8,113 research outputs found
Hawking Radiation and Analogue Experiments: A Bayesian Analysis
We present a Bayesian analysis of the epistemology of analogue experiments
with particular reference to Hawking radiation. First, we prove that such
experiments can be confirmatory in Bayesian terms based upon appeal to
'universality arguments'. Second, we provide a formal model for the scaling
behaviour of the confirmation measure for multiple distinct realisations of the
analogue system and isolate a generic saturation feature. Finally, we
demonstrate that different potential analogue realisations could provide
different levels of confirmation. Our results provide a basis both to formalise
the epistemic value of analogue experiments that have been conducted and to
advise scientists as to the respective epistemic value of future analogue
experiments.Comment: 25 pages, 5 figure
Anomalous diffusion and elastic mean free path in disorder-free multi-walled carbon nanotubes
We explore the nature of anomalous diffusion of wave packets in disorder-free
incommensurate multi-walled carbon nanotubes. The spectrum-averaged diffusion
exponent is obtained by calculating the multifractal dimension of the energy
spectrum. Depending on the shell chirality, the exponent is found to lie within
the range . For large unit cell mismatch between
incommensurate shells, approaches the value 1/2 for diffusive motion.
The energy-dependent quantum spreading reveals a complex
density-of-states-dependent pattern with ballistic, super-diffusive or
diffusive character.Comment: 4 pages, 4 figure
Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
We will present a new extension of the standard model of particle physics in
its almostcommutative formulation. This extension has as its basis the algebra
of the standard model with four summands [11], and enlarges only the particle
content by an arbitrary number of generations of left-right symmetric doublets
which couple vectorially to the U(1)_YxSU(2)_w subgroup of the standard model.
As in the model presented in [8], which introduced particles with a new colour,
grand unification is no longer required by the spectral action. The new model
may also possess a candidate for dark matter in the hundred TeV mass range with
neutrino-like cross section
Almost-Commutative Geometries Beyond the Standard Model II: New Colours
We will present an extension of the standard model of particle physics in its
almost-commutative formulation. This extension is guided by the minimal
approach to almost-commutative geometries employed in [13], although the model
presented here is not minimal itself.
The corresponding almost-commutative geometry leads to a Yang-Mills-Higgs
model which consists of the standard model and two new fermions of opposite
electro-magnetic charge which may possess a new colour like gauge group. As a
new phenomenon, grand unification is no longer required by the spectral action.Comment: Revised version for publication in J.Phys.A with corrected Higgs
masse
IST Austria Thesis
The first part of the thesis considers the computational aspects of the homotopy groups πd(X) of a topological space X. It is well known that there is no algorithm to decide whether the fundamental group π1(X) of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with π1(X) trivial), compute the higher homotopy group πd(X) for any given d ≥ 2.
However, these algorithms come with a caveat: They compute the isomorphism type of πd(X), d ≥ 2 as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of πd(X). We present an algorithm that, given a simply connected space X, computes πd(X) and represents its elements as simplicial maps from suitable triangulations of the d-sphere Sd to X. For fixed d, the algorithm runs in time exponential in size(X), the number of simplices of X. Moreover, we prove that this is optimal: For every fixed d ≥ 2,
we construct a family of simply connected spaces X such that for any simplicial map representing a generator of πd(X), the size of the triangulation of S d on which the map is defined, is exponential in size(X).
In the second part of the thesis, we prove that the following question is algorithmically undecidable for d < ⌊3(k+1)/2⌋, k ≥ 5 and (k, d) ̸= (5, 7), which covers essentially everything outside the meta-stable range: Given a finite simplicial complex K of dimension k, decide whether there exists a piecewise-linear (i.e., linear on an arbitrarily fine subdivision of K) embedding f : K ↪→ Rd of K into a d-dimensional Euclidean space
From brain to earth and climate systems: Small-world interaction networks or not?
We consider recent reports on small-world topologies of interaction networks
derived from the dynamics of spatially extended systems that are investigated
in diverse scientific fields such as neurosciences, geophysics, or meteorology.
With numerical simulations that mimic typical experimental situations we have
identified an important constraint when characterizing such networks:
indications of a small-world topology can be expected solely due to the spatial
sampling of the system along with commonly used time series analysis based
approaches to network characterization
Schwinger model on a half-line
We study the Schwinger model on a half-line in this paper. In particular, we
investigate the behavior of the chiral condensate near the edge of the line.
The effect of the chosen boundary condition is emphasized. The extension to the
finite temperature case is straightforward in our approach.Comment: 4 pages, no figure. Final version to be published on Phys. Rev.
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