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Exceptional points (EPs) are distinct characteristics of non-Hermitian Hamiltonians that have no counterparts in Hermitian systems. In this study, we focus on EPs in continuous systems rather than discrete non-Hermitian systems, which are…
We construct an infinite system of non-linear duality equations, including fermions, that are invariant under global E11 and gauge invariant under generalised diffeomorphisms upon the imposition of a suitable section constraint. We use…
Exceptional points (EPs) have recently attracted considerable attention in the study of non-Hermitian systems and in applications such as sensors and mode switching. In particular, nontrivial topological structures of EPs have been studied…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
Topological defects are central to modern physics, from spintronics to photonics, due to their robustness and potential application in information processing. In this work, we discuss topological point defects that spontaneously emerge at…
We describe a diagrammatic technique for non-Hermitian fermionic systems that is applicable in the steady state, and which allows addressing correlations effects by systematic expansion. Applying this method to exceptional points or rings,…
We propose a noncommutative version of the Euclidean Lie algebra $E_2$. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of…
Non-Hermitian, tight-binding $\mathcal{PT}$-symmetric models are extensively studied in the literature. Here, we investigate two forms of non-Hermitian Hamiltonians to study the $\mathcal{PT}$-symmetry breaking thresholds and features of…
Several works have recently addressed the emergence of exceptional points (EPs), i.e., spectral singularities of non-Hermitian Hamiltonians, in the long-wavelength dynamics of coupled magnetic systems. Here, by focusing on the driven…
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…
A new diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it…
An interplay of an exotic quantum holonomy and exceptional points is examined in one-dimensional Bose systems. The eigenenergy anholonomy, in which Hermitian adiabatic cycle induces nontrivial change in eigenenergies, can be interpreted as…
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…
Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of…
Exceptional points (EP) in non-Hermitian systems have been widely investigated due to their enhanced sensitivity in comparison to standard systems. In this letter, we report the observation of higher-order pseudo-Hermitian degeneracies in…
We examine the physical manifestations of exceptional points and passage times in a two-level system which is subjected to quantum measurements and which admits a non-Hermitian description. Using an effective Hamiltonian acting in the…
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite…
Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce…
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the ones appearing in lattice gauge theories…
When sources of energy gain and loss are introduced to a wave-scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, where eigenmodes are linearly…