相关论文: Emergence of a confined state in a weakly bent wir…

We consider a simple model of an electron moving in a T-shaped confinement potential. This model allows for an analytical solution that explicitly demonstrates the existence of laterally bound electron states in quantum wires obtained by…

We study the low-temperature transport properties of 1D quantum wires as the confinement strength V_conf and the carrier density n_1D are varied using a combination of split gates and a top gate in GaAs/AlGaAs heterostructures. At…

We have discovered an unexpected and surprising fact: a 2D axially symmetric short-range potential contains {\it infinite} number of the levels of negative energy {\it if one takes into account the spin-orbit (SO) interaction.} For a…

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.…

The main question studied in this paper concerns the weak-coupling behavior of the geometrically induced bound states of singular Schr\"odinger operators with an attractive $\delta$ interaction supported by a planar, asymptotically straight…

The effect of the uniform magnetic field on the electron in the spherically symmetric square-well potential is studied. A transcendental equation that determines the electron energy spectrum is derived. The approximate value of the lowest…

We provide a systematic quantitative description of the structure of edge states and magnetosubband evolution in hard wall quantum wires in the integer quantum Hall regime. Our calculations are based on the self-consistent Green's function…

We study the effect of a constant uniform magnetic field on an electrically charged massive particle (an electron) bound by a potential well, which is described by means of a single attractive $\lambda\delta({\bf r})$ potential. A…

It is well-known that a delta potential well in 1D has only one bound state but that in 3D it supports an {\it infinite} number of bound states with {\it infinite} binding energy for the lowest level. We show how this also holds for the…

We study the bound states of a Kronig Penney potential for a nonlinear one-dimensional Schroedinger equation. This potential consists of a large, but not necessarily infinite, number of equidistant delta-function wells. We show that the…

We analyze spectral properties of a leaky wire model with a potential bias. It describes a two-dimensional quantum particle exposed to a potential consisting of two parts. One is an attractive $\delta$-interaction supported by a…

By introducing a boundary condition for the quantum wire, the Hubbard model is solved exactly by means of Bethe ansatz. The wave function for the bounded state is clearly defined, and the secular equation for the spectrum is exactly…

We report measurements of the compressibility of a one-dimensional (1D) quantum wire, defined in the upper well of a GaAs/AlGaAs double quantum well heterostructure. A wire defined simultaneously in the lower well probes the ability of the…

We report results of a numerical study of non-interacting electrons moving in a random potential in two dimensions in the presence of a weak perpendicular magnetic field. We study the topological properties of the electronic eigenstates…

Energies and wave functions of edge states in twodimensional electron gas are evaluated for a finite step potential barrier model. The spectrum, instead of smooth bending of Landau branches in the vicinity of the barrier acquires a steplike…

We describe a perturbation expansion for the energy and wave function of a weakly bound particle in a short-range potential in one space dimension.

We study a set of crossed 1D systems, which are coupled with each other via tunnelling at the crossings. We begin with the simplest case with no electron-electron interactions and find that besides the expected level splitting, bound states…

We discuss the emergence of bound states in the low-energy spectrum of the string-net Hamiltonian in the presence of a string tension. In the ladder geometry, we show that a single bound state arises either for a finite tension or in the…

We study the critical behaviour near the threshold where a first bound state appears at some value of coupling constant in an attractive short-range potential in $2+\epsilon $ dimensions. We obtain general expression for the binding energy…

From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…