713,170 research outputs found
The Cohomology of Transitive Lie Algebroids
For a transitive Lie algebroid A on a connected manifold M and its a
representation on a vector bundle F, we study the localization map Y^1:
H^1(A,F)-> H^1(L_x,F_x), where L_x is the adjoint algebra at x in M. The main
result in this paper is that: Ker Y^1_x=Ker(p^{1*})=H^1_{deR}(M,F_0). Here
p^{1*} is the lift of H^1(\huaA,F) to its counterpart over the universal
covering space of M and H^1_{deR}(M,F_0) is the F_0=H^0(L,F)-coefficient deRham
cohomology. We apply these results to study the associated vector bundles to
principal fiber bundles and the structure of transitive Lie bialgebroids.Comment: 17pages, no figure
Floquet spin states in graphene under ac driven spin-orbit interaction
We study the role of periodically driven time-dependent Rashba spin-orbit
coupling (RSOC) on a monolayer graphene sample. After recasting the originally
system of dynamical equations as two time-reversal related
two-level problems, the quasi-energy spectrum and the related dynamics are
investigated via various techniques and approximations. In the static case the
system is a gapped at the Dirac point. The rotating wave approximation (RWA)
applied to the driven system unphysically preserves this feature, while the
Magnus-Floquet approach as well as a numerically exact evaluation of the
Floquet equation show that this gap is dynamically closed. In addition, a
sizable oscillating pattern of the out-of-plane spin polarization is found in
the driven case for states which completely unpolarized in the static limit.
Evaluation of the autocorrelation function shows that the original uniform
interference pattern corresponding to time-independent RSOC gets distorted. The
resulting structure can be qualitatively explained as a consequence of the
transitions induced by the ac driving among the static eigenstates, i.e., these
transitions modulate the relative phases that add up to give the quantum
revivals of the autocorrelation function. Contrary to the static case, in the
driven scenario, quantum revivals (suppresions) are correlated to spin up
(down) phases.Comment: 10 pages, 8 figures. Typos corrected. Accepted for publication in PR
Hybrid quantum repeater based on resonant qubit-field interactions
We propose a hybrid quantum repeater based on ancillary coherent field states
and material qubits coupled to optical cavities. For this purpose, resonant
qubit-field interactions and postselective field measurements are determined
which are capable of realizing all necessary two-qubit operations for the
actuation of the quantum repeater. We explore both theoretical and experimental
possibilities of generating near-maximally-entangled qubit pairs ()
over long distances. It is shown that our scheme displays moderately low
repeater rates, between and pairs per second, over
distances up to km, and it relies completely on current technology of
cavity quantum electrodynamics.Comment: 18 pages, 13 figures, corrected according to published Erratu
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