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Non-Hermitian systems have attracted significant interest because of their intriguing and useful properties, including exceptional points (EPs), where eigenvalues and the corresponding eigenstates of non-Hermitian operators become…
We study a system of phase oscillators with nonlocal coupling in a ring that supports self-organized patterns of coherence and incoherence, called chimera states. Introducing a global feedback loop, connecting the phase lag to the order…
We examine a mechanism of spontaneous decoherence in which the generator of quantum dynamics is deformed to a logarithmically modified self-adjoint operator \begin{equation*} F_\beta(H) = H + \beta H \log \frac{H}{E_*} \end{equation*} for a…
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…
A particle system with a (2+1)D exotic Newton-Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and…
The states of an open quantum system interact ("talk") with one another via the extended environment into which the localized system is embedded. This interaction is mediated by the source term of the Schr\"odinger equation which describes…
We identify a class of trapping potentials in cubic nonlinear Schr\"{o}dinger equations (NLSEs) that make them non-integrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by…
The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates…
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…
Gravity in nonlinear and dynamical regimes underpins spectacular astrophysical phenomena and observable consequences, from the early universe to black hole collisions. In these extreme environments, inverse energy cascades - mediated by…
Exceptional orthogonal Laguerre polynomials can be viewed as an extension of the classical Laguerre polynomials per excluding polynomials of certain order(s) from being eigenfunctions for the corresponding exceptional differential operator.…
We study a system involving a single quantum degree of freedom per site of the lattice interacting with a few neighbors (up to second neighbors), with the interactions chosen as to produce frustration. At zero temperature, this system…
We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrodinger-type equations. For illustrative…
The squeezing in a nonlinear system with chaotic dynamics is considered. The model describing interaction of collection of two-level atoms with a single-mode of self-consistent field and an external field is analyzed. It is shown that in…
We consider the nonlinear Schr{\"o}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} (\psi^\star \psi)^{\kappa+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx +…
In this paper we will demonstrate possible existence of more exotic forms of interaction taking into account, that dark energy can be parametrized as a varying polytropic uid suggested recently by the first author. On going research in both…
Aligning with the everlasting search for quantum spin liquids (QSLs), identifying the QSL in Kitaev magnets has garnered great research interest during the past decade and remains nevertheless an enormous challenge. One of the major…
We report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without…
We report generation of a new quantum interference effect in spontaneous emission from a resonantly driven system of two identical two-level atoms due to the spatial variation of the laser phase at the positions of the atoms. This…
One of the most fascinating and puzzling aspects of non-Hermitian systems is their spectral degeneracies, i.e., exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce to form a defective state space. While coupled…