Related papers: Leaky quantum wire and dots: a resonance model
A fundamental feature of the quasi-normal modes (QNMs), which describe light interaction with open (leaky) systems like nanoparticles, lies in the question of the completeness of the QNMs representation and in the divergence of their field…
Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that…
A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple,…
The transport through a quantum wire exposed to two magnetic spikes in series is modeled. We demonstrate that quantum dots can be formed this way which couple to the leads via magnetic barriers. Conceptually, all quantum dot states are…
We investigate the conductance of a quantum wire with two embedded quantum dots using a T-matrix approach based on the Lippmann-Schwinger formalism. The quantum dots are represented by a quantum well with Gaussian shape and the wire is…
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…
Single quantum dots are solid-state emitters which mimic two-level atoms but with a highly enhanced spontaneous emission rate. A single quantum dot is the basis for a potentially excellent single photon source. One outstanding problem is…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling and the dot is modeled as an interacting resonant…
In this paper we present and discuss our results for the conductance and conductance fluctuations of narrow quantum wires with two types of disorder: boundary roughness (hard wall confining potential) and islands of strongly scattering…
We study the spectral properties of one-dimensional quantum wire with a single defect. We reveal the existence of the non-trivial topological structures in the spectral space of the system, which are behind the exotic quantum phenomena that…
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain with the Dirichlet boundary conditions on the boundary of the domain. The transition from the…
The aim of this review is to provide an overview of a recent work concerning ``leaky'' quantum graphs described by Hamiltonians given formally by the expression $-\Delta -\alpha \delta (x-\Gamma)$ with a singular attractive interaction…
Resonance and decay phenomena are ubiquitous in the quantum world. To understand them in their complexity it is useful to study solvable models in a wide sense, that is, systems which can be treated by analytical means. The present review…
We study the conductance threshold of clean nearly straight quantum wires in the magnetic field. As a quantitative example we solve exactly the scattering problem for two-electrons in a wire with planar geometry and a weak bulge. From the…
Within an effective Dirac-Weyl theory we solve the scattering problem for massless chiral fermions impinging on a cylindrical time-dependent potential barrier. The set-up we consider can be used to model the electron propagation in a…
We consider some perturbations of a family of pairwise commuting linear quantum Hamiltonians on the torus with possibly dense pure point spectra. We prove that the Rayleigh-Schr{\"o}dinger perturbation series converge near each unperturbed…
We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonisation and re-fermionisation methods, we find a mapping to a Kondo-type problem which possesses a non-trivial…
The quantum dynamics of a compound sample consisting from a semiconductor double quantum dot (DQD) system non-linearly coupled with a leaking single-mode micro-resonator is theoretically investigated. The focus is on the resonance condition…
We present experiments in which self-assembled InAs quantum dots are coupled to a thin, suspended-beam GaAs resonator. The quantum dots are driven resonantly and the resonance fluorescence is detected. The narrow quantum-dot linewidths,…