76,490 research outputs found
Spin tunneling in magnetic molecules: Quantitative estimates for Fe8 clusters
Spin tunneling in the particular case of the magnetic molecular cluster
octanuclear iron(III), Fe8, is treated by an effective Hamiltonian that allows
for an angle-based description of the process. The presence of an external
magnetic field along the easy axis is also taken into account in this
description. Analytic expressions for the energy levels and barriers are
obtained from a harmonic approximation of the potential function which give
results in good agreement with the experimental results. The energy splittings
due to spin tunneling is treated in an adapted WKB approach and it is shown
that the present description can give results to a reliable degree of accuracy.Comment: 17 pages, 2 figures, preprint submitted to Physica
Interpolation of bilinear operators and compactness
The behavior of bilinear operators acting on interpolation of Banach spaces
for the method in relation to the compactness is analyzed. Similar
results of Lions-Peetre, Hayakawa and Person's compactness theorems are
obtained for the bilinear case and the method.Comment: This work was published at "Nonlinear Analysis: Theory, Methods and
Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some
gaps in the original proof of Theorem 4.3, Here we give a new proof. For
this, we change the Lemma 4.
A proof of the conjecture of Cohen and Mullen on sums of primitive roots
We prove that for all , every non-zero element in the finite field
can be written as a linear combination of two primitive roots
of . This resolves a conjecture posed by Cohen and Mullen.Comment: 8 pages; to appear in Mathematics of Computatio
On Grosswald's conjecture on primitive roots
Grosswald's conjecture is that , the least primitive root modulo ,
satisfies for all . We make progress towards
this conjecture by proving that for all and for all .Comment: 7 page
On consecutive primitive elements in a finite field
For an odd prime power with we prove that there are always three
consecutive primitive elements in the finite field . Indeed,
there are precisely eleven values of for which this is false. For
we present conjectures on the size of such that
guarantees the existence of consecutive primitive elements in
, provided that has characteristic at
least~. Finally, we improve the upper bound on for all .Comment: 10 pages, 2 table
The Jacobi identity for Dirac-like brackets
For redundant second-class constraints the Dirac brackets cannot be defined
and new brackets must be introduced. We prove here that the Jacobi identity for
the new brackets must hold on the surface of the second-class constraints. In
order to illustrate our proof we work out explicitly the cases of a fractional
spin particle in 2+1 dimensions and the original Brink-Schwarz massless
superparticle in D=10 dimensions in a Lorentz covariant constraints separation.Comment: 14 pages, Latex. Final version to be published in Int. J. Mod. Phys.
Oxygen clamps in gold nanowires
We investigate how the insertion of an oxygen atom in an atomically thin gold
nanowire can affect its rupture. We find, using ab initio total energy density
functional theory calculations, that O atoms when inserted in gold nanowires
form not only stable but also very strong bonds, in such a way that they can
extract atoms from a stable tip, serving in this way as a clamp that could be
used to pull a string of gold atoms.Comment: 4 pages; 4 figure
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