10 research outputs found
Multiple bound states in scissor-shaped waveguides
We study bound states of the two-dimensional Helmholtz equations with
Dirichlet boundary conditions in an open geometry given by two straight leads
of the same width which cross at an angle . Such a four-terminal
junction with a tunable can realized experimentally if a right-angle
structure is filled by a ferrite. It is known that for there is
one proper bound state and one eigenvalue embedded in the continuum. We show
that the number of eigenvalues becomes larger with increasing asymmetry and the
bound-state energies are increasing as functions of in the interval
. Moreover, states which are sufficiently strongly bent exist in
pairs with a small energy difference and opposite parities. Finally, we discuss
how with increasing the bound states transform into the quasi-bound
states with a complex wave vector.Comment: 6 pages, 6 figure
Observation of Quantum Asymmetry in an Aharonov-Bohm Ring
We have investigated the Aharonov-Bohm effect in a one-dimensional
GaAs/GaAlAs ring at low magnetic fields. The oscillatory magnetoconductance of
these systems are for the first time systematically studied as a function of
density. We observe phase-shifts of in the magnetoconductance
oscillations, and halving of the fundamental period, as the density is
varied. Theoretically we find agreement with the experiment, by introducing an
asymmetry between the two arms of the ring.Comment: 4 pages RevTex including 3 figures, submitted to Phys. Rev.
Feshbach projection-operator formalism to resonance scattering on Bargmann-type potentials
The projection-operator formalism of Feshbach is applied to resonance
scattering in a single-channel case. The method is based on the division of the
full function space into two segments, internal (localized) and external
(infinitely extended). The spectroscopic information on the resonances is
obtained from the non-Hermitian effective Hamilton operator
appearing in the internal part due to the coupling to the external part. As
well known, additional so-called cut-off poles of the -matrix appear,
generally, due to the truncation of the potential. We study the question of
spurious matrix poles in the framework of the Feshbach formalism. The
numerical analysis is performed for exactly solvable potentials with a finite
number of resonance states. These potentials represent a generalization of
Bargmann-type potentials to accept resonance states. Our calculations
demonstrate that the poles of the matrix obtained by using the Feshbach
projection-operator formalism coincide with both the complex energies of the
physical resonances and the cut-off poles of the -matrix.Comment: 12 pages, 9 figure
Simulations of interference effects in gated two-dimensional ballistic electron systems
We present detailed simulations addressing recent electronic interference
experiments, where a metallic gate is used to locally modify the Fermi
wave-length of the charge carriers. Our numerical calculations are based on a
solution of the one-particle Schroedinger equation for a realistic model of the
actual sample geometry, including a Poisson equation based determination of the
potential due to the gate. The conductance is determined with the multiprobe
Landauer-Buettiker formula, and in general we find conductance vs. gate voltage
characteristics which closely resemble the experimental traces. A detailed
examination based on quantum mechanical streamlines suggests that the simple
one-dimensional semiclassical model often used to describe the experiments has
only a limited range of validity, and that certain 'unexpected' periodicities
should not be assigned any particular significance, they arise due to the
complicated multiple scattering processes occurring in certain sample
geometries.Comment: 7 pages, 10 embedded figures, higher quality figures available in
tif-format (or as a hard copy) from [email protected]
Conformal and Affine Hamiltonian Dynamics of General Relativity
The Hamiltonian approach to the General Relativity is formulated as a joint
nonlinear realization of conformal and affine symmetries by means of the Dirac
scalar dilaton and the Maurer-Cartan forms. The dominance of the Casimir vacuum
energy of physical fields provides a good description of the type Ia supernova
luminosity distance--redshift relation. Introducing the uncertainty principle
at the Planck's epoch within our model, we obtain the hierarchy of the Universe
energy scales, which is supported by the observational data. We found that the
invariance of the Maurer-Cartan forms with respect to the general coordinate
transformation yields a single-component strong gravitational waves. The
Hamiltonian dynamics of the model describes the effect of an intensive vacuum
creation of gravitons and the minimal coupling scalar (Higgs) bosons in the
Early Universe.Comment: 37 pages, version submitted to Gen. Rel. Gra