798 research outputs found
Primitive geodesic lengths and (almost) arithmetic progressions
In this article, we investigate when the set of primitive geodesic lengths on
a Riemannian manifold have arbitrarily long arithmetic progressions. We prove
that in the space of negatively curved metrics, a metric having such arithmetic
progressions is quite rare. We introduce almost arithmetic progressions, a
coarsification of arithmetic progressions, and prove that every negatively
curved, closed Riemannian manifold has arbitrarily long almost arithmetic
progressions in its primitive length spectrum. Concerning genuine arithmetic
progressions, we prove that every non-compact, locally symmetric, arithmetic
manifold has arbitrarily long arithmetic progressions in its primitive length
spectrum. We end with a conjectural characterization of arithmeticity in terms
of arithmetic progressions in the primitive length spectrum. We also suggest an
approach to a well known spectral rigidity problem based on the scarcity of
manifolds with arithmetic progressions.Comment: v3: 23 pages. To appear in Publ. Ma
Applying quantitative semantics to higher-order quantum computing
Finding a denotational semantics for higher order quantum computation is a
long-standing problem in the semantics of quantum programming languages. Most
past approaches to this problem fell short in one way or another, either
limiting the language to an unusably small finitary fragment, or giving up
important features of quantum physics such as entanglement. In this paper, we
propose a denotational semantics for a quantum lambda calculus with recursion
and an infinite data type, using constructions from quantitative semantics of
linear logic
Quantum Hall resistance standards from graphene grown by chemical vapor deposition on silicon carbide
Replacing GaAs by graphene to realize more practical quantum Hall resistance
standards (QHRS), accurate to within in relative value, but operating
at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date,
the required accuracy has been reported, only few times, in graphene grown on
SiC by sublimation of Si, under higher magnetic fields. Here, we report on a
device made of graphene grown by chemical vapour deposition on SiC which
demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4
K. This is explained by a quantum Hall effect with low dissipation, resulting
from strongly localized bulk states at the magnetic length scale, over a wide
magnetic field range. Our results show that graphene-based QHRS can replace
their GaAs counterparts by operating in as-convenient cryomagnetic conditions,
but over an extended magnetic field range. They rely on a promising hybrid and
scalable growth method and a fabrication process achieving low-electron density
devices.Comment: 12 pages, 8 figure
Microstructural Characterization of Graphite Spheroids in Ductile Iron
The present work brings new insights by transmission electron microscopy allowing disregarding or supporting some of the models proposed for spheroidal growth of graphite in cast irons. Nodules consist of sectors made of graphite plates elongated along a hai direction and stack on each other with their c axis aligned with the radial direction. These plates are the elementary units for spheroidal growth and a calculation supports the idea that new units continuously nucleate at the ledge between sectors
Generalised Compositional Theories and Diagrammatic Reasoning
This chapter provides an introduction to the use of diagrammatic language, or
perhaps more accurately, diagrammatic calculus, in quantum information and
quantum foundations. We illustrate the use of diagrammatic calculus in one
particular case, namely the study of complementarity and non-locality, two
fundamental concepts of quantum theory whose relationship we explore in later
part of this chapter.
The diagrammatic calculus that we are concerned with here is not merely an
illustrative tool, but it has both (i) a conceptual physical backbone, which
allows it to act as a foundation for diverse physical theories, and (ii) a
genuine mathematical underpinning, permitting one to relate it to standard
mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G.
Chirabella, R. Spekken
Metric trees of generalized roundness one
Every finite metric tree has generalized roundness strictly greater than one.
On the other hand, some countable metric trees have generalized roundness
precisely one. The purpose of this paper is to identify some large classes of
countable metric trees that have generalized roundness precisely one.
At the outset we consider spherically symmetric trees endowed with the usual
combinatorial metric (SSTs). Using a simple geometric argument we show how to
determine decent upper bounds on the generalized roundness of finite SSTs that
depend only on the downward degree sequence of the tree in question. By
considering limits it follows that if the downward degree sequence of a SST satisfies , then has generalized roundness one. Included among the
trees that satisfy this condition are all complete -ary trees of depth
(), all -regular trees () and inductive limits
of Cantor trees.
The remainder of the paper deals with two classes of countable metric trees
of generalized roundness one whose members are not, in general, spherically
symmetric. The first such class of trees are merely required to spread out at a
sufficient rate (with a restriction on the number of leaves) and the second
such class of trees resemble infinite combs.Comment: 14 pages, 2 figures, 2 table
A Submillimeter HCN Laser in IRC+10216
We report the detection of a strong submillimeter wavelength HCN laser line
at a frequency near 805 GHz toward the carbon star IRC+10216. This line, the
J=9-8 rotational transition within the (04(0)0) vibrationally excited state, is
one of a series of HCN laser lines that were first detected in the laboratory
in the early days of laser spectroscopy. Since its lower energy level is 4200 K
above the ground state, the laser emission must arise from the inner part of
IRC+10216's circumstellar envelope. To better characterize this environment, we
observed other, thermally emitting, vibrationally excited HCN lines and find
that they, like the laser line, arise in a region of temperature approximately
1000 K that is located within the dust formation radius; this conclusion is
supported by the linewidth of the laser. The (04(0)0), J=9-8 laser might be
chemically pumped and may be the only known laser (or maser) that is excited
both in the laboratory and in space by a similar mechanism.Comment: 11 pages, 3 figure
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