10,941 research outputs found
Infinitesimal 2-braidings and differential crossed modules
We categorify the notion of an infinitesimal braiding in a linear strict
symmetric monoidal category, leading to the notion of a (strict) infinitesimal
2-braiding in a linear symmetric strict monoidal 2-category. We describe the
associated categorification of the 4-term relation, leading to six categorified
relations. We prove that any infinitesimal 2-braiding gives rise to a flat and
fake flat 2-connection in the configuration space of particles in the
complex plane, hence to a categorification of the Knizhnik-Zamolodchikov
connection. We discuss infinitesimal 2-braidings in a 2-category naturally
assigned to every differential crossed module, leading to the notion of a
quasi-invariant tensor in a differential crossed module. Finally we prove that
quasi-invariant tensors exist in the differential crossed module associated to
the String Lie-2-algebra.Comment: v3 - the introduction has been expanded, overall improvements in the
presentation. Final version, to appear in Adv. Mat
Categorifying the Knizhnik-Zamolodchikov Connection via an Infinitesimal 2-Yang-Baxter Operator in the String Lie-2-Algebra
We construct a flat (and fake-flat) 2-connection in the configuration space
of indistinguishable particles in the complex plane, which categorifies the
-Knizhnik-Zamolodchikov connection obtained from the adjoint
representation of . This will be done by considering the adjoint
categorical representation of the string Lie 2-algebra and the notion of an
infinitesimal 2-Yang-Baxter operator in a differential crossed module.
Specifically, we find an infinitesimal 2-Yang-Baxter operator in the string Lie
2-algebra, proving that any (strict) categorical representation of the string
Lie-2-algebra, in a chain-complex of vector spaces, yields a flat and (fake
flat) 2-connection in the configuration space, categorifying the
-Knizhnik-Zamolodchikov connection. We will give very detailed
explanation of all concepts involved, in particular discussing the relevant
theory of 2-connections and their two dimensional holonomy, in the specific
case of 2-groups derived from chain complexes of vector spaces.Comment: The main result was considerably sharpened. Title, abstract and
introduction updated. 50 page
Currents and pseudomagnetic fields in strained graphene rings
We study the effects of strain on the electronic properties and persistent
current characteristics of a graphene ring using the Dirac representation. For
a slightly deformed graphene ring flake, one obtains sizable pseudomagnetic
(gauge) fields that may effectively reduce or enhance locally the applied
magnetic flux through the ring. Flux-induced persistent currents in a flat ring
have full rotational symmetry throughout the structure; in contrast, we show
that currents in the presence of a circularly symmetric deformation are
strongly inhomogeneous, due to the underlying symmetries of graphene. This
result illustrates the inherent competition between the `real' magnetic field
and the `pseudo' field arising from strains, and suggest an alternative way to
probe the strength and symmetries of pseudomagnetic fields on graphene systems
Categorical Groups, Knots and Knotted Surfaces
We define a knot invariant and a 2-knot invariant from any finite categorical
group. We calculate an explicit example for the Spun Trefoil.Comment: 40 pages, lots of figures. Second version: Added example and
discussion, clarification of the fact that the maps associated with
Reidemeister Moves are well define
GOVERNMENT REVENUES AND EXPENDITURES IN GUINEA-BISSAU: CAUSALITY AND COINTEGRATION
The paper establishes empirically the temporal causality and long run relationship between government expenditures and government revenues for the case of Guinea-Bissau - a low income country under stress (LICUS) in Africa. A macroeconomic model is developed to lay out the hypothesis of a spend-tax behavior in the country¡¯s public finances management system. Empirical validation is carried out by means of a traditional Granger-causality test and the estimation of an error correction model between expenditures and revenues.Public Finances, Causality Tests, Cointegration Analysis
Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules
The relation between high-harmonic spectra and the geometry of the molecular
orbitals in position and momentum space is investigated. In particular we
choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such
that the highest occupied molecular orbital of the former exhibit at least one
nodal plane. The imprint of such planes is a strong suppression in the harmonic
spectra, for particular alignment angles. We are able to identify two distinct
types of nodal planes. If the nodal planes are determined by the atomic
wavefunctions only, the angle for which the yield is suppressed will remain the
same for both types of molecules. In contrast, if they are determined by the
linear combination of atomic orbitals at different centers in the molecule,
there will be a shift in the angle at which the suppression occurs for the
heteronuclear molecules, with regard to their homonuclear counterpart. This
shows that, in principle, molecular imaging, which uses the homonuclear
molecule as a reference and enables one to observe the wavefunction distortions
in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order
to comply with the arXiv size requirement
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