220 research outputs found
Schroedinger operators with singular interactions: a model of tunneling resonances
We discuss a generalized Schr\"odinger operator in , with an attractive singular interaction supported by a
-dimensional hyperplane and a finite family of points. It can be
regarded as a model of a leaky quantum wire and a family of quantum dots if
, or surface waves in presence of a finite number of impurities if .
We analyze the discrete spectrum, and furthermore, we show that the resonance
problem in this setting can be explicitly solved; by Birman-Schwinger method it
is cast into a form similar to the Friedrichs model.Comment: LaTeX2e, 34 page
Quantum properties of the Dirac field on BTZ black hole backgrounds
We consider a Dirac field on a -dimensional uncharged BTZ black hole
background. We first find out the Dirac Hamiltonian, and study its
self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS
Dirac Hamiltonian in dimensions, essential self-adjointness on
of the reduced (radial) Hamiltonian is implemented
only if a suitable relation between the mass of the Dirac field and the
cosmological radius holds true. The very presence of a boundary-like
behaviour of is at the root of this problem. Also, we determine in a
complete way qualitative spectral properties for the non-extremal case, for
which we can infer the absence of quantum bound states for the Dirac field.
Next, we investigate the possibility of a quantum loss of angular momentum for
the -dimensional uncharged BTZ black hole. Unlike the corresponding
stationary four-dimensional solutions, the formal treatment of the level
crossing mechanism is much simpler. We find that, even in the extremal case, no
level crossing takes place. Therefore, no quantum loss of angular momentum via
particle pair production is allowed.Comment: 19 pages; IOP styl
A Conformal Affine Toda Model of 2D-Black Holes the End-Point State and the S-Matrix
In this paper we investigate in more detail our previous formulation of the
dilaton-gravity theory by Bilal--Callan--de~Alwis as a -conformal affine
Toda (CAT) theory. Our main results are: i) a field redefinition of the
CAT-basis in terms of which it is possible to get the black hole solutions
already known in the literature; ii) an investigation the scattering matrix
problem for the quantum black hole states. It turns out that there is a range
of values of the free-falling shock matter fields forming the black hole
solution, in which the end-point state of the black hole evaporation is a zero
temperature regular remnant geometry. It seems that the quantum evolution to
this final state is non-unitary, in agreement with Hawking's scenario for the
black hole evaporation.Comment: ROM2F-93-03, 27 pages, phyzz
Quantum harmonic oscillator systems with disorder
We study many-body properties of quantum harmonic oscillator lattices with
disorder. A sufficient condition for dynamical localization, expressed as a
zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the
eigenfunction correlators for an effective one-particle Hamiltonian. We show
how state-of-the-art techniques for proving Anderson localization can be used
to prove that these properties hold in a number of standard models. We also
derive bounds on the static and dynamic correlation functions at both zero and
positive temperature in terms of one-particle eigenfunction correlators. In
particular, we show that static correlations decay exponentially fast if the
corresponding effective one-particle Hamiltonian exhibits localization at low
energies, regardless of whether there is a gap in the spectrum above the ground
state or not. Our results apply to finite as well as to infinite oscillator
systems. The eigenfunction correlators that appear are more general than those
previously studied in the literature. In particular, we must allow for
functions of the Hamiltonian that have a singularity at the bottom of the
spectrum. We prove exponential bounds for such correlators for some of the
standard models
Strain Relaxation Mechanisms and Local Structural Changes in Si_{1-x}$Ge_{x} Alloys
In this work, we address issues pertinent to the understanding of the
structural and electronic properties of Si_{1-x} Ge_{x}alloys, namely, (i) how
does the lattice constant mismatch between bulk Si and bulk Ge manifests itself
in the alloy system? and (ii) what are the relevant strain release mechanisms?
To provide answers to these questions, we have carried out an in-depth study of
the changes in the local geometric and electronic structures arising from the
strain relaxation in Si_{1-x} Ge_{x} alloys using an ab initio molecular
dynamics scheme. The optimized lattice constant, while exhibiting a general
trend of linear dependence on the composition (Vegard's law), shows a negative
deviation from Vegard's law in the vicinity of x=0.5. We delineate the
mechanisms responsible for each one of the above features. We show that the
radial-strain relaxation through bond stretching is responsible for the overall
trend of linear dependence of the lattice constant on the composition. On the
other hand, the negative deviation from Vegard's law is shown to arise from the
angular-strain relaxation.Comment: 21 pages, 7 figure
Pedestrian Traffic: on the Quickest Path
When a large group of pedestrians moves around a corner, most pedestrians do
not follow the shortest path, which is to stay as close as possible to the
inner wall, but try to minimize the travel time. For this they accept to move
on a longer path with some distance to the corner, to avoid large densities and
by this succeed in maintaining a comparatively high speed. In many models of
pedestrian dynamics the basic rule of motion is often either "move as far as
possible toward the destination" or - reformulated - "of all coordinates
accessible in this time step move to the one with the smallest distance to the
destination". Atop of this rule modifications are placed to make the motion
more realistic. These modifications usually focus on local behavior and neglect
long-ranged effects. Compared to real pedestrians this leads to agents in a
simulation valuing the shortest path a lot better than the quickest. So, in a
situation as the movement of a large crowd around a corner, one needs an
additional element in a model of pedestrian dynamics that makes the agents
deviate from the rule of the shortest path. In this work it is shown, how this
can be achieved by using a flood fill dynamic potential field method, where
during the filling process the value of a field cell is not increased by 1, but
by a larger value, if it is occupied by an agent. This idea may be an obvious
one, however, the tricky part - and therefore in a strict sense the
contribution of this work - is a) to minimize unrealistic artifacts, as naive
flood fill metrics deviate considerably from the Euclidean metric and in this
respect yield large errors, b) do this with limited computational effort, and
c) keep agents' movement at very low densities unaltered
Sturm-Liouville operators with measure-valued coefficients
We give a comprehensive treatment of Sturm-Liouville operators with
measure-valued coefficients including, a full discussion of self-adjoint
extensions and boundary conditions, resolvents, and Weyl-Titchmarsh theory. We
avoid previous technical restrictions and, at the same time, extend all results
to a larger class of operators. Our operators include classical Sturm-Liouville
operators, Lax operators arising in the treatment of the Camassa-Holm equation,
Jacobi operators, and Sturm-Liouville operators on time scales as special
cases.Comment: 58 page
Mathematical surprises and Dirac's formalism in quantum mechanics
By a series of simple examples, we illustrate how the lack of mathematical
concern can readily lead to surprising mathematical contradictions in wave
mechanics. The basic mathematical notions allowing for a precise formulation of
the theory are then summarized and it is shown how they lead to an elucidation
and deeper understanding of the aforementioned problems. After stressing the
equivalence between wave mechanics and the other formulations of quantum
mechanics, i.e. matrix mechanics and Dirac's abstract Hilbert space
formulation, we devote the second part of our paper to the latter approach: we
discuss the problems and shortcomings of this formalism as well as those of the
bra and ket notation introduced by Dirac in this context. In conclusion, we
indicate how all of these problems can be solved or at least avoided.Comment: Largely extended and reorganized version, with new title and abstract
and with 2 figures added (published version), 54 page
The Role of Mobile Phones in Governance-Driven Technology Exports in Sub-Saharan Africa
This study assesses how the mobile phone influences governance to improve information and communication technology (ICT) exports in Sub-Saharan Africa with data from 2000-2012. The empirical evidence is based on Generalised Method of Moments and three main governance concepts are used, namely: (i) institutional (comprising the rule of law and corruption-control); (ii) political (involving political stability/no violence and voice & accountability) and (iii) economic (including regulation quality and government effectiveness) governance. The following findings are established. First, there are positive net effects on ICT goods exports from independent interactions between mobile phones and ‘political stability’ ‘voice and accountability’ and corruption-control. Second, significant net effects are not apparent from independent interactions between mobile phones and government effectiveness, regulation quality and the rule of law. Theoretical and practical implications are discussed
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