相关论文: Linear and Nonlinear PT-symmetric Oligomers: A Dyn…

We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure…

In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…

We investigate the temporal dynamics of the PT-Symmetric nonlinear oscillators in the presence of Duffing nonlinearity for two forms of oscillator configuration. In the former, we consider two oscillator coupled to each other. One…

We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT-symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we employ PT-symmetry as a guiding principle to…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

We review some recent results on how PT-symmetry, that is a simultaneous time-reversal and parity transformation, can be used to construct new integrable models. Some complex valued multi-particle systems, such as deformations of the…

The effect of PT-symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. Here…

Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with…

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing,…

Many physical systems can be described by nonlinear eigenvalues and bifurcation problems with a linear part that is non-selfadjoint e.g. due to the presence of loss and gain. The balance of these effects is reflected in an antilinear…

Nonlinearity and non-Hermiticity, for example due to environmental gain-loss processes, are a common occurrence throughout numerous areas of science and lie at the root of many remarkable phenomena. For the latter, parity-time-reflection…

In this work we investigate a one-dimensional parity-time (PT)-symmetric magnetic metamaterial consisting of split-ring dimers having gain or loss. Employing a Melnikov analysis we study the existence of localized travelling waves, i.e.…

We report the existence of a universal trimer state induced by an impurity interacting with a two-component spin-orbit coupled Fermi gas in two dimensions. In the zero-density limit with a vanishing Fermi sea, the trimer is stabilized by…

The interplay between topology and quantum criticality has given rise to the notion of symmetry-enriched criticality, which has attracted considerable attention in recent years. In this Letter, we demonstrate that parity time (PT) symmetry…

We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as…

Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we…

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…

Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and…

We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…

Recently, a new type of duality was reported in some deformable mechanical networks which exhibit Kramers-like degeneracy in phononic spectrum at the self-dual point. In this work, we clarify the origin of this duality and propose a design…