相关论文: Quantum wires with magnetic fluxes

In the present work the possibility of regulating local magnetic field in a quantum ring is investigated theoretically. The ring is coupled to a quantum wire and subjected to an in-plane electric field. Under a finite bias voltage across…

We quantize the electromagnetic field in the presence of a static magnetic monopole, within the loop-representation formalism. We find that the loop-dependent wave functional becomes multivalued, in the sense that it acquires a dependence…

We give a construction of a class of magnetic Laplacian operators on finite directed graphs. We study some general combinatorial and algebraic properties of operators in this class before applying the Harrell-Stubbe Averaged Variational…

We study the two-dimensional magnetic Laplacian when the magnetic field is allowed to be complex-valued. Under the assumption that the imaginary part of the magnetic potential is relatively form-bounded with respect to the real part of the…

The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplace's equation that is accessible for an…

Here we introduce connectivity operators, namely, diffusion operators, general Laplacian operators, and general adjacency operators for hypergraphs. These operators are generalisations of some conventional notions of apparently different…

We compare the magnetic field at the center of and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of…

We consider compact metric graphs with an arbitrary self adjoint realisation of the differential Laplacian. After discussing spectral properties of Laplacians, we prove several versions of trace formulae, relating Laplace spectra to sums…

The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux…

We consider an ideal parabolic quantum wire in a perpendicular magnetic field. A simple Gaussian shaped scattering potential well or hill is flashed softly on and off with its maximum at $t=0$, mimicking a temporary broadening or narrowing…

This paper is devoted to the spectral analysis of the Laplacian with constant magnetic field on a cone of aperture $\alpha$ and Neumann boundary condition. We analyze the influence of the orientation of the magnetic field. In particular,…

Recently normalized Laplacian matrices of graphs are studied as density matrices in quantum mechanics. Separability and entanglement of density matrices are important properties as they determine the nonclassical behavior in quantum…

We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero,…

We consider Laplacians on periodic metric graphs with unit-length edges. The spectrum of these operators consists of an absolutely continuous part (which is a union of an infinite number of non-degenerated spectral bands) plus an infinite…

We develop the theory of torsional rigidity -- a quantity routinely considered for Dirichlet Laplacians on bounded planar domains -- for Laplacians on metric graphs with at least one Dirichlet vertex. Using a variational characterization…

We consider the Hamiltonian for a charged particle in a harmonic potential in the presence of a magnetic field. The most symmetric case depends on one parameter, the variation of which leads from a spectrum bounded from below to an…

Quantum graphs are defined by having a Laplacian defined on the edges of a metric graph with boundary conditions on each vertex such that the resulting operator, $\mathbf{L}$, is self-adjoint. We use Neumann boundary conditions although we…

We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…

In this paper, we investigate the spectrum of a class of weighted Laplacians on Cayley graphs and determine under what conditions the corresponding eigenspaces are generically irreducible. Specifically, we analyze the spectrum on…

We consider a model of leaky quantum wire in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that…