111,528 research outputs found
Deformation quantization of principal bundles
We outline how Drinfeld twist deformation techniques can be applied to the
deformation quantization of principal bundles into noncommutative principal
bundles, and more in general to the deformation of Hopf-Galois extensions.
First we twist deform the structure group in a quantum group, and this leads to
a deformation of the fibers of the principal bundle. Next we twist deform a
subgroup of the group of authomorphisms of the principal bundle, and this leads
to a noncommutative base space. Considering both deformations we obtain
noncommutative principal bundles with noncommutative fiber and base space as
well.Comment: 20 pages. Contribution to the volume in memory of Professor Mauro
Francaviglia. Based on joint work with Pierre Bieliavsky, Chiara Pagani and
Alexander Schenke
Thermal Fluctuations of Elastic Filaments with Spontaneous Curvature and Torsion
We study the effects of thermal flucutations on thin elastic filaments with
spontaneous curvature and torsion. We derive analytical expressions for the
orientational correlation functions and for the persistence length of helices,
and find that this length varies non-monotonically with the strength of thermal
fluctuations. In the weak fluctuation regime, the persistence length of a
spontaneously twisted helix has three resonance peaks as a function of the
twist rate. In the limit of strong fluctuations, all memory of the helical
shape is lost.Comment: 1 figur
Music History- Laugh and Learn
The project I have chosen aligns with my curriculum project and research. Data will be gathered on the effects of laughter in the classroom. This research will show that humor can motivate students as well as aide memory. Overall, the project should conclude that laughter aids in the learning process. This project has great importance in the field of education, especially music education. Students have come to memorize for the tests, soon forgetting what they have learned. Adding a fun twist on a class that will aide students in their first year of college may increase enrollment. This may also help teachers discover that within reason, laughter plays an important role in education
Renormalization of twist-four operators in light-cone gauge
We compute one-loop renormalization group equations for non-singlet
twist-four operators in QCD. The calculation heavily relies on the light-cone
gauge formalism in the momentum fraction space that essentially rephrases the
analysis of all two-to two and two-to-three transition kernels to purely
algebraic manipulations both for non- and quasipartonic operators. This is the
first brute force calculation of this sector available in the literature.
Fourier transforming our findings to the coordinate space, we checked them
against available results obtained within a conformal symmetry-based formalism
that bypasses explicit diagrammatic calculations and confirmed agreement with
the latter.Comment: 58 pages, 16 figures; dedicated to the memory of Eduard A. Kurae
Screw dislocations in the field theory of elastoplasticity
A (microscopic) static elastoplastic field theory of dislocations with moment
and force stresses is considered. The relationship between the moment stress
and the Nye tensor is used for the dislocation Lagrangian. We discuss the
stress field of an infinitely long screw dislocation in a cylinder, a dipole of
screw dislocations and a coaxial screw dislocation in a finite cylinder. The
stress fields have no singularities in the dislocation core and they are
modified in the core due to the presence of localized moment stress.
Additionally, we calculated the elastoplastic energies for the screw
dislocation in a cylinder and the coaxial screw dislocation. For the coaxial
screw dislocation we find a modified formula for the so-called Eshelby twist
which depends on a specific intrinsic material length.Comment: 19 pages, LaTeX, 2 figures, Extended version of a contribution to the
symposium on "Structured Media'' dedicated to the memory of Professor
Ekkehart Kr\"oner, 16-21 September 2001, Pozna\'n, Poland. to appear in
Annalen der Physik 11 (2002
Entanglement Scrambling in 2d Conformal Field Theory
We investigate how entanglement spreads in time-dependent states of a 1+1
dimensional conformal field theory (CFT). The results depend qualitatively on
the value of the central charge. In rational CFTs, which have central charge
below a critical value, entanglement entropy behaves as if correlations were
carried by free quasiparticles. This leads to long-term memory effects, such as
spikes in the mutual information of widely separated regions at late times.
When the central charge is above the critical value, the quasiparticle picture
fails. Assuming no extended symmetry algebra, any theory with has
diminished memory effects compared to the rational models. In holographic CFTs,
with , these memory effects are eliminated altogether at strong
coupling, but reappear after the scrambling time at
weak coupling.Comment: 52 pages, 7 figure; v2: references adde
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