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Thermal spin-transfer in Fe-MgO-Fe tunnel junctions
We compute thermal spin transfer torques (TST) in Fe-MgO-Fe tunnel junctions
using a first principles wave function-matching method. At room temperature,
the TST in a junction with 3 MgO monolayers amounts to 10^-7J/m^2/K, which is
estimated to cause magnetization reversal for temperature differences over the
barrier of the order of 10 K. The large TST can be explained by multiple
scattering between interface states through ultrathin barriers. The angular
dependence of the TST can be very skewed, possibly leading to thermally induced
high-frequency generation.Comment: 5 pages, 5 figure
Proof of a Conjecture of Hirschhorn and Sellers on Overpartitions
Let denote the number of overpartitions of . It was
conjectured by Hirschhorn and Sellers that \bar{p}(40n+35)\equiv 0\ ({\rm
mod\} 40) for . Employing 2-dissection formulas of quotients of theta
functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating
function for modulo 5. Using the -parametrization of
theta functions given by Alaca, Alaca and Williams, we give a proof of the
congruence \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 5). Combining this congruence
and the congruence \bar{p}(4n+3)\equiv 0\ ({\rm mod\} 8) obtained by
Hirschhorn and Sellers, and Fortin, Jacob and Mathieu, we give a proof of the
conjecture of Hirschhorn and Sellers.Comment: 11 page
The q-WZ Method for Infinite Series
Motivated by the telescoping proofs of two identities of Andrews and Warnaar,
we find that infinite q-shifted factorials can be incorporated into the
implementation of the q-Zeilberger algorithm in the approach of Chen, Hou and
Mu to prove nonterminating basic hypergeometric series identities. This
observation enables us to extend the q-WZ method to identities on infinite
series. As examples, we will give the q-WZ pairs for some classical identities
such as the q-Gauss sum, the sum, Ramanujan's sum and
Bailey's sum.Comment: 17 page
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