630 research outputs found
Explicit determination of a 727-dimensional root space of the hyperbolic Lie algebra
The 727-dimensional root space associated with the level-2 root \bLambda_1
of the hyperbolic Kac--Moody algebra is determined using a recently
developed string theoretic approach to hyperbolic algebras. The explicit form
of the basis reveals a complicated structure with transversal as well as
longitudinal string states present.Comment: 12 pages, LaTeX 2
On the fundamental representation of Borcherds algebras with one imaginary simple root
Borcherds algebras represent a new class of Lie algebras which have almost
all the properties that ordinary Kac-Moody algebras have, and the only major
difference is that these generalized Kac-Moody algebras are allowed to have
imaginary simple roots. The simplest nontrivial examples one can think of are
those where one adds ``by hand'' one imaginary simple root to an ordinary
Kac-Moody algebra. We study the fundamental representation of this class of
examples and prove that an irreducible module is given by the full tensor
algebra over some integrable highest weight module of the underlying Kac-Moody
algebra. We also comment on possible realizations of these Lie algebras in
physics as symmetry algebras in quantum field theory.Comment: 8 page
Precision spectroscopy by photon-recoil signal amplification
Precision spectroscopy of atomic and molecular ions offers a window to new
physics, but is typically limited to species with a cycling transition for
laser cooling and detection. Quantum logic spectroscopy has overcome this
limitation for species with long-lived excited states. Here, we extend quantum
logic spectroscopy to fast, dipole-allowed transitions and apply it to perform
an absolute frequency measurement. We detect the absorption of photons by the
spectroscopically investigated ion through the photon recoil imparted on a
co-trapped ion of a different species, on which we can perform efficient
quantum logic detection techniques. This amplifies the recoil signal from a few
absorbed photons to thousands of fluorescence photons. We resolve the line
center of a dipole-allowed transition in 40Ca+ to 1/300 of its observed
linewidth, rendering this measurement one of the most accurate of a broad
transition. The simplicity and versatility of this approach enables
spectroscopy of many previously inaccessible species.Comment: 25 pages, 6 figures, 1 table, updated supplementary information,
fixed typo
Computing Tropical Varieties
The tropical variety of a -dimensional prime ideal in a polynomial ring
with complex coefficients is a pure -dimensional polyhedral fan. This fan is
shown to be connected in codimension one. We present algorithmic tools for
computing the tropical variety, and we discuss our implementation of these
tools in the Gr\"obner fan software \texttt{Gfan}. Every ideal is shown to have
a finite tropical basis, and a sharp lower bound is given for the size of a
tropical basis for an ideal of linear forms.Comment: 22 pages, 2 figure
Six topics on inscribable polytopes
Inscribability of polytopes is a classic subject but also a lively research
area nowadays. We illustrate this with a selection of well-known results and
recent developments on six particular topics related to inscribable polytopes.
Along the way we collect a list of (new and old) open questions.Comment: 11 page
The Quest for Light Sea Quarks: Algorithms for the Future
As part of a systematic algorithm study, we present first results on a
performance comparison between a multibosonic algorithm and the hybrid Monte
Carlo algorithm as employed by the SESAM collaboration. The standard Wilson
fermion action is used on 32*16^3 lattices at beta=5.5.Comment: LaTeX, 3 pages, Lattice2001(algorithms
Realizability of Polytopes as a Low Rank Matrix Completion Problem
This article gives necessary and sufficient conditions for a relation to be
the containment relation between the facets and vertices of a polytope. Also
given here, are a set of matrices parameterizing the linear moduli space and
another set parameterizing the projective moduli space of a combinatorial
polytope
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Anelastic-like nature of the rejuvenation of metallic glasses by cryogenic thermal cycling
Cryogenic thermal cycling (CTC) is an effective treatment for improving the room-temperature plasticity and toughness in metallic glasses. Despite considerable attention to characterizing the effects of CTC, they remain poorly understood. A prominent example is that, contrary to expectation, the stored energy in a metallic glass first rises, and then decreases, as CTC progresses. In this work, CTC is applied to bulk metallic glasses based on Pd, Pt, Ti, or Zr. The effects on calorimetric and mechanical properties are evaluated. Critically, CTC-induced effects, at whatever stage, are found to decay over about one week at room temperature after CTC, returning the properties to those of the as-cast glass. A model is proposed for CTC-induced effects, treating them as analogous to the accumulation of anelastic strain. The implications for analysis of existing data, and for future research on CTC effects, are highlighted
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