Related papers: Bound states in open coupled asymmetrical waveguid…
Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help…
The ballistic conductance through a device consisting of quantum wires, to which two stubs are attached laterally, is calculated assuming parabolic confining potentials of frequencies $\omega_w$ for the wires and $\omega_s$ for the stubs.…
Properties of the bound states of two quantum waveguides coupled via the window of the width $s$ in their common boundary are calculated under the assumption that the transverse electric field $\pmb{\mathscr{E}}$ is applied to the…
The bound state energies of L-shaped or T-shaped quantum wires in inhomogeous magnetic fields are found to depend strongly on the asymmetric parameter $\alpha =W_{2}/W_{1}$, i.e. the ratio of the arm widths. Two effects of magnetic field on…
It is shown that in a double-cavity, two-dimensional electron waveguide, the interplay between quasi-bound states of each cavity leads to the appearance of bound states in continuum for certain distances between the cavities. These bound…
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…
The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can…
We address a two-dimensional parity-time (PT)-symmetric structure built as a chain of waveguides, where all waveguides except for the central one are conservative, while the central one is divided into two halves with gain and losses. We…
We investigate Luttinger junctions of quantum wires away from criticality. The one-body scattering matrix, corresponding to the off-critical boundary conditions at the junction, admits in general antibound and/or bound states. Their…
We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by…
We investigate properties of a particle confined to a hard-wall spiral-shaped region. As a case study we analyze in detail the Archimedean spiral for which the spectrum above the continuum threshold is absolutely continuous away from the…
The response of a mesoscopic homogeneous superconducting wire, connected with bulk normal metal reservoirs, is theoretically investigated as function of the applied voltage. The finite relaxation length of the nonequilibrium quasiparticle…
We theoretically study the appearance of bound states around impurities in a superconducting bilayer. We focus our attention on $s$-wave pairing, which includes unconventional odd-parity states permitted by the layer degree of freedom.…
We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width $ \ell $ in the common boundary. We show that such a system has at least one bound state for any $ \ell>0 $. We find the corresponding…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
We study numerically the existence and character of bound states for positive and negative point charges shielded by the response of a two-dimensional homogeneous electron gas. The problem is related to many physical situations and has…
Bound states in the continuum (BIC), i.e. normalizable modes with an energy embedded in the continuous spectrum of scattered states, are shown to exist in certain optical waveguide lattices with $\mathcal{PT}$-symmetric defects. Two…
We consider the Laplace operator in a thin three dimensional tube with a Robin type condition on its boundary and study, asymptotically, the spectrum of such operator as the diameter of the tube's cross section becomes infinitesimal. In…
This paper presents a rigorous mathematical analysis for symmetry-based Bound States in the Continuum (BICs) in optical waveguide arrays. Different from existing research, we consider a finite system of horizontally and equidistantly…
We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a…