Related papers: Real eigenvalues in non-Hermitian Hamilton quantum…
Non-Hermitian physics exhibits unique physical properties beyond those of traditional Hermitian systems, such as symmetry breaking, the emergence of exceptional points, topological phase transitions, and more. These phenomena have been…
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…
We systematically characterize the dynamical evolution of time-parity (PT )-symmetric two-level systems with spin-dependent dissipations. If the control parameters of the gap are linearly tuned with time, the dynamical evolution can be…
Non-Hermitian quantum systems have recently attracted considerable attention due to their exotic properties. Though many experimental realizations of non-Hermitian systems have been reported, the non-Hermiticity usually resorts to the…
We report a novel mechanism of boundary-sensitive PT symmetry breaking in one-dimensional Floquet systems. By designing a time-periodic driving protocol, we realize a Floquet Hamiltonian that is Hermitian under periodic boundary conditions…
We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial…
Realistic quantum mechanical systems are always exposed to an external environment. The presence of the environment often gives rise to a Markovian process in which the system loses information to its surroundings. However, many quantum…
Three-parametric family of non-Hermitian but ${\cal PT}-$symmetric six-by-six matrix Hamiltonians $H^{(6)}(x,y,z)$ is considered. The ${\cal PT}-$symmetry remains spontaneously unbroken (i.e., the spectrum of the bound-state energies…
We report a kind of quantum phase transition which takes place in isolated quantum systems with non-thermal equilibrium states and an extra symmetry that commutes with the Hamiltonian for any values of the system parameters. A critical…
The phase shift rules enable the estimation of the derivative of a quantum state with respect to phase parameters, providing valuable insights into the behavior and dynamics of quantum systems. This capability is essential in quantum…
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…
We survey some of the main conceptual developments in the study of PT-symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past ten years or so. We offer a precise mathematical description of a quantum…
The single orbital, one-dimensional, Hatano-Nelson Hamiltonian provides deep insight into the physics of non-Hermiticity, resulting from asymmetric left/right hopping, and its connections to localization. In the absence of disorder, its…
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…
A non-Markovian stochastic Schroedinger equation for a quantum system coupled to an environment of harmonic oscillators is presented. Its solutions, when averaged over the noise, reproduce the standard reduced density operator without any…
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…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new…
We review some recent work on the occurrence of coalescing eigenstates at exceptional points in non-Hermitian systems and their influence on physical quantities. We particularly focus on quantum dynamics near exceptional points in open…