2,191 research outputs found

    Sufficient conditions for the anti-Zeno effect

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    The ideal anti-Zeno effect means that a perpetual observation leads to an immediate disappearance of the unstable system. We present a straightforward way to derive sufficient conditions under which such a situation occurs expressed in terms of the decaying states and spectral properties of the Hamiltonian. They show, in particular, that the gap between Zeno and anti-Zeno effects is in fact very narrow.Comment: LatEx2e, 9 pages; a revised text, to appear in J. Phys. A: Math. Ge

    Lieb-Thirring inequalities for geometrically induced bound states

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    We prove new inequalities of the Lieb-Thirring type on the eigenvalues of Schr\"odinger operators in wave guides with local perturbations. The estimates are optimal in the weak-coupling case. To illustrate their applications, we consider, in particular, a straight strip and a straight circular tube with either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page

    Edge currents in the absence of edges

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    We investigate a charged two-dimensional particle in a homogeneous magnetic field interacting with a periodic array of point obstacles. We show that while Landau levels remain to be infinitely degenerate eigenvalues, between them the system has bands of absolutely continuous spectrum and exhibits thus a transport along the array. We also compute the band functions and the corresponding probability current.Comment: Final version, to appear in Phys. Lett. A; 10 LaTeX pages with 3 eps figure

    Spectra of soft ring graphs

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    We discuss of a ring-shaped soft quantum wire modeled by ÎŽ\delta interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the dependence of eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is investigated also in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov-Bohm flux and the system exhibits persistent currents.Comment: LaTeX 2e, 17 pages, with 10 ps figure

    Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

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    We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page

    On the spectrum of a waveguide with periodic cracks

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    The spectral problem on a periodic domain with cracks is studied. An asymptotic form of dispersion relations is calculated under assumption that the opening of the cracks is small

    Topologically non-trivial quantum layers

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    Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original paper by Duclos et al. to the situation when the surface does not possess poles. This enables us to consider topologically more complicated layers and state new spectral results. In particular, we are interested in layers built over surfaces with handles or several cylindrically symmetric ends. We also discuss more general regions obtained by compact deformations of certain layers.Comment: 15 pages, 6 figure

    Spectroscopy of annular drums and quantum rings: perturbative and nonperturbative results

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    We obtain systematic approximations to the states (energies and wave functions) of quantum rings (annular drums) of arbitrary shape by conformally mapping the annular domain to a simply connected domain. Extending the general results of Ref.\cite{Amore09} we obtain an analytical formula for the spectrum of quantum ring of arbirtrary shape: for the cases of a circular annulus and of a Robnik ring considered here this formula is remarkably simple and precise. We also obtain precise variational bounds for the ground state of different quantum rings. Finally we extend the Conformal Collocation Method of \cite{Amore08,Amore09} to the class of problems considered here and calculate precise numerical solutions for a large number of states (≈2000\approx 2000).Comment: 12 pages, 12 figures, 2 table
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