Related papers: Straight quantum layer with impurities inducing re…
The behavior of the residual (impurity-dominated) resistivity is computed for a material near a two dimensional quantum critical point characterized by a divergent $q=0$ susceptibility. A singular renormalization of the amplitude for…
An new eigenvalue $\mathbb R$-linear problem arisen in the theory of metamaterials is stated and constructively investigated for circular non-overlapping inclusions. An asymptotic formula for eigenvalues is deduced when the radii of…
We study the effects of the spacial structure of localized losses in weakly-interacting fermionic quantum wires. We show that multiple dissipative impurities give rise to resonant effects visible in the transport properties and the…
Three dimensional topological insulators are bulk insulators with $\mathbf{Z}_2$ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by…
The conductance through a quantum wire of cylindrical cross section and a weak bulge is solved exactly for two electrons within the Landauer-Buettiker formalism. We show that this 'open' quantum dot exhibits spin-dependent Coulomb blockade…
We study the occurrence of negative differential conductance induced by resonance effects in a model for a multilayer heterostructure. In particular, we consider a system consisting of several correlated and non-correlated monoatomic…
This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact…
We study a one-dimensional interacting quantum liquid hosting a pair of mobile impurities causing backscattering. We determine the effective retarded interaction between the two impurities mediated by the liquid. We show that for strong…
We reveal that metasurfaces created by seemingly different lattices of (dielectric or metallic) meta-atoms with broken in-plane symmetry can support sharp high-$Q$ resonances that originate from the physics of bound states in the continuum.…
We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…
We review recent results on the linear and non-linear optical response of realistic quantum-wire structures. Our theoretical approach is based on a set of generalized semiconductor Bloch equations, and allows a full three-dimensional…
We show that the scaling exponent for tunneling into a quantum wire in the "Coulomb Tonks gas" regime of impenetrable, but otherwise free, electrons is affected by impurity scattering in the wire. The exponent for tunneling into such a wire…
Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a…
We develop a theoretical formalism to model the linear spectrum of a quantum dot embedded in a high quality cavity, in presence of an arbitrary mechanism modifying the homogeneous spectrum of the quantum dot. Within the simple assumption of…
We show that, in odd dimensions, any real valued, bounded potential of compact support has at least one scattering resonance. For dimensions three and higher this was previously known only for sufficiently smooth potentials. The proof is…
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original…
An eigenvalue problem relevant for non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime…
Quantum embedding methods have become a powerful tool to overcome deficiencies of traditional quantum modelling in materials science. However, while these are systematically improvable in principle, in practice it is rarely possible to…
Analytic and approximate solutions for the energy eigenvalues generated by a confined softcore Coulomb potentials of the form a/(r+\beta) in d>1 dimensions are constructed. The confinement is effected by linear and harmonic-oscillator…
Consider the transverse magnetic polarization of the electromagnetic scattering of a plane wave by a perfectly conducting plane surface, which contains a two-dimensional subwavelength rectangular cavity. The enhancement is investigated…