8,123 research outputs found
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
Entanglement entropies and fermion signs of critical metals
The fermion sign problem is often viewed as a sheer inconvenience that
plagues numerical studies of strongly interacting electron systems. Only
recently, it has been suggested that fermion signs are fundamental for the
universal behavior of critical metallic systems and crucially enhance their
degree of quantum entanglement. In this work we explore potential connections
between emergent scale invariance of fermion sign structures and scaling
properties of bipartite entanglement entropies. Our analysis is based on a
wavefunction ansatz that incorporates collective, long-range backflow
correlations into fermionic Slater determinants. Such wavefunctions mimic the
collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces --
a representation of the fermion sign structure in many-particle configurations
space -- show fractal behavior up to a length scale that diverges at a
critical backflow strength. We show that the Hausdorff dimension of the fractal
nodal surface depends on , the number of fermions and the exponent of the
backflow. For the same wavefunctions we numerically calculate the second
R\'enyi entanglement entropy . Our results show a cross-over from volume
scaling, ( in dimensions), to the
characteristic Fermi-liquid behavior on scales larger
than . We find that volume scaling of the entanglement entropy is a robust
feature of critical backflow fermions, independent of the backflow exponent and
hence the fractal dimension of the scale invariant sign structure.Comment: 9.5 pages, 10 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
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
The Forward-backward asymmetry in the angular distribution of is
studied in the process . The
possibility of observing CP violation through the asymmetries in these two
processes is examined.Comment: 5 pages, latex formatte
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