411 research outputs found
On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios
Different change-point type models encountered in statistical inference for
stochastic processes give rise to different limiting likelihood ratio
processes. In a previous paper of one of the authors it was established that
one of these likelihood ratios, which is an exponential functional of a
two-sided Poisson process driven by some parameter, can be approximated (for
sufficiently small values of the parameter) by another one, which is an
exponential functional of a two-sided Brownian motion. In this paper we
consider yet another likelihood ratio, which is the exponent of a two-sided
compound Poisson process driven by some parameter. We establish, that similarly
to the Poisson type one, the compound Poisson type likelihood ratio can be
approximated by the Brownian type one for sufficiently small values of the
parameter. We equally discuss the asymptotics for large values of the parameter
and illustrate the results by numerical simulations
Stein--Sahi complementary series and their degenerations
The aim of the paper is an introduction to Stein--Sahi complementary series,
holomorphic series, and 'unipotent representations'. We also discuss some open
problems related to these objects. For the sake of simplicity, we consider only
the groups U(n,n).Comment: 40pp, 7fig, revised versio
Mesoscopic spin confinement during acoustically induced transport
Long coherence lifetimes of electron spins transported using moving potential
dots are shown to result from the mesoscopic confinement of the spin vector.
The confinement dimensions required for spin control are governed by the
characteristic spin-orbit length of the electron spins, which must be larger
than the dimensions of the dot potential. We show that the coherence lifetime
of the electron spins is independent of the local carrier densities within each
potential dot and that the precession frequency, which is determined by the
Dresselhaus contribution to the spin-orbit coupling, can be modified by varying
the sample dimensions resulting in predictable changes in the spin-orbit length
and, consequently, in the spin coherence lifetime.Comment: 10 pages, 2 figure
Allowed and forbidden transitions in artificial hydrogen and helium atoms
The strength of radiative transitions in atoms is governed by selection
rules. Spectroscopic studies of allowed transitions in hydrogen and helium
provided crucial evidence for the Bohr's model of an atom. Forbidden
transitions, which are actually allowed by higher-order processes or other
mechanisms, indicate how well the quantum numbers describe the system. We apply
these tests to the quantum states in semiconductor quantum dots (QDs), which
are regarded as artificial atoms. Electrons in a QD occupy quantized states in
the same manner as electrons in real atoms. However, unlike real atoms, the
confinement potential of the QD is anisotropic, and the electrons can easily
couple with phonons of the material. Understanding the selection rules for such
QDs is an important issue for the manipulation of quantum states. Here we
investigate allowed and forbidden transitions for phonon emission in one- and
two-electron QDs (artificial hydrogen and helium atoms) by electrical
pump-and-probe experiments, and find that the total spin is an excellent
quantum number in artificial atoms. This is attractive for potential
applications to spin based information storage.Comment: slightly longer version of Nature 419, 278 (2002
Electric Field Control of Spin Transport
Spintronics is an approach to electronics in which the spin of the electrons
is exploited to control the electric resistance R of devices. One basic
building block is the spin-valve, which is formed if two ferromagnetic
electrodes are separated by a thin tunneling barrier. In such devices, R
depends on the orientation of the magnetisation of the electrodes. It is
usually larger in the antiparallel than in the parallel configuration. The
relative difference of R, the so-called magneto-resistance (MR), is then
positive. Common devices, such as the giant magneto-resistance sensor used in
reading heads of hard disks, are based on this phenomenon. The MR may become
anomalous (negative), if the transmission probability of electrons through the
device is spin or energy dependent. This offers a route to the realisation of
gate-tunable MR devices, because transmission probabilities can readily be
tuned in many devices with an electrical gate signal. Such devices have,
however, been elusive so far. We report here on a pronounced gate-field
controlled MR in devices made from carbon nanotubes with ferromagnetic
contacts. Both the amplitude and the sign of the MR are tunable with the gate
voltage in a predictable manner. We emphasise that this spin-field effect is
not restricted to carbon nanotubes but constitutes a generic effect which can
in principle be exploited in all resonant tunneling devices.Comment: 22 pages, 5 figure
Demonstration of conditional gate operation using superconducting charge qubits
Since the first demonstration of coherent control of a quantum state of a
superconducting charge qubit a variety of Josephson-junction-based qubits have
been implemented with remarkable progress in coherence time and read-out
schemes. Although the current level of this solid-state device is still not as
advanced as that of the most advanced microscopic-system-based qubits, these
developments, together with the potential scalability, have renewed its
position as a strong candidate as a building block for the quantum computer.
Recently, coherent oscillation and microwave spectroscopy in
capacitively-coupled superconducting qubits have been reported. The next
challenging step toward quantum computation is a realization of logic gates.
Here we demonstrate a conditional gate operation using a pair of coupled
superconducting charge qubits. Using a pulse technique, we prepare different
input states and show that they can be transformed by controlled-NOT (C-NOT)
gate operation in the amplitude of the states. Although the phase evolution
during the gate operation is still to be clarified, the present results are a
major step toward the realization of a universal solid-state quantum gate
Higher Order Quantum Superintegrability: a new "Painlev\'e conjecture"
We review recent results on superintegrable quantum systems in a
two-dimensional Euclidean space with the following properties. They are
integrable because they allow the separation of variables in Cartesian
coordinates and hence allow a specific integral of motion that is a second
order polynomial in the momenta. Moreover, they are superintegrable because
they allow an additional integral of order . Two types of such
superintegrable potentials exist. The first type consists of "standard
potentials" that satisfy linear differential equations. The second type
consists of "exotic potentials" that satisfy nonlinear equations. For , 4
and 5 these equations have the Painlev\'e property. We conjecture that this is
true for all . The two integrals X and Y commute with the Hamiltonian,
but not with each other. Together they generate a polynomial algebra (for any
) of integrals of motion. We show how this algebra can be used to calculate
the energy spectrum and the wave functions.Comment: 23 pages, submitted as a contribution to the monographic volume
"Integrability, Supersymmetry and Coherent States", a volume in honour of
Professor V\'eronique Hussin. arXiv admin note: text overlap with
arXiv:1703.0975
A data preparation and migration framework for implementing modular product structures in PLM
This paper reports the research on the complex process of implementing modular product structures in a Product Lifecycle Management (PLM) system. There are many challenges in implementing the system. One main challenge is organising or mapping existing product data and migrating it to the new PLM system. Companies often use a PLM tool for management of CAD files, documents and drawings, but they do not take advantage of the full potential of the PLM system to support the development activities of modular products. Product data management tools are used mainly for product CAD data management and PLM systems support by automating and managing some of the operational complexity of modular product design. The aim of this research is to propose a data model that can be used for implementing modular product structures in a PLM system and a tool that can formalise the existing data so as to migrate it into the PLM system
Magnetoresistance in Sn-Doped In2O3Nanowires
In this work, we present transport measurements of individual Sn-doped In2O3nanowires as a function of temperature and magnetic field. The results showed a localized character of the resistivity at low temperatures as evidenced by the presence of a negative temperature coefficient resistance in temperatures lower than 77 K. The weak localization was pointed as the mechanism responsible by the negative temperature coefficient of the resistance at low temperatures
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