Related papers: Symmetry-Breaking Transition and Spectral Singular…
Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…
We describe one-dimensional stationary scattering of a two-component wave field by a non-Hermitian matrix potential which features odd-$PT$ symmetry, i.e., symmetry with $(PT)^2=-1$. The scattering is characterized by a $4\times 4$ transfer…
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In…
In this work, we study the transmission properties of one dimensional finite periodic systems with $\mathcal{PT}$-symmetry. A simple closed form expression is obtained for the total transmittance from a lattice of N cells, that allows us to…
We outline a global approach to scattering theory in one dimension that allows for the description of a large class of scattering systems and their $\mathcal{P}$-, $\mathcal{T}$-, and $\mathcal{P}\mathcal{T}$-symmetries. In particular, we…
A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the…
Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…
We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer…
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…
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…
We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is…
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring…
We study spectral and transport properties of one-dimensional tight-binding $\mathcal{PT}$-symmetric chains with alternating couplings. Based on the transfer matrix method, we have analytically developed the expressions for the transmission…
In this letter, we study the scattering of spin-$\frac{1}{2}$ particles from a spin-independent parity time ($\cal PT$)-symmetric complex potential, and for the first time, theoretically demonstrate the coexistence of $\cal PT$-symmetric…
The parity-time ($\mathcal{PT}$) symmetric structures have exhibited potential applications in developing various robust quantum devices. In an optical trimmer with balanced loss and gain, we analytically study the $\mathcal{PT}$ symmetric…
We present an analytical study for the scattering amplitudes (Reflection $|R|$ and Transmission $|T|$), of the periodic ${\cal{PT}}$ symmetric optical potential $ V(x) = \displaystyle W_0 \left( \cos ^2 x + i V_0 \sin 2x \right) $ confined…
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss…
One-dimensional scattering problem admitting a complex, PT-symmetric short-range potential V(x) is considered. Using a Runge-Kutta-discretized version of Schroedinger equation we derive the formulae for the reflection and transmission…
In quantum mechanics textbooks, a single-particle scattering theory is introduced. In the present work, a generalized scattering theory is presented, which can be in principle applied to the scattering problems of arbitrary number of…