scholarly journals On the holonomic equivalence of two curves

2016 ◽  
Vol 27 (06) ◽  
pp. 1650055
Author(s):  
Tamer Tlas
Keyword(s):  
Parallel Transport ◽  
Smooth Connection

Given a principal [Formula: see text]-bundle [Formula: see text] and two [Formula: see text] curves in [Formula: see text] with coinciding endpoints, we say that the two curves are holonomically equivalent if the parallel transport along them is identical for any smooth connection on [Formula: see text]. The main result in this paper is that if [Formula: see text] is semi-simple, then the two curves are holonomically equivalent if and only if there is a thin, i.e. of rank at most one, [Formula: see text] homotopy linking them. Additionally, it is also demonstrated that this is equivalent to the factorizability through a tree of the loop formed from the two curves and to the reducibility of a certain transfinite word associated to this loop. The curves are not assumed to be regular.

Electronic Transport Properties of a-Si:H,F/a-Si,Ge:H,F Superlattices

1987 ◽  
Vol 95 ◽  
Author(s):  
J. P. Conde ◽  
S. Aljishi ◽  
D. S. Shen ◽  
V. Chu ◽  
Z E. Smith ◽  
...  
Keyword(s):  
Barrier Layer ◽  
Electronic Transport ◽  
Thermal Emission ◽  
Parallel Transport ◽  
Dark Conductivity ◽  
Alloy Layer ◽  
Conductivity Activation Energy ◽  
Superlattice Structures ◽  
Deposition Conditions ◽  
Extract Information

AbstractWe study the dark conductivity σd, dark conductivity activation energy Ea and photoconductivity σph of a-Si:H,F/a-Si,Ge:H,F superlattices both perpendicular and parallel to the plane of the layers. In parallel transport, both the σph and σd are dominated by the alloy layer characteristics with the superposition of carrier confinement quantum effects. In perpendicular transport, the σd shows an interplay of quantum mechanical tunneling through the barriers and of classical thermal emission over the barrier layer and the σph is controlled by the decreasing absorption by the silicon barrier layer as the optical gap Eopt of the structure decreases.We also found that the multilayer structure allows to grow lower gap a-Si,Ge:H,F alloys than achievable under the same deposition conditions for bulk materials. This stabilizing effect allowed us to study low-gap superlattice structures and extract information about these very low gap (<1.2 eV) a- Si,Ge:H,F alloys.

CIRCULAR ORBITS AROUND SCHWARZSCHILD–AdS SPACETIME

2004 ◽  
Vol 19 (36) ◽  
pp. 2683-2695 ◽  
Author(s):  
A. M. DE M. CARVALHO ◽  
CLAUDIO FURTADO ◽  
FERNANDO MORAES
Keyword(s):  
Band Structure ◽  
Parallel Transport ◽  
Circular Orbits ◽  
Global Properties ◽  
Ads Spacetime

In this paper we discuss parallel transport of vectors and spinors around circular orbits in Schwarzschild–AdS spacetime. We study the global properties of this spacetime via loop variables or holonomy. A set of paths in this background is considered. We demonstrate that for some special radii there appears the so-called quantized band structure of holonomy invariance. This analysis is also extended to parallel transport of a spinor in this spacetime.

LOCALIZATION OF MATTERS ON A NON-Z2-SYMMETRIC THICK BRANE

2010 ◽  
Vol 25 (07) ◽  
pp. 511-523
Author(s):  
JUN LIANG ◽  
YI-SHI DUAN
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Yukawa Coupling ◽  
Spinor Field ◽  
Zero Mode ◽  
Parallel Transport ◽  
Type Coupling ◽  
Matter Fields

We study localization of various matter fields on a non-Z2-symmetric scalar thick brane in a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. It is shown that, for spin 0 scalar field, the massless zero mode can be normalized on the brane. Spin 1 vector field cannot be normalized on the brane. And there is no spinor field which can be trapped on the brane for the case of no Yukawa-type coupling. By introducing the appropriate Yukawa coupling, the left or right chiral fermionic zero mode can be localized on the brane.

scholarly journals Generic Dynamical Properties of Connections on Vector Bundles

2021 ◽  
Author(s):  
Mihajlo Cekić ◽  
Thibault Lefeuvre
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Differential Operators ◽  
Parallel Transport ◽  
Conformal Killing ◽  
Generic Properties ◽  
Geometric Problems ◽  
Pseudo Differential Operators ◽  
Divergence Type ◽  
Open Question

Abstract Given a smooth Hermitian vector bundle $\mathcal{E}$ over a closed Riemannian manifold $(M,g)$, we study generic properties of unitary connections $\nabla ^{\mathcal{E}}$ on the vector bundle $\mathcal{E}$. First of all, we show that twisted conformal Killing tensors (CKTs) are generically trivial when $\dim (M) \geq 3$, answering an open question of Guillarmou–Paternain–Salo–Uhlmann [ 14]. In negative curvature, it is known that the existence of twisted CKTs is the only obstruction to solving exactly the twisted cohomological equations, which may appear in various geometric problems such as the study of transparent connections. The main result of this paper says that these equations can be generically solved. As a by-product, we also obtain that the induced connection $\nabla ^{\textrm{End}({\operatorname{{\mathcal{E}}}})}$ on the endomorphism bundle $\textrm{End}({\operatorname{{\mathcal{E}}}})$ has generically trivial CKTs as long as $(M,g)$ has no nontrivial CKTs on its trivial line bundle. Eventually, we show that, under the additional assumption that $(M,g)$ is Anosov (i.e., the geodesic flow is Anosov on the unit tangent bundle), the connections are generically opaque, namely that generically there are no non-trivial subbundles of $\mathcal{E}$ that are preserved by parallel transport along geodesics. The proofs rely on the introduction of a new microlocal property for (pseudo)differential operators called operators of uniform divergence type, and on perturbative arguments from spectral theory (especially on the theory of Pollicott–Ruelle resonances in the Anosov case).

Parallel Transport and Thomas-Wigner Rotation

2009 ◽  
Vol 116 (5) ◽  
pp. 439-446
Author(s):  
Nieves Alamo ◽  
Carlos Criado
Keyword(s):  
Parallel Transport ◽  
Wigner Rotation
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