arXiv subjects
Publications and source records attributed to G. Pan.
A string theoretic framework is presented for the work of Hausel and Rodriguez-Vilegas as well as de Cataldo, Hausel and Migliorini on the cohomology of character varieties. The central element of this construction is an identification of the cohomology of the Hitchin moduli space with BPS states in a local Calabi-Yau threefold. This is a summary of several talks given during the Moduli Space Program 2011 at Isaac Newton Institute.
A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane configuration, and is naturally obtained by dimensional reduction of a quiver $(0,2)$ gauged linear sigma model. In a special stability chamber, the resulting moduli space of quiver representations is shown to be virtually smooth and isomorphic to a moduli space of framed quotients on the projective plane. A precise conjecture relating a K-theoretic partition function of this moduli space to refined open string invariants of toric lagrangian branes is formulated for conifold and local P^1 x P^1 geometries.
We investigated the mean-free path effects on the magnetoresistance of ferromagnetic nanocontacts. For most combinations of parameters the magnetoresistance monotonously decreases with increasing the contact cross-section. However, for a certain choice of parameters the calculations show non-monotonous behavior of the magnetoresistance in the region in which the diameter of the contact becomes comparable with the mean-free path of electrons. We attribute this effect to different conduction regimes in the vicinity of the nanocontact: ballistic for electrons of one spin projection, and simultaneously diffusive for the other. Furthermore, at certain combinations of spin asymmetries of the bulk mean-free paths in a heterocontact, the magnetoresistance can be almost constant, or may even grow as the contact diameter increases. Thus, our calculations suggest a way to search for combinations of material parameters, for which high magnetoresistances can be achieved not only at the nanometric size of the contact, but also at much larger cross-sections of nanocontacts which can be easier for fabrication with current technologies. The trial calculations of the magnetoresistance with material parameters close to those for the Mumetal-Ni heterocontacts agree satisfactorily with the available experimental data.
A quasiclassical theory of giant magnetoresistance in nanoscale point contacts between different ferromagnetic metals is developed. The contacts were sorted by three types of mutual positions of the conduction spin-subband bottoms which are shifted one against another by the exchange interaction. A model of linear domain wall has been used to account for the finite contact length. The magnetoresistance is plotted against the size of the nanocontact. In heterocontacts the magnetoresistance effect turned out to be not only negative, as usual, but can be positive as well. Relevance of the results to existing experiments on GMR in point heterocontacts is discussed.