564 research outputs found
Modal Logics of Topological Relations
Logical formalisms for reasoning about relations between spatial regions play
a fundamental role in geographical information systems, spatial and constraint
databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's
modal logic of time intervals based on the Allen relations, we introduce a
family of modal logics equipped with eight modal operators that are interpreted
by the Egenhofer-Franzosa (or RCC8) relations between regions in topological
spaces such as the real plane. We investigate the expressive power and
computational complexity of logics obtained in this way. It turns out that our
modal logics have the same expressive power as the two-variable fragment of
first-order logic, but are exponentially less succinct. The complexity ranges
from (undecidable and) recursively enumerable to highly undecidable, where the
recursively enumerable logics are obtained by considering substructures of
structures induced by topological spaces. As our undecidability results also
capture logics based on the real line, they improve upon undecidability results
for interval temporal logics by Halpern and Shoham. We also analyze modal
logics based on the five RCC5 relations, with similar results regarding the
expressive power, but weaker results regarding the complexity
Andreev-Tunneling, Coulomb Blockade, and Resonant Transport of Non-Local Spin-Entangled Electrons
We propose and analyze a spin-entangler for electrons based on an s-wave
superconductor coupled to two quantum dots each of which is tunnel-coupled to
normal Fermi leads. We show that in the presence of a voltage bias and in the
Coulomb blockade regime two correlated electrons provided by the Andreev
process can coherently tunnel from the superconductor via different dots into
different leads. The spin-singlet coming from the Cooper pair remains preserved
in this process, and the setup provides a source of mobile and nonlocal
spin-entangled electrons. The transport current is calculated and shown to be
dominated by a two-particle Breit-Wigner resonance which allows the injection
of two spin-entangled electrons into different leads at exactly the same
orbital energy, which is a crucial requirement for the detection of spin
entanglement via noise measurements. The coherent tunneling of both electrons
into the same lead is suppressed by the on-site Coulomb repulsion and/or the
superconducting gap, while the tunneling into different leads is suppressed
through the initial separation of the tunneling electrons. In the regime of
interest the particle-hole excitations of the leads are shown to be negligible.
The Aharonov-Bohm oscillations in the current are shown to contain single- and
two-electron periods with amplitudes that both vanish with increasing Coulomb
repulsion albeit differently fast.Comment: 11 double-column pages, 2 figures, REVTeX, minor revision
Lorentz and CPT tests with spin-polarized solids
Experiments using macroscopic samples of spin-polarized matter offer
exceptional sensitivity to Lorentz and CPT violation in the electron sector.
Data from existing experiments with a spin-polarized torsion pendulum provide
sensitivity in this sector rivaling that of all other existing experiments and
could reveal spontaneous violation of Lorentz symmetry at the Planck scale.Comment: 4 pages, accepted for publication in Physical Review Letter
Influence of the in-medium pion dispersion relation in heavy ion collisions
We investigate the influence of medium corrections to the pion dispersion
relation on the pion dynamics in intermediate energy heavy ion collisions. To
do so a pion potential is extracted from the in-medium dispersion relation and
used in QMD calculations and thus we take care of both, real and imaginary part
of the pion optical potential. The potentials are determined from different
sources, i.e. from the --hole model and from phenomenological
approaches. Depending on the strength of the potential a reduction of the
anti-correlation of pion and nucleon flow in non-central collisions is observed
as well as an enhancement of the high energetic yield in transverse pion
spectra. A comparison to experiments, in particular to -spectra for the
reaction Ca+Ca at 1 GeV/nucleon and the pion in-plane flow in Ne+Pb collisions
at 800 MeV/nucleon, generally favours a weak potential.Comment: 25 pages, using REVTeX, 6 postscript figures; replaced by published
versio
Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism
This essay examines the philosophical significance of -logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of -logical validity can then be countenanced within a coalgebraic logic, and -logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of -logical validity correspond to those of second-order logical consequence, -logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
van der Waals interaction in nanotube bundles : consequences on vibrational modes
We have developed a pair-potential approach for the evaluation of van der
Waals interaction between carbon nanotubes in bundles.
Starting from a continuum model, we show that the intertube modes range from
to . Using a non-orthogonal tight-binding approximation
for describing the covalent intra-tube bonding in addition, we confirme a
slight chiral dependance of the breathing mode frequency and we found that this
breathing mode frequency increase by 10 % if the nanotube lie inside a
bundle as compared to the isolated tube.Comment: 5 pages, 2 figure
Nonlinear surface waves in left-handed materials
We study both linear and nonlinear surface waves localized at the interface
separating a left-handed medium (i.e. the medium with both negative dielectric
permittivity and negative magnetic permeability) and a conventional (or
right-handed) dielectric medium. We demonstrate that the interface can support
both TE- and TM-polarized surface waves - surface polaritons, and we study
their properties. We describe the intensity-dependent properties of nonlinear
surface waves in three different cases, i.e. when both the LH and RH media are
nonlinear and when either of the media is nonlinear. In the case when both
media are nonlinear, we find two types of nonlinear surface waves, one with the
maximum amplitude at the interface, and the other one with two humps. In the
case when one medium is nonlinear, only one type of surface wave exists, which
has the maximum electric field at the interface, unlike waves in right-handed
materials where the surface-wave maximum is usually shifted into a
self-focussing nonlinear medium. We discus the possibility of tuning the wave
group velocity in both the linear and nonlinear cases, and show that
group-velocity dispersion, which leads to pulse broadening, can be balanced by
the nonlinearity of the media, so resulting in soliton propagation.Comment: 9 pages, 10 figure
Quantum systems in weak gravitational fields
Fully covariant wave equations predict the existence of a class of
inertial-gravitational effects that can be tested experimentally. In these
equations inertia and gravity appear as external classical fields, but, by
conforming to general relativity, provide very valuable information on how
Einstein's views carry through in the world of the quantum.Comment: 22 pages. To be published in Proceedings of the 17th Course of the
International School of Cosmology and Gravitation "Advances in the interplay
between quantum and gravity physics" edited by V. De Sabbata and A.
Zheltukhin, Kluwer Academic Publishers, Dordrech
Measurement of mechanical vibrations excited in aluminium resonators by 0.6 GeV electrons
We present measurements of mechanical vibrations induced by 0.6 GeV electrons
impinging on cylindrical and spherical aluminium resonators. To monitor the
amplitude of the resonator's vibrational modes we used piezoelectric ceramic
sensors, calibrated by standard accelerometers. Calculations using the
thermo-acoustic conversion model, agree well with the experimental data, as
demonstrated by the specific variation of the excitation strengths with the
absorbed energy, and with the traversing particles' track positions. For the
first longitudinal mode of the cylindrical resonator we measured a conversion
factor of 7.4 +- 1.4 nm/J, confirming the model value of 10 nm/J. Also, for the
spherical resonator, we found the model values for the L=2 and L=1 mode
amplitudes to be consistent with our measurement. We thus have confirmed the
applicability of the model, and we note that calculations based on the model
have shown that next generation resonant mass gravitational wave detectors can
only be expected to reach their intended ultra high sensitivity if they will be
shielded by an appreciable amount of rock, where a veto detector can reduce the
background of remaining impinging cosmic rays effectively.Comment: Tex-Article with epsfile, 34 pages including 13 figures and 5 tables.
To be published in Rev. Scient. Instr., May 200
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