Generic Conditions for Forecast Dominance

Recent studies have analyzed whether one forecast method dominates another under a class of consistent scoring functions. While the existing literature focuses on empirical tests of forecast dominance, little is known about the theoretical conditions under which one forecast dominates another. To address this question, we derive a new characterization of dominance among forecasts of the mean functional. We present various scenarios under which dominance occurs. Unlike existing results, our results allow for the case that the forecasts' underlying information sets are not nested, and allow for uncalibrated forecasts that suffer, e.g., from model misspecification or parameter estimation error. We illustrate the empirical relevance of our results via data examples from finance and economics

Bose and Mott Glass Phases in Dimerized Quantum Antiferromagnets

We examine the effects of disorder on dimerized quantum antiferromagnets in a magnetic field, using the mapping to a lattice gas of hard-core bosons with finite-range interactions. Combining a strong-coupling expansion, the replica method, and a one-loop renormalization group analysis, we investigate the nature of the glass phases formed. We find that away from the tips of the Mott lobes, the transition is from a Mott insulator to a compressible Bose glass, however the compressibility at the tips is strongly suppressed. We identify this finding with the presence of a rare Mott glass phase not previously described by any analytic theory for this model and demonstrate that the inclusion of replica symmetry breaking is vital to correctly describe the glassy phases. This result suggests that the formation of Bose and Mott glass phases is not simply a weak localization phenomenon but is indicative of much richer physics. We discuss our results in the context of both ultracold atomic gases and spin-dimer materials.Comment: 10 pages (including supplementary material), 3 figure

Entropy of unimodular Lattice Triangulations

Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where its entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achive excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is $C=2.196(3)$ consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.Comment: 6 pages, 7 figure

Theoretical investigation of the magnetic structure in YBa_2Cu_3O_6

As experimentally well established, YBa_2Cu_3O_6 is an antiferromagnet with the magnetic moments lying on the Cu sites. Starting from this experimental result and the assumption, that nearest-neighbor Cu atoms within a layer have exactly antiparallel magnetic moments, the orientation of the magnetic moments has been determined within a nonadiabatic extension of the Heisenberg model of magnetism, called nonadiabatic Heisenberg model. Within this group-theoretical model there exist four stable magnetic structures in YBa_2Cu_3O_6, two of them are obviously identical with the high- and low-temperature structure established experimentally. However, not all the magnetic moments which appear to be antiparallel in neutron-scattering experiments are exactly antiparallel within this group-theoretical model. Furthermore, within this model the magnetic moments are not exactly perpendicular to the orthorhombic c axis

Flight of a heavy particle nonlinearly coupled to a quantum bath

Fluctuation and dissipation are by-products of coupling to the `environment.' The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of L\'evy flights. We suggest condensed matter analogs where similar effects may arise.Comment: Introduction expanded. Appendices adde

One-Nucleon Effective Generators of the Poincare Group derived from a Field Theory: Mass Renormalization

We start from a Lagrangian describing scalar "nucleons" and mesons which interact through a simple vertex. Okubo's method of unitary transformation is used to describe a single nucleon dressed by its meson cloud. We find an expression for the physical mass of the nucleon being correct up to second order in the coupling constant. It is then verified that this result is the same as the corresponding expression found by Feynman techniques. Finally we also express the three boost operators in terms of the physical nucleon mass. Doing so we find expressions for all the ten generators of Poincar\'e transformations for the system of one single dressed nucleon.Comment: 19 pages, no figure

Forward-Backward Asymmetry in B→Xde+e−B\to X_d e^+e^-

The Forward-backward asymmetry in the angular distribution of $e^+e^-$ is studied in the process $B\to e^+e^- and \bar{B}\to \bar{X}_d e^+e^-$ . The possibility of observing CP violation through the asymmetries in these two processes is examined.Comment: 5 pages, latex formatte

Electronic spin-triplet nematic with a twist

We analyze a model of itinerant electrons interacting through a quadrupole density-density repulsion in three dimensions. At the mean field level, the interaction drives a continuous Pomeranchuk instability towards $d$-wave, spin-triplet nematic order, which simultaneously breaks the SU(2) spin-rotation and spatial rotational symmetries. This order results in spin antisymmetric, elliptical deformations of the Fermi surfaces of up and down spins. We show that the effects of quantum fluctuations are similar to those in metallic ferromagnets, rendering the nematic transition first-order at low temperatures. Using the fermionic quantum order-by-disorder approach to self-consistently calculate fluctuations around possible modulated states, we show that the first-order transition is pre-empted by the formation of a nematic state that is intertwined with a helical modulation in spin space. Such a state is closely related to $d$-wave bond density wave order in square-lattice systems. Moreover, we show that it may coexist with a modulated, $p$-wave superconducting state.Comment: 15 pages, 9 figure