Related papers: Conserved Correlation in PT -symmetric Systems: Sc…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
R. Labouvie et al. [Phys. Rev. Lett. 116, 235302 (2016)] have described an experiment with a weakly interacting Bose-Einstein condensate trapped in a one-dimensional optical lattice with localized loss created by a focused electron beam. We…
Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-symmetric scattering eigenstates, which are norm…
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes…
The phenomenon of PT (parity- and time-reversal) symmetry breaking is conventionally associated with a change in the complex mode spectrum of a non-Hermitian system that marks a transition from a purely oscillatory to an exponentially…
We analyze the optical properties of one-dimensional (1D) PT-symmetric structures of arbitrary complexity. These structures violate normal unitarity (photon flux conservation) but are shown to satisfy generalized unitarity relations, which…
The Hamiltonian for a PT-symmetric chain of coupled oscillators is constructed. It is shown that if the loss-gain parameter $\gamma$ is uniform for all oscillators, then as the number of oscillators increases, the region of unbroken…
With perfectly balanced gain and loss, dynamical systems with indefinite damping can obey the exact PT-symmetry being marginally stable with a pure imaginary spectrum. At an exceptional point where the symmetry is spontaneously broken, the…
The scattering matrix $S$ obeys the unitary relation $S^\dagger S=1$ in a Hermitian system and the symmetry property ${\cal PT}S{\cal PT}=S^{-1}$ in a Parity-Time (${\cal PT}$) symmetric system. Here we report a different symmetry relation…
Using a scattering matrix formalism, we derive the general scattering properties of optical structures that are symmetric under a combination of parity and time-reversal (PT). We demonstrate the existence of a transition beween PT-symmetric…
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…
The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric…
The inspiration for this theoretical paper comes from recent experiments on a PT-symmetric system of two coupled optical whispering galleries (optical resonators). The optical system can be modeled as a pair of coupled linear oscillators,…
A real potential Hamiltonian has real energy bound states below the scattering threshold and complex energy resonances above it. Scattering states are not square integrable, being instead delta function normalized. This lack of square…
Non-Hermitian photonic systems with loss and gain attract much attention due to their exceptional abilities in molding the flow of light. Introducing asymmetry to the $\mathcal{PT}$-symmetric system with perfectly balanced loss and gain, we…
We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the…
Parity-time (PT) symmetry has attracted a lot of attention since the concept of pseudo-Hermitian dynamics of open quantum systems was first demonstrated two decades ago. Contrary to their Hermitian counterparts, non-conservative…
Open, non-equilibrium systems with balanced gain and loss, known as parity-time ($\mathcal{PT}$)-symmetric systems, exhibit properties that are absent in closed, isolated systems. A key property is the $\mathcal{PT}$-symmetry breaking…
$\mathcal{PT}$ symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken $\mathcal{PT}$-symmetric states in non-Hermitian open systems are described by…
PT-symmetric scattering systems with balanced gain and loss can undergo a symmetry-breaking transition in which the eigenvalues of the non-unitary scattering matrix change their phase shifts from real to complex values. We relate the…