Generalized self-energy embedding theory

Ab initio quantum chemistry calculations for systems with large active spaces are notoriously difficult and cannot be successfully tackled by standard methods. In this letter, we generalize a Green's function QM/QM embedding method called self-energy embedding theory (SEET) that has the potential to be successfully employed to treat large active spaces. In generalized SEET, active orbitals are grouped into intersecting groups of few orbitals allowing us to perform multiple parallel calculations yielding results comparable to the full active space treatment. We examine generalized SEET on a series of examples and discuss a hierarchy of systematically improvable approximations

Gauge Mediation in F-Theory GUT Models

We study a simple framework for gauge-mediated supersymmetry-breaking in local GUT models based on F-theory 7-branes and demonstrate that a mechanism for solving both the \mu and \mu/B_{\mu} problems emerges in a natural way. In particular, a straightforward coupling of the messengers to the Higgs sector leads to a geometry which not only provides us with an approximate U(1)_{PQ} symmetry that forbids the generation of \mu at the GUT scale, it also forces the SUSY-breaking spurion field to carry a nontrivial PQ charge. This connects the breaking of SUSY to the generation of \mu so that the same scale enters both. Moreover, the messenger sector naturally realizes the D3-instanton triggered Polonyi model of arXiv:0808.1286 so this scale is exponentially suppressed relative to M_{GUT}. The effective action at low scales is in fact precisely of the form of the "sweet spot supersymmetry" scenario studied by Ibe and Kitano in arXiv:0705.3686.Comment: 34 pages, 4 figures; v4 revisions to section

Factoring in the hyperelliptic Torelli group

The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. The authors and Putman proved that this group is generated by Dehn twists about separating curves fixed by the hyperelliptic involution. In this paper, we introduce an algorithmic approach to factoring a wide class of elements of the hyperelliptic Torelli group into such Dehn twists, and apply our methods to several basic elements.Comment: 9 pages, 7 figure

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure