Related papers: A physical interpretation for the non-Hermitian Ha…

We present a geometric construction of a lattice that emulates the action of a gauge field on a fermion. The construction consists of a square lattice made of polymeric sites, where all clustered atoms are identical and represented by…

In this paper we analyze a recently proposed approach for the construction of antisymmetric functions for atomic and molecular systems. It is based on the assumption that the main problems with Hartree-Fock wavefunctions stem from their…

This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed…

We study the transport and spectral properties of a non-Hermitian one-dimensional disordered lattice, the diagonal matrix elements of which are random complex variables taking both positive (loss) and negative (gain) imaginary values: Their…

A condition to have a real spectrum for a non-Hermitian Hamiltonian is given. As special cases, it is shown that the condition is reduced to Hermiticity and PT symmetric conditions.

Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows…

In this study, the non-Hermitian scattering of gravitational waves is examined, and their behavior at spectral singularities is discussed. We investigate the non-Hermitian properties of gravitational waves through the construction of a…

The spectral and transport properties of a non-Hermitian tight-binding lattice with unidirectional hopping are theoretically investigated in three different geometrical settings. It is shown that, while for the infinitely-extended (open)…

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the…

We observe that the reflection and transmission coefficients of a particle within a double, PT symmetric heterojunction with spatially varying mass, show interesting features, depending on the degree of non Hermiticity, although there is no…

We examine a non-Hermitian (NH) tight-binding system comprising of two orbitals per unit cell and their electrical circuit analogues. We distinguish the PT-symmetric and non-PT symmetric cases characterised by non-reciprocal nearest…

We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is…

There has been much recent work on the spectrum of the random non-hermitean Hamiltonian which models the physics of vortex line pinning in superconductors. This note is loosely based on the talk I gave at the conference "New Directions in…

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…

A system of interacting spins that are under the influence of spin-polarized currents can be described using a complex functional, or a non-Hermitian (NH) Hamiltonian. We study the dynamics of two exchange-coupled spins on the Bloch sphere.…

Recently, open systems with balanced, spatially separated loss and gain have been realized and studied using non-Hermitian Hamiltonians that are invariant under the combined parity and time-reversal ($\mathcal{PT}$) operations. Here, we…

Optical trapping and binding systems are non-Hermitian. On one hand, the optical force is non-Hermitian and may pump energy into the trapped particle when the non-Hermiticity is sufficiently large. On the other hand, the ambient damping…

For one-dimensional PT -symmetric systems, it is observed that the non-local product obtained from the continuity equation can be interpreted as a conserved corre- lation function. This leads to physical conclusions, regarding both discrete…

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-enviroment interaction. A simple and paradigmatic example of non-Hermitian…

We establish that a perfect-transmission scattering problem can be described by a class of parity and time reversal symmetric operators and hereby we provide a scenario for understanding and implementing the corresponding quasi-Hermitian…