708,554 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
Product formulas in the framework of mean ergodic theorems
An extension of Chernoff's product formula for one-parameter functions taking
values in the space of bounded linear operators on a Banach space is given.
Essentially, the -th one-parameter function in the product formula is mapped
by the -th iterate of a contraction acting on the space of the one-parameter
functions. The motivation to study this specific product formula lies in the
growing field of dynamical control of quantum systems, involving the procedure
of dynamical decoupling and also the Quantum Zeno effect.Comment: 10 page
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