Related papers: Understanding the Complex Position in a PT-symmetr…
For an invertible (bounded) linear operator Q acting in a Hilbert space ${\cal H}$, we consider the consequences of the QT-symmetry of a non-Hermitian Hamiltonian $H:{\cal H}\to{\cal H}$ where T is the time-reversal operator. If H is…
We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…
We review the methodology to theoretically treat parity-time- ($\mathcal{PT}$-) symmetric, non-Hermitian quantum many-body systems... (For the full abstract see paper)
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…
We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of…
We apply the quantum Hamilton-Jacobi formalism, naturally defined in the complex domain, to a number of complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and…
The observation that PT-symmetric Hamiltonians can have real-valued energy levels even if they are non-Hermitian has triggered intense activities, with experiments, in particular, focusing on optical systems, where Hermiticity can be broken…
While non-Hermitian systems are normally constructed through incoherent coupling to a larger environment, recent works have shown that under certain conditions coherent couplings can be used to similar effect. We show that this new paradigm…
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…
We show that parity-time and partial parity-time symmetries are particular cases of antiunitary symmetry. This point is illustrated by means of a recently discussed system of non-Hermitian coupled harmonic oscillators that also exhibits…
We formulate gaussian and circular random-matrix models representing a coupled system consisting of an absorbing and an amplifying resonator, which are mutually related by a generalized time-reversal symmetry. Motivated by optical…
In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x…
Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing…
While a Hamiltonian can be both Hermitian and $PT$ symmetric, it is $PT$ symmetry that is the more general, as it can lead to real energy eigenvalues even if the Hamiltonian is not Hermitian. We discuss some specific ways in which $PT$…
Based on the reciprocity theorem, we put forward a generalized parametric space for an arbitrary transfer matrix with parity time (PT) symmetry. Through this space, one can extract complete information involving PT phases, reflectances,…
The classical trajectories of the family of complex PT-symmetric Hamiltonians $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) form closed orbits. All such complex orbits that have been studied in the past are PT symmetric (left-right symmetric).…
We theoretically study the non-Hermitian systems, the non-Hermiticity of which arises from the unequal hopping amplitude (UHA) dimers. The distinguishing features of these models are that they have full real spectra if all of the…
$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This…
We provide a time-dependent Dyson map and metric for the two dimensional harmonic oscillator with a non-Hermitian $i xy$ coupling term. This particular time-independent model exhibits spontaneously broken $\mathcal{PT}$-symmetry and becomes…
We introduce a very simple, exactly solvable PT-symmetric non-Hermitian model with real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.