相关论文: Quantum strips on surfaces

We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…

We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for…

We consider a quantum particle constrained to a curved layer of a constant width built over an infinite smooth surface. We suppose that the latter is a locally deformed plane and that the layer has the hard-wall boundary. Under this…

Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $ b$ located…

Let $\Omega$ be an unbounded two dimensional strip on a ruled surface in $\mathbb{R}^d$, $d\geq2$. Consider the Laplacian operator in $\Omega$ with Dirichlet and Neumann boundary conditions on opposite sides of $\Omega$. We prove some…

We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition ensuring the existence of the discrete spectrum in the strong magnetic field limit.

We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we…

The Dirichlet p-Laplacian in tubes of arbitrary cross-section along infinite curves in Euclidean spaces of arbitrary dimension is investigated. First, it is shown that the gap between the lowest point of the generalised spectrum and the…

For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable. Any perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, a magnetic field is…

We study the interplay between spectrum, geometry and boundary conditions for two distinguished self-adjoint realisations of the Laplacian on infinite metric graphs, the so-called riedrichs and Neumann extensions. We introduce a new…

We investigate spectral properties of the Laplacian in $L^2(Q)$, where $Q$ is a tubular region in $\mathbb{R}^3$ of a fixed cross section, and the boundary conditions combined a Dirichlet and a Neumann part. We analyze two complementary…

Consider the Laplacian in a straight planar strip of width $\,d\,$, with the Neumann boundary condition at a segment of length $\,2a\,$ of one of the boundaries, and Dirichlet otherwise. For small enough $\,a\,$ this operator has a single…

This article is devoted to the numerical study of the existence of the eigenvalues of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ in the presence of an electric field of constant…

Let $\Omega \subset \mathbb R^3$ be a waveguide which is obtained by translating a cross-section in a constant direction along an unbounded spatial curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in $\Omega$. Under the…

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…

We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and…

We consider the Laplacian in a tubular neighbourhood of a hyperplane subjected to non-self-adjoint $\mathcal{PT}$-symmetric Robin boundary conditions. Its spectrum is found to be purely essential and real for constant boundary conditions.…

We study the behavior of a quantum particle confined to a hard--wall strip of a constant width in which there is a finite number $ N $ of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's…

The spectral properties of the restricted fractional Laplacian with Dirichlet boundary conditions in a smoothly bent waveguide is investigated. The existence of eigenvalues below the threshold of the continuous spectrum is proved,…

We consider a family of open sets $M_\epsilon$ which shrinks with respect to an appropriate parameter $\epsilon$ to a graph. Under the additional assumption that the vertex neighbourhoods are small we show that the appropriately shifted…