318 research outputs found
Absolute continuity in periodic thin tubes and strongly coupled leaky wires
Using a perturbative argument, we show that in any finite region containing
the lowest transverse eigenmode, the spectrum of a periodically curved smooth
Dirichlet tube in two or three dimensions is absolutely continuous provided the
tube is sufficiently thin. In a similar way we demonstrate absolute continuity
at the bottom of the spectrum for generalized Schr\"odinger operators with a
sufficiently strongly attractive interaction supported by a periodic
curve in .Comment: LaTeX 2e, 10 page
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 . 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 geometrically induced bound states.Comment: 20 pages in LaTe
On the skeleton method and an application to a quantum scissor
In the spectral analysis of few one dimensional quantum particles interacting
through delta potentials it is well known that one can recast the problem into
the spectral analysis of an integral operator (the skeleton) living on the
submanifold which supports the delta interactions. We shall present several
tools which allow direct insight into the spectral structure of this skeleton.
We shall illustrate the method on a model of a two dimensional quantum particle
interacting with two infinitely long straight wires which cross one another at
a certain angle : the quantum scissor.Comment: Submitte
On critical stability of three quantum charges interacting through delta potentials
We consider three one dimensional quantum, charged and spinless particles
interacting through delta potentials. We derive sufficient conditions which
guarantee the existence of at least one bound state
Effective Hamiltonians for atoms in very strong magnetic fields
We propose three effective Hamiltonians which approximate atoms in very
strong homogeneous magnetic fields modelled by the Pauli Hamiltonian, with
fixed total angular momentum with respect to magnetic field axis. All three
Hamiltonians describe electrons and a fixed nucleus where the Coulomb
interaction has been replaced by -dependent one-dimensional effective
(vector valued) potentials but without magnetic field. Two of them are solvable
in at least the one electron case. We briefly sketch how these Hamiltonians can
be used to analyse the bottom of the spectrum of such atoms.Comment: 43 page
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A new model for quantum dot light emitting-absorbing devices : dedicated to the memory of Pierre Duclos
Motivated by the Jaynes-Cummings (JC) model, we consider here a quantum dot coupled simultaneously
to a reservoir of photons and to two electric leads (free-fermion reservoirs). This
Jaynes-Cummings-Leads (JCL) model makes possible that the fermion current through the dot
creates a photon flux, which describes a light-emitting device. The same model also describes a
transformation of the photon flux into a fermion current, i.e. a quantum dot light-absorbing device.
The key tool to obtain these results is an abstract Landauer-Büttiker formula
Bounds on resolvents of dilated Schrödinger operators with non trapping potentials
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