Related papers: Restricted Hilbert transform for non-Hermitian man…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
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…
Two alternative scenarios are shown possible in Quantum Mechanics working with non-Hermitian $PT-$symmetric form of observables. While, usually, people assume that $P$ is a self-adjoint indefinite metric in Hilbert space (and that their…
PT-symmetric systems can have a real spectrum even when their Hamiltonian is non-hermitian, but develop a complex spectrum when the degree of non-hermiticity increases. Here we utilize random-matrix theory to show that this spontaneous…
Non-Hermiticity has recently emerged as a rapidly developing field due to its exotic characteristics related to open systems, where the dissipation plays a critical role. In the presence of balanced energy gain and loss with environment,…
The one-dimensional Hatano-Nelson model with non-reciprocal hoppings is a prominent example of a relatively simple non-Hermitian quantum-mechanical system, which allows to study various phenomena in open quantum systems without adding extra…
I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
Non-Hermitian systems based on parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. So far, realizations of PT-symmetric systems have been limited to the spatial domain. Here we theoretically and experimentally…
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
We report a novel mechanism of boundary-sensitive PT symmetry breaking in one-dimensional Floquet systems. By designing a time-periodic driving protocol, we realize a Floquet Hamiltonian that is Hermitian under periodic boundary conditions…
We illustrate that a Hermitian nonlinear optical system consisting of hybridized parametric amplification and second harmonic generation mimics non-Hermitian evolution dynamics. Oscillation damping, evolution to a static steady state, and…
This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…
Metasurfaces based on subwavelength resonators enable novel ways to manipulate the flow of light at optical interfaces. In pursuit of multifunctional or reconfigurable metadevices, efficient tuning of macroscopic performance with little…
Engineering quantum bath networks through non-Hermitian subsystem Hamiltonians has recently emerged as a promising strategy for qubit cooling, state stabilization, and fault-tolerant quantum computation. However, scaling these systems while…
In this article, the non-Hermitian characteristics of three-dimensional PT-symmetric coupled electronic resonators are theoretically analyzed. First, the concept of non-Hermitian PT symmetry is illustrated in the context of electronics…
The local reggeon field theory is studied perturbatively taking advantage of the PT symmetry in the Hamiltonian formulation. In the lowest non trivial order we show that the pomeron interactions renormalize the slope. In the same order we…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
Temporal interfaces introduced by abrupt switching of the constitutive parameters of unbounded media enable unusual wave phenomena. So far, their explorations have been mostly limited to lossless media. Yet, non-Hermitian phenomena…