Some Global Aspects of Duality is String Theory

We explore some of the global aspects of duality transformations in String Theory and Field Theory. We analyze in some detail the equivalence of dual models corresponding to different topologies at the level of the partition function and in terms of the operator correspondence for abelian duality. We analyze the behavior of the cosmological constant under these transformations. We also explore several examples of non-abelian duality where the classical background interpretation can be maintained for the original and the dual theories. In particular we construct a non-abelian dual of $SL(2,R)$ which turns out to be a three-dimensional black holeComment: 31pp. One figure available upon request. CERN-TH-6991/6

Competing Ferromagnetic and Charge-Ordered States in Models for Manganites: the Origin of the CMR Effect

The one-orbital model for manganites with cooperative phonons and superexchange coupling $J_{\rm AF}$ has been investigated via large-scale Monte Carlo (MC) simulations. Results for two-orbitals are also briefly discussed. Focusing on electronic density $n$=0.75, a regime of competition between ferromagnetic (FM) metallic and charge-ordered (CO) insulating states was identified. In the vicinity of the associated bicritical point, colossal magnetoresistance (CMR) effects were observed. The CMR is associated with the development of short-distance correlations among polarons, above the spin ordering temperatures, resembling the charge arrangement of the low-temperature CO state.Comment: 4 pages, 4 figures, accepted for publication in the Phys. Rev. Let

Reionization Histories of Milky Way Mass Halos

We investigate the connection between the epoch of reionization and the present day universe, by examining the extended mass reionization histories of dark matter halos identified at z=0. We combine an N-body dark matter simulation of a 600 Mpc volume with a three-dimensional, seminumerical reionization model. This provides reionization redshifts for each particle, which can then be connected with the properties of their halos at the present time. We find that the vast majority of present-day halos with masses larger than ~ few x 10^11 Msun reionize earlier than the rest of the universe. We also find significant halo-to-halo diversity in mass reionization histories, and find that in realistic inhomogenous models, the material within a given halo is not expected to reionize at the same time. In particular, the scatter in reionization times within individual halos is typically larger than the scatter among halos. From our fiducial reionization model, we find that the typical 68% scatter in reionization times within halos is ~ 115 Myr for 10^(12 \pm 0.25) Msun halos, decreasing slightly to ~ 95 Myr for 10^(15 \pm 0.25) Msun halos. We find a mild correlation between reionization history and environment: halos with shorter reionization histories are typically in more clustered environments, with the strongest trend on a scale of ~ 20 Mpc. Material in Milky Way mass halos with short reionization histories is preferentially reionized in relatively large HII regions, implying reionization mostly by sources external to the progenitors of the present-day halo. We investigate the impact on our results of varying the reionization model parameters, which span a range of reionization scenarios with varying timing and morphology.Comment: 11 pages, 10 figures, 1 table. Submitted to Ap

Non-Abelian Duality and Canonical Transformations

We construct explicit canonical transformations producing non-abelian duals in principal chiral models with arbitrary group G. Some comments concerning the extension to more general $\sigma$-models, like WZW models, are given.Comment: 9 pags, latex fil

Fragility of the A-type AF and CE Phases of Manganites: An Exotic Insulator-to-Metal Transition Induced by Quenched Disorder

Using Monte Carlo simulations and the two eg-orbital model for manganites, the stability of the CE and A-type antiferromagnetic insulating states is analyzed when quenched disorder in the superexchange JAF between the t2g localized spins and in the on-site energies is introduced. At vanishing or small values of the electron-(Jahn-Teller)phonon coupling, the previously hinted "fragility" of these insulating states is studied in detail, focusing on their charge transport properties. This fragility is here found to induce a rapid transition from the insulator to a (poor) metallic state upon the introduction of disorder. A possible qualitative explanation is presented based on the close proximity in energy of ferromagnetic metallic phases, and also on percolative ideas valid at large disorder strength. The scenario is compared with previously discussed insulator-to-metal transitions in other contexts. It is argued that the effect unveiled here has unique properties that may define a new class of giant effects in complex oxides. This particularly severe effect of disorder must be present in other materials as well, in cases involving phases that arise as a compromise between very different tendencies, as it occurs with striped states in the cuprates.Comment: 13 pages, 17 figures, RevTex 4, submitted for publicatio

Pseudospectral Model Predictive Control under Partially Learned Dynamics

Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of model knowledge can be overcome with machine learning techniques, utilizing measurements to build a dynamical model from the data. This paper aims to take the middle ground between these two approaches by introducing a semi-parametric representation of the underlying system dynamics. Our goal is to leverage the considerable information contained in a traditional physics based model and combine it with a data-driven, non-parametric regression technique known as a Gaussian Process. Integrating this semi-parametric model with model predictive pseudospectral control, we demonstrate this technique on both a cart pole and quadrotor simulation with unmodeled damping and parametric error. In order to manage parametric uncertainty, we introduce an algorithm that utilizes Sparse Spectrum Gaussian Processes (SSGP) for online learning after each rollout. We implement this online learning technique on a cart pole and quadrator, then demonstrate the use of online learning and obstacle avoidance for the dubin vehicle dynamics.Comment: Accepted but withdrawn from AIAA Scitech 201