Related papers: Exactly solvable $\mathcal{PT}$-symmetric models i…
This paper investigates finite-dimensional representations of PT-symmetric Hamiltonians. In doing so, it clarifies some of the claims made in earlier papers on PT-symmetric quantum mechanics. In particular, it is shown here that there are…
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…
We discuss the phase diagram and properties of global vortices in the non-Hermitian parity-time-symmetric relativistic model possessing two interacting scalar complex fields. The phase diagram contains stable PT-symmetric regions and…
A generic PT-symmetric Hamiltonian is assumed tridiagonalized and truncated to N dimensions, and its up-down symmetrized special cases with J=[N/2] real couplings are considered. In the strongly non-Hermitian regime the secular equation…
Parity-time (PT) symmetry has attracted a lot of attention since the concept of pseudo-Hermitian dynamics of open quantum systems was first demonstrated two decades ago. Contrary to their Hermitian counterparts, non-conservative…
We find that a broken PT-symmetry operator when interacts with suitable Hermitian operator, new system becomes completely un-broken PT symmetry. Further on varying the contribution of Hermiticity one can delay or control the broken…
A new family of non-Hermitian PT-symmetric quantum models is proposed in which the Hamiltonians $H=T+V$ are finite-dimensional and in which the dynamical-input potential $V$ is multi-parametric and non-local. The choice is supported by the…
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…
Recent progress on nonlinear properties of parity-time ($\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\cal PT$…
Non-Hermiticity has recently emerged as a rapidly developing field due to its exotic characteristics related to open systems, where the dissipation plays a critical role. In the presence of balanced energy gain and loss with environment,…
We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and…
We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system…
We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian…
Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if PT-symmetry is respected, and in that case an equivalent Hermitian description exists via the so-called Dyson map.…
We study a non-Hermitian two-level system with square-wave modulated dissipation and coupling. Based on the Floquet theory, we achieve an effective Hamiltonian from which the boundaries of the $\mathcal{PT}$ phase diagram are captured…
Searching for non-Hermitian (parity-time)$\mathcal{PT}$-symmetric Hamiltonians \cite{bender} with real spectra has been acquiring much interest for fourteen years. In this article, we have introduced a $\mathcal{PT}$ symmetric non-Hermitian…
The $\mathcal{PT}$ symmetry breaking threshold in discrete realizations of systems with balanced gain and loss is determined by the effective coupling between the gain and loss sites. In one dimensional chains, this threshold is maximum…
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…
The theory of a two-level $\eta$-Hermitian Hamiltonian with $\mathcal{PT}$ symmetry is reviewed and extended to include open system dynamics. A first-principles derivation of the generalized Gorini-Kossakowski-Sudarshan-Lindblad master…
In this article, the non-Hermitian characteristics of three-dimensional PT-symmetric coupled electronic resonators are theoretically analyzed. First, the concept of non-Hermitian PT symmetry is illustrated in the context of electronics…