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 $\bar{p}(n)$ denote the number of overpartitions of $n$. It was conjectured by Hirschhorn and Sellers that \bar{p}(40n+35)\equiv 0\ ({\rm mod\} 40) for $n\geq 0$. Employing 2-dissection formulas of quotients of theta functions due to Ramanujan, and Hirschhorn and Sellers, we obtain a generating function for $\bar{p}(40n+35)$ modulo 5. Using the $(p, k)$-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 $_6\phi_5$ sum, Ramanujan's $_1\psi_1$ sum and Bailey's $_6\psi_6$ sum.Comment: 17 page