Related papers: Biorthogonal scattering and generalized unitarity …
For a subclass of a general $\mathcal{PT}-$symmetric Hamiltonian obeying anti-commutation relation with its conjugate, a Hermitian basis is found that spans the bi-orthonormal energy eigenvectors. Using the modified projectors constructed…
Using transfer-matrix methods, we investigate the response of a multilayered metamaterial system containing defects to an incident acoustic plane wave at normal or oblique incidence. The transmission response is composed of pass-bands with…
Evolutions under non-Hermitian Hamiltonians with unbroken $\mathcal{PT}$ symmetry can be considered unitary under appropriate choices of inner products, facilitated by the so-called metric operator. While it is understood that the choice of…
We introduce a procedure to generate scattering states which display trajectory-like wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
We present a simple non-hermitian model to describe the phenomenon of asymmetric tunneling between two energy-degenerate sites coupled by a non-reciprocal interaction without dissipation. The system was described using a biorthogonal family…
In mesoscopic systems to study the role of inelastic scattering on the phase coherent motion of electrons two phenomenological models have been proposed. In the first one, due to B\"uttiker, one adds a voltage probe into the system (or in…
A non-Hermitian region connected to semi-infinite Hermitian lattices acts either as a source or as a sink and the probability current is not conserved in a scattering typically. Even a $\mathcal{P}\mathcal{T}$-symmetric region that contains…
A non-Hermitian PT-symmetric system can have full real spectrum but does not ensure probability preserving time evolution, in contrast to that of a Hermitian system. We present a non-Hermitian two-band model, which is comprised of dimerized…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection…
We present an evaluation of some recent attempts at understanding the role of pseudo-Hermitian and PT-symmetric Hamiltonians in modeling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in…
Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$),…
A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we…
Resonances of open non-Hermitian systems are associated with the poles of the system scattering matrix. Perturbations of the system cause these poles to shift in the complex frequency plane. In this work, we introduce a novel method for…
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…
We consider a generalisation of the p+ip pairing Hamiltonian with external interaction terms. These terms allow for the exchange of particles between the system and its environment. As a result the u(1) symmetry associated with conservation…
A recursive scheme for the design of scatterers acting simultaneously as emitters and absorbers, such as lasers and coherent perfect absorbers in optics, at multiple prescribed frequencies is proposed. The approach is based on the assembly…
Open classical and quantum systems with effective parity-time ($\mathcal{PT}$) symmetry, over the past five years, have shown tremendous promise for advances in lasers, sensing, and non-reciprocal devices. And yet, how such effective…
We study two-body non-Hermitian physics in the context of an open dissipative system depicted by the Lindblad master equation. Adopting a minimal lattice model of a handful of interacting fermions with single-particle dissipation, we show…