Related papers: Two patterns of PT-symmetry breakdown in a non-num…
In 1998, Carl Bender challenged the perceived wisdom of quantum mechanics that the Hamiltonian operator describing any quantum mechanical system has to be Hermitian. He showed that Hamiltonians that are invariant under combined parity-time…
Exceptional points (EPs) of non-Hermitian (NH) systems have recently attracted increasing attention due to their rich phenomenology and intriguing applications. Compared to the predominantly studied second-order EPs, higher-order EPs have…
In many PT symmetric models with real spectra, apparently, energy levels "merge and disappear" at a point of the spontaneous PT-symmetry breaking. We argue that such an oversimplified and discontinuous physical interpretation of this…
Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are $\mathcal{PT}$-symmetric. These exhibit exceptional points (EPs) where the eigenspectrum changes from purely real to purely imaginary…
We consider bipartite tight-binding graphs composed by $N$ nodes split into two sets of equal size: one set containing nodes with on-site loss, the other set having nodes with on-site gain. The nodes are connected randomly with probability…
Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
We extend the application of the techniques developed within the framework of the pseudo-Hermitian quantum mechanics to study a unitary quantum system described by an imaginary PT-symmetric potential v(x) having a continuous real spectrum.…
In this work, $\mathcal{PT}$-symmetric Hamiltonians defined on quantum $sl(2, \mathbb R)$ algebras are presented. We study the spectrum of a family of non-Hermitian Hamiltonians written in terms of the generators of the non-standard…
Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
Over the past decade, parity-time ($\mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
Parity-time (PT) symmetry and anti-PT symmetry have attracted extensive interest for their non-Hermitian spectral properties, particularly the emergence of purely real and imaginary eigenvalues in their symmetry-unbroken regime,…
Eigenspectra of a spinless quantum particle trapped inside a rigid, rectangular, two-dimensional (2D) box subject to diverse inner potential distributions are investigated under hermitian, as well as non-hermitian antiunitary $\mathcal{PT}$…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
Non-Hermitian systems distinguish themselves from Hermitian systems by exhibiting a phase transition point called an exceptional point (EP), which is the point at which two eigenstates coalesce under a system parameter variation. Many…
We propose a non-Hermitian deformation of the Mathieu equation that preserves $\mathcal{PT}$ symmetry and study its spectrum and the transition from $\mathcal{PT}$-unbroken to $\mathcal{PT}$-broken phases. We show that our model not only…
Quantum phase transition is interpreted as an evolution, at the end of which a parameter-dependent Hamiltonian $H(g)$ loses its observability. In the language of mathematics, such a quantum catastrophe occurs at an exceptional point of…
The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates…