Related papers: Non-Hermiticity and conservation of orthogonal rel…

In the Feshbach projection operator (FPO) formalism the whole function space is divided into two subspaces. One of them contains the wave functions localized in a certain finite region while the continuum of extended scattering wave…

We review analyses of open quantum systems. We show how non-Hermiticity arises in an open quantum system with an infinite environment, focusing on the one-body problem. One of the reasons for taking the present approach is that we can solve…

Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical…

Non-Hermitian theory is a theoretical framework that excels at describing open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom (DOFs) of a system and the interactions with the external…

The Hamilton operator of an open quantum system is non-Hermitian. Its eigenvalues are, generally, complex and provide not only the energies but also the lifetimes of the states of the system. The states may couple via the common environment…

We consider different properties of small open quantum systems coupled to an environment and described by a non-Hermitian Hamilton operator. Of special interest is the non-analytical behavior of the eigenvalues in the vicinity of singular…

Non-orthogonal eigenstates are a fundamental feature of non-Hermitian systems and are accompanied by the emergence of nontrivial features. However, the platforms to explore non-Hermitian mode couplings mainly measure near-field effects, and…

The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard…

In the presence of Lindblad decoherence, i.e. dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by…

Standard quantum mechanics predicts the non-conservation of state norms and probability when the fundamental requirement of the Hermiticity of the Hamiltonian is relaxed. Biorthogonal quantum mechanics, or the more general metric formalism,…

This topical review article reports rapid progress on the generalization and application of entanglement in non-Hermitian free-fermion quantum systems. We begin by examining the realization of non-Hermitian quantum systems through the…

We investigate the eigenstate thermalization in terms of a Hermitian operator and the complex eigenkets that follows Gaussian ensemble distribution. With the non-Hermitian open bipartite system, there are, however, some global restrictions…

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems.…

The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…

Two theoretical methods of finding resonant states in open quantum systems, namely the approach of the Siegert boundary condition and the Feshbach formalism, are reviewed and shown to be algebraically equivalent to each other for a simple…

The eigenvalues of a non-Hermitian Hamilton operator are complex and provide not only the energies but also the lifetimes of the states of the system. They show a non-analytical behavior at singular (exceptional) points (EPs). The…

This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case…

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…

A defining quantity of a physical system is its energy which is represented by the Hamiltonian. In closed quantum mechanical or/and coherent wave-based systems the Hamiltonian is introduced as a Hermitian operator which ensures real energy…

We demonstrate three types of transformations that establish connections between Hermitian and non-Hermitian quantum systems at criticality, which can be described by conformal field theories (CFTs). For the transformation preserving both…