Related papers: Global and Local Aspects of Exceptional Point
The concept of critical points in nuclear phase transitional regions is discussed from the standpoints of Q-invariants, simple observables and wave function entropy. It is shown that these critical points very closely coincide with the…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
Standard exceptional points (EPs) are non-Hermitian degeneracies that occur in open systems. At an EP, the Taylor series expansion becomes singular and fails to converge -- a feature that was exploited for several applications. Here, we…
In our recent paper (Li and Batchelor J. Phys. A: Math. Theor. 48, 454005 (2015)) we obtained exceptional points in the eigenspectrum of the generalized Rabi model in terms of a set of algebraic equations. We also gave a proof for the…
Exceptional points (EPs) are singularities in the spectra of non-Hermitian operators, where eigenvalues and eigenvectors coalesce. Recently, open quantum systems have been increasingly explored as EP testbeds due to their natural…
Recent study demonstrated that steady states of a polariton system may show a first-order dissipative phase transition with an exceptional point that appears as an endpoint of the phase boundary [R. Hanai et al., Phys. Rev. Lett. 122,…
We discuss the geometry of the unit ball -- specifically, the structure of its extreme points (if any) -- in subspaces of $L^1$ and $L^\infty$ on the circle that are formed by functions with prescribed spectral gaps. A similar issue is…
Singularities, such as poles and branch points, play a crucial role in investigating the analytic properties of scattering amplitudes that inform new computational techniques. In this note, we point out that scattering amplitudes can also…
Random graphs defined by an occurrence probability that is invariant under node aggregation have been identified recently in the context of network renormalization. The invariance property requires that edges are drawn with a specific…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
Let $K_n$ denote the number of distinct values among the first $n$ terms of an infinite exchangeable sequence of random variables $(X_1,X_2,\ldots)$. We prove for $n=3$ that the extreme points of the convex set of all possible laws of $K_3$…
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…
Exceptional points (EPs) are singularities of energy levels in non-Hermitian systems. In this Letter, we demonstrate the surface of EPs on a magnon polariton platform composed of coupled magnons and microwave photons. Our experiments show…
We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to…
The Petermann factor and the phase rigidity are convenient measures for various aspects of open quantum and wave systems, such as the sensitivity of energy eigenvalues to perturbations or the magnitude of quantum excess noise in lasers. We…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
In this paper, we use graph theory to solve wave scattering problems in the discrete dipole approximation. As a key result of this work, in the presence of active scatterers, we present a systematic method to find arbitrary large-order zero…
We explore different (and complementary) views of spinors and their exotic counterparts, linking the very existence of the later to the presence of black holes. Moreover, we investigate the effects of the exotic term in the Hawking…
Recently, presence of hidden singularities known as exceptional points (EPs) in non-Hermitian quantum systems has opened up a tremendous interest in different domains of physics owing to their unique unconventional physical effects.…
We suggest to employ the dissipative nature of open quantum systems for the purpose of parameter estimation: The dynamics of open quantum systems is typically described by a quantum dynamical semigroup generator ${\cal L}$. The eigenvalues…