Related papers: Evidence for Exceptional Points as Topological Def…

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…

Exceptional points (EPs), singularities of non-Hermitian physics where complex spectral resonances degenerate, are one of the most exotic features of nonequilibrium open systems with unique properties. For instance, the emission rate of…

Complex spectra of dissipative quantum systems may exhibit degeneracies known as exceptional points (EPs). At these points the systems' dynamics may undergo drastic changes. Phenomena associated with EPs and their applications have been…

Non-Hermitian systems and their topological singularities, such as exceptional points (EPs), lines, and surfaces, have recently attracted intense interest. The investigation of these exceptional constituents has led to fruitful…

The emergence of exceptional points in non-Hermitian systems represents an intriguing phenomenon characterized by the coalescence of eigenenergies and eigenstates. When a system approaches an exceptional point, it exhibits a heightened…

The description of a closed quantum system is extended with the identification of an underlying substructure enabling an expanded formulation of dynamics in the Heisenberg picture. Between measurements a ``state point" moves in an…

We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…

Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…

It is widely accepted that the states of any quantum system are vectors in a Hilbert space. Not everyone agrees, however. The recent paper ``The unphysicality of Hilbert spaces'' by Carcassi, Calder\'on and Aidala is a thoughtful dissection…

We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic…

We give a geometric interpretation for superconformal quantum mechanics defined on a hyper-Kahler cone which has an equivariant symplectic resolution. BPS states are identified with certain twisted Dolbeault cohomology classes on the…

Exceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, corresponding eigenmodes become degenerate. Classical and quantum photonic systems with EPs have attracted tremendous attention due…

It is well-known that the standard bulk-boundary correspondence does not hold for non-Hermitian systems in which also new phenomena such as exceptional points do occur. Here we study, mostly by analytical means, a paradigmatic…

Geometrical properties of energy bands underlie fascinating phenomena in a wide-range of systems, including solid-state materials, ultracold gases and photonics. Most famously, local geometrical characteristics like the Berry curvature can…

In this study, we have analytically considered a dislocation in three-dimensional Weyl semimetal and its holographic model. A quantum singularity that originated in the dislocation creates a defect in momentum space. This defect causes…

Exceptional points and double poles of the S matrix are both characterized by the coalescence of a pair of eigenvalues. In the first case, the coalescence causes a defect of the Hilbert space. In the second case, this is not so as shown in…

We systematically study the topology of the exceptional point (EP) in the finite non-Hermitian system. Based on the concrete form of the Berry connection, we demonstrate that the exceptional line (EL), at which the eigenstates coalesce, can…

Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology.…

The discovery of novel topological phase advances our knowledge of nature and stimulates the development of applications. In non-Hermitian topological systems, the topology of band touching exceptional points is very important. Here we…

We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a…