2,038 research outputs found
Bound states in point-interaction star-graphs
We discuss the discrete spectrum of the Hamiltonian describing a
two-dimensional quantum particle interacting with an infinite family of point
interactions. We suppose that the latter are arranged into a star-shaped graph
with N arms and a fixed spacing between the interaction sites. We prove that
the essential spectrum of this system is the same as that of the infinite
straight "polymer", but in addition there are isolated eigenvalues unless N=2
and the graph is a straight line. We also show that the system has many
strongly bound states if at least one of the angles between the star arms is
small enough. Examples of eigenfunctions and eigenvalues are computed
numerically.Comment: 17 pages, LaTeX 2e with 9 eps figure
On the spectrum of a bent chain graph
We study Schr\"odinger operators on an infinite quantum graph of a chain form
which consists of identical rings connected at the touching points by
-couplings with a parameter . If the graph is "straight",
i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum
with all the gaps open whenever . We consider a "bending"
deformation of the chain consisting of changing one position at a single ring
and show that it gives rise to eigenvalues in the open spectral gaps. We
analyze dependence of these eigenvalues on the coupling and the
"bending angle" as well as resonances of the system coming from the bending. We
also discuss the behaviour of the eigenvalues and resonances at the edges of
the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to
appear in J. Phys. A: Math. Theo
Exponential splitting of bound states in a waveguide with a pair of distant windows
We consider Laplacian in a straight planar strip with Dirichlet boundary
which has two Neumann ``windows'' of the same length the centers of which are
apart, and study the asymptotic behaviour of the discrete spectrum as
. It is shown that there are pairs of eigenvalues around each
isolated eigenvalue of a single-window strip and their distances vanish
exponentially in the limit . We derive an asymptotic expansion also
in the case where a single window gives rise to a threshold resonance which the
presence of the other window turns into a single isolated eigenvalue
Dispersion for the Schr\"odinger Equation on Networks
In this paper we consider the Schr\"odinger equation on a network formed by a
tree with the last generation of edges formed by infinite strips. We give an
explicit description of the solution of the linear Schr\"odinger equation with
constant coefficients. This allows us to prove dispersive estimates, which in
turn are useful for solving the nonlinear Schr\"odinger equation. The proof
extends also to the laminar case of positive step-function coefficients having
a finite number of discontinuities.Comment: 16 pages, 2 figure
Scattering through a straight quantum waveguide with combined boundary conditions
Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with
Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and
Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is
considered using stationary scattering theory. The existence of a matching
conditions solution at x=0 is proved. The use of stationary scattering theory
is justified showing its relation to the wave packets motion. As an
illustration, the matching conditions are also solved numerically and the
transition probabilities are shown.Comment: 26 pages, 3 figure
On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach
We consider a metric graph made of two graphs
and attached at one point. We derive a formula relating the
spectral determinant of the Laplace operator
in terms of the spectral
determinants of the two subgraphs. The result is generalized to describe the
attachment of graphs. The formulae are also valid for the spectral
determinant of the Schr\"odinger operator .Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and
ref adde
Sigmund Exner's (1887) einige beobachtungen über bewegungsnachbilder (some observations on movement aftereffects):an illustrated translation with commentary
In his original contribution, Exner’s principal concern was a comparison between the properties of different aftereffects, and particularly to determine whether aftereffects of motion were similar to those of color and whether they could be encompassed within a unified physiological framework. Despite the fact that he was unable to answer his main question, there are some excellent—so far unknown—contributions in Exner’s paper. For example, he describes observations that can be related to binocular interaction, not only in motion aftereffects but also in rivalry. To the best of our knowledge, Exner provides the first description of binocular rivalry induced by differently moving patterns in each eye, for motion as well as for their aftereffects. Moreover, apart from several known, but beautifully addressed, phenomena he makes a clear distinction between motion in depth based on stimulus properties and motion in depth based on the interpretation of motion. That is, the experience of movement, as distinct from the perception of movement. The experience, unlike the perception, did not result in a motion aftereffect in depth
A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
We demonstrate that any self-adjoint coupling in a quantum graph vertex can
be approximated by a family of magnetic Schroedinger operators on a tubular
network built over the graph. If such a manifold has a boundary, Neumann
conditions are imposed at it. The procedure involves a local change of graph
topology in the vicinity of the vertex; the approximation scheme constructed on
the graph is subsequently `lifted' to the manifold. For the corresponding
operator a norm-resolvent convergence is proved, with the natural
identification map, as the tube diameters tend to zero.Comment: 19 pages, one figure; introduction amended and some references added,
to appear in CM
In Vitro Inhibition of Coagulase-Negative Staphylococci by Vancomycin/Aminoglycoside-Loaded Cement Spacers
Background:: Successful treatment of allograft infections by the temporary implantation of an antibiotic-loaded polymethylmethacrylate cement spacer depends on the diffusion of antibiotics out of the cement and inhibition of bacterial growth in the surrounding tissue. We investigated with an in vitro model how long antibiotics are released by the cement and if gentamicin-resistant coagulase-negative staphylococci (CNS) are inhibited by vancomycin mixed with the gentamicin-loaded cement. Materials and Methods:: Four formulations of antibiotic-loaded cement disks, i.e. gentamicin, tobramycin, vancomycin and tobramycin combined with vancomycin, respectively, were used to test the inhibition of eight isolates of Staphylococcus epidermidis and two reference strains of Staphylococcus aureus by an agar diffusion test on Mueller-Hinton (MH) agar similar to the routine laboratory disk diffusion method. Moreover, cement spacer cylinders loaded with gentamicin alone or combined with vancomycin were submerged in MH agar for weeks and the capacity to inhibit five different isolates of S. epidermidis was measured. Results:: The size of the inhibition zones around the antibiotic-loaded cement disks correlated with the minimal inhibitory concentration (MIC) of the antibiotics against the tested strains. All five strains of S. epidermidis were inhibited by vancomycin-loaded cement spacers for at least 30 days. However, two gentamicin-resistant S. epidermidis strains with MICs of 4 mg/l and 16 mg/l could not be inhibited longer than 3 days by the gentamicin-loaded cement spacer. Conclusion:: The in vitro data suggest that antibiotic-loaded cement spacers inhibit susceptible bacteria for 4-6 weeks. The addition of vancomycin to commercial aminoglycoside-loaded cements might be helpful in allograft infections in tumor patients to inhibit a broad range of bacteria including gentamicin-resistant CNS very commonly found in such infection
Avoided crossings in mesoscopic systems: electron propagation on a non-uniform magnetic cylinder
We consider an electron constrained to move on a surface with revolution
symmetry in the presence of a constant magnetic field parallel to the
surface axis. Depending on and the surface geometry the transverse part of
the spectrum typically exhibits many crossings which change to avoided
crossings if a weak symmetry breaking interaction is introduced. We study the
effect of such perturbations on the quantum propagation. This problem admits a
natural reformulation to which tools from molecular dynamics can be applied. In
turn, this leads to the study of a perturbation theory for the time dependent
Born-Oppenheimer approximation
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