hamiltonian presenting codimension one eigen-value crossings. In particular, we calculate precisely the non adiabatic effects…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…