Related papers: Non-Hermitian Dynamics Mimicked by a Hermitian Non…
We present three different linearizable extensions of the Gurevich-Zybin system. Their general solutions are found by reciprocal transformations. In this paper we rewrite the Gurevich-Zybin system as a Monge-Ampere equation. By application…
We employ transformation optics to optimize the generic nonlinear wave interaction of second-harmonic generation from a pair of touching metallic wires. We demonstrate a 10 orders of magnitude increase in the second-harmonic scattering…
We introduce a continuous one-dimensional non-Hermitian matrix gauge potential and study its effect on dynamics of a two-component field. The model is emulated by a system of evanescently coupled nonlinear waveguides with distributed gain…
Quadratic optical parametric processes form the foundation for a variety of applications related to classical and quantum frequency conversion, which have attracted significant interest recently in on-chip implementation. These processes…
Starting from a Hermitian operator with two distinct eigenvalues, we construct a non-Hermitian bipartite system in Gaussian orthogonal ensemble according to random matrix theory, where we introduce the off-diagonal fluctuations through…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion…
We present a second-order extension of the first-order Lohe hermitian sphere(LHS) model and study its emergent asymptotic dynamics. Our proposed model incorporates an inertial effect as a second-order extension. The inertia term can…
The non-hermitian quantum dynamics of excitonic energy transfer in photosynthetic systems is investigated using a dissipative two-level dimer model. The approach is based on the Green's function formalism which permits consideration of…
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…
We investigate enhanced harmonic generation processes in gain-assisted, near-zero permittivity metamaterials composed of spherical plasmonic nanoshells. We report the presence of narrow-band features in transmission, reflection and…
This research paper explores the potential of nonlinear magnetic levitation systems for energy harvesting by developing a modified system that incorporates a more realistic energy harvesting circuit, enabling a better representation of…
Non-Hermitian Hamiltonians and Lindblad operators are some of the most important generators of dynamics for describing quantum systems interacting with different kinds of environments. The first type differs from conservative evolution by…
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An…
Topological phases in spinless non-Hermitian models have been widely studied both theoretically and experimentally in some artificial materials using photonics, phononics and magnon. In this work, we investigate the interplay between…
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…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian…
We reelaborate on a general method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the su(2) algebra that arises as the dynamical…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…