Related papers: Nonlinear waves in an anti-Hermitian lattice with …
We develop a framework to solve a large class of linearly driven non-Hermitian quantum systems. Such a class of models in the Hermitian scenario is commonly known as multi-state Landau-Zener models. The non-hermiticity is due to the…
We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which…
In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice. We examine the stationary states of such chains in the form of plane waves, and…
Parametric simultaneous solitary wave (simulton) excitations are shown possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example we consider the nonlinear coupling between the upper…
We formulate non-Hermitian Landau levels in two-dimensional systems under a complex perpendicular magnetic field. In the symmetric gauge, we derive their discretely spaced, highly degenerate complex spectra and biorthogonal eigenstates, and…
Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin effect…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
In this paper, we consider the resonance problem for the cubic nonlinear Helmholtz equation in the subwavelength regime. We derive a discrete model for approximating the subwavelength resonances of finite systems of high-contrast resonators…
A prominent feature of some one-dimensional non-Hermitian systems is that all right-eigenstates of the non-Hermitian Hamiltonian are localized in one end of the chain. The topological and trivial phases are distinguished by the emergence of…
We study a non-Hermitian variant of the (2+1)-dimensional Dirac wave equation, which hosts a real energy spectrum with pairwise-orthogonal eigenstates. In the spatially uniform case, the Hamiltonian's non-Hermitian symmetries allow its…
Non-Hermitian systems enable continuous and smooth tuning of topological phases through externally controllable loss/gain parameters. Without altering the intrinsic lattice structure, merely fine-tuning the intensity or spatial distribution…
A systematic approach for deriving tight-binding approximations in general longitudinally driven lattices is presented. As prototypes, honeycomb and staggered square lattices are considered. Time-reversal symmetry is broken by…
For one-dimensional PT -symmetric systems, it is observed that the non-local product obtained from the continuity equation can be interpreted as a conserved corre- lation function. This leads to physical conclusions, regarding both discrete…
Non-Hermitian systems, with symmetric or antisymmetric Hamiltonians under the parity-time ($\mathcal{PT}$) operations, can have entirely real eigenvalues. This fact has led to surprising discoveries such as loss-induced lasing and…
In the present work, we consider a prototypical example of a PT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the PT-phase transition in an analytical form. We then focus on the…
It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear…
We report a study on a closed-form nonlinear parity-time symmetric optical quadrimer waveguides system with a specific coupling scheme. The system yields power saturation behavior in the modes, which may be attributed to the inherent…
Topological winding in non-Hermitian systems are generally associated to the Bloch band properties of lattice Hamiltonians. However, in certain non-Hermitian models topological winding naturally arise from the dynamical evolution of the…
We propose a lattice model, in both one- and multidimensional versions, which may give rise to matching conditions necessary for the generation of solitons through the second-harmonic generation. The model describes an array of linearly…
Wave motion is fundamentally constrained by the dispersion properties of the medium, often making it challenging -- or even impossible -- to guide wave packets along desired trajectories, particularly when wave inversion is required. The…