Curvature{induced Bound States in Quantum Waveguides in Two and Three Dimensions
نویسنده
چکیده
Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions is investigated. It is shown that if the tube is non{straight and its curvature vanishes asymptotically, there is always a bound state below the bottom of the essential spectrum. An upper bound to the number of these bound states in thin tubes is derived. Furthermore, if the tube is only slightly bent, there is just one bound state; we derive its behaviour with respect to the bending angle. Finally, perturbation theory of these eigenvalues in any thin tube with respect to the tube radius is constructed and some open questions are formulated.
منابع مشابه
Bound States in Curved Quantum Layers
We consider a nonrelativistic quantum particle constrained to a curved layer of constant width built over a non-compact surface embedded in R. We suppose that the latter is endowed with the geodesic polar coordinates and that the layer has the hard-wall boundary. Under the assumption that the surface curvatures vanish at infinity we find sufficient conditions which guarantee the existence of ge...
متن کاملBound states in straight quantum waveguides with combined boundary conditions
Quantum waveguides with Dirichlet boundary conditions were extensively studied (e.g. [1], [2], [3], [4], [5], [6] and references therein). Their spectral properties essentially depends on the geometry of the waveguide, especially the existence of bound states induced by curvature [1], [2], [3] or by coupling of straight waveguides through windows [4],[5] were shown. The waveguides with Neumann ...
متن کاملar X iv : h ep - l at / 9 20 50 29 v 1 1 J un 1 99 2 ILL – ( TH ) – 92 – 7 Three – Dimensional Quantum Gravity Coupled to Ising Matter
We establish the phase diagram of three–dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two spin phases with a first order transitio...
متن کاملThree Dimensional Quantum Gravity Coupled to Ising Matter
We establish the phase diagram of three–dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two spin phases with a first order transitio...
متن کاملBound states in waveguides and bent quantum wires. I. Applications to waveguide systems
It has been shown that in quantum wires which contain bends there will be one or more bound states for electrons placed in such systems. Bound states have been observed in quantum wires, but detailed mapping of such states is difficult. However, there is a one-to-one correspondence between wave functions of free electrons in two-dimensional ~2D! systems, and electric fields of TE modes in recta...
متن کامل