3,055 research outputs found
Spectral correlations in systems undergoing a transition from periodicity to disorder
We study the spectral statistics for extended yet finite quasi 1-d systems
which undergo a transition from periodicity to disorder. In particular we
compute the spectral two-point form factor, and the resulting expression
depends on the degree of disorder. It interpolates smoothly between the two
extreme limits -- the approach to Poissonian statistics in the (weakly)
disordered case, and the universal expressions derived for the periodic case.
The theoretical results agree very well with the spectral statistics obtained
numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late
The grass is not always greener in the neighbor's yard:Bayesian and frequentist inference methods for network autocorrelated data
People do not live in isolation. Instead, we constantly interact with others, which affects our actions, opinions, or well-being. Throughout the last decades, the network autocorrelation model has been the workhorse for modeling network influence on individual behavior. In the network autocorrelation model, actor observations for a variable of interest are allowed to be correlated, where a network autocorrelation parameter represents and quantifies the strength of a network influence on the variable of interest. More precisely, an actor’s observation is assumed to be a function not only of a set of explanatory variables but also of the observations for the actor's neighbors, i.e., other actors in the network this actor is tied to. In this thesis, we develop a fully Bayesian framework to estimate the network autocorrelation model and to test multiple hypotheses on the network autocorrelation parameter(s) against each other. Taking the Bayesian route hereto has at least three attractive features that are not shared by classical statistical methods such as maximum likelihood estimation and null hypothesis significance testing. First, the Bayesian approach enables researchers to include previous empirical information about the network autocorrelation parameter through a prior distribution, which may attenuate the underestimation of the network autocorrelation parameter associated with maximum likelihood estimation of the model. Concomitantly, we also derive Bayesian default procedures for situations in which such prior information is completely unavailable. Second, Bayesian techniques do not rely on asymptotic approximations when estimating uncertainty and performing inference about the network autocorrelation parameter but yield accurate results even in case of small networks. Third, using Bayes factors as opposed to null hypothesis significance testing, researchers can test any number of hypotheses on the network autocorrelation parameter and quantify the amount of relative evidence in the data for each tested hypothesis. We provide several such Bayes factors and generalize the presented methodology to test order hypotheses on multiple network autocorrelation parameters, representing the strength of multiple influence mechanisms that may have some connection to the variable of interest. Furthermore, we introduce a discrete exponential family model to analyze network autocorrelated count data for which the network autocorrelation model itself is not well-suited. This novel model permits principled statistical inference without making any potentially limiting distributional assumptions on the marginal or conditional counts but is flexible enough to accommodate a wide range of count patterns. In sum, the methods developed in this thesis allow researchers studying network influence to quantify and test the strength of network influence(s) on a variable of interest in ways that go beyond the current state of the art
(Broken) Gauge Symmetries and Constraints in Regge Calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of
(quantum) gravity, in particular for Regge calculus. We find that for a
solution with curvature there do not exist exact gauge symmetries on the
discrete level. Furthermore we derive a canonical formulation that exactly
matches the dynamics and hence symmetries of the covariant picture. In this
canonical formulation broken symmetries lead to the replacements of constraints
by so--called pseudo constraints. These considerations should be taken into
account in attempts to connect spin foam models, based on the Regge action,
with canonical loop quantum gravity, which aims at implementing proper
constraints. We will argue that the long standing problem of finding a
consistent constraint algebra for discretized gravity theories is equivalent to
the problem of finding an action with exact diffeomorphism symmetries. Finally
we will analyze different limits in which the pseudo constraints might turn
into proper constraints. This could be helpful to infer alternative
discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure
Photon propagation in a cold axion background with and without magnetic field
A cold relic axion condensate resulting from vacuum misalignment in the early
universe oscillates with a frequency m, where m is the axion mass. We determine
the properties of photons propagating in a simplified version of such a
background where the sinusoidal variation is replaced by a square wave profile.
We prove that previous results that indicated that charged particles moving
fast in such a background radiate, originally derived assuming that all momenta
involved were much larger than m, hold for long wavelengths too. We also
analyze in detail how the introduction of a magnetic field changes the
properties of photon propagation in such a medium. We briefly comment on
possible astrophysical implications of these results.Comment: 17 pages, 4 figures, revised version includes an extended discussion
on physical implication
Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]
Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for
convergent series representations of both the real and the imaginary part of
the QED effective action; these derivations were based on correct intermediate
steps. In this comment, we argue that the physical significance of the
"logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86,
1947 (2001)] in comparison to the usual expression for the QED effective action
remains to be demonstrated. Further information on related subjects can be
found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update
Uni-directional transport properties of a serpent billiard
We present a dynamical analysis of a classical billiard chain -- a channel
with parallel semi-circular walls, which can serve as a model for a bended
optical fiber. An interesting feature of this model is the fact that the phase
space separates into two disjoint invariant components corresponding to the
left and right uni-directional motions. Dynamics is decomposed into the jump
map -- a Poincare map between the two ends of a basic cell, and the time
function -- traveling time across a basic cell of a point on a surface of
section. The jump map has a mixed phase space where the relative sizes of the
regular and chaotic components depend on the width of the channel. For a
suitable value of this parameter we can have almost fully chaotic phase space.
We have studied numerically the Lyapunov exponents, time auto-correlation
functions and diffusion of particles along the chain. As a result of a
singularity of the time function we obtain marginally-normal diffusion after we
subtract the average drift. The last result is also supported by some
analytical arguments.Comment: 15 pages, 9 figure (19 .(e)ps files
From the discrete to the continuous - towards a cylindrically consistent dynamics
Discrete models usually represent approximations to continuum physics.
Cylindrical consistency provides a framework in which discretizations mirror
exactly the continuum limit. Being a standard tool for the kinematics of loop
quantum gravity we propose a coarse graining procedure that aims at
constructing a cylindrically consistent dynamics in the form of transition
amplitudes and Hamilton's principal functions. The coarse graining procedure,
which is motivated by tensor network renormalization methods, provides a
systematic approximation scheme towards this end. A crucial role in this coarse
graining scheme is played by embedding maps that allow the interpretation of
discrete boundary data as continuum configurations. These embedding maps should
be selected according to the dynamics of the system, as a choice of embedding
maps will determine a truncation of the renormalization flow.Comment: 22 page
Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
We develop a gauge invariant canonical perturbation scheme for perturbations
around symmetry reduced sectors in generally covariant theories, such as
general relativity. The central objects of investigation are gauge invariant
observables which encode the dynamics of the system. We apply this scheme to
perturbations around a homogeneous and isotropic sector (cosmology) of general
relativity. The background variables of this homogeneous and isotropic sector
are treated fully dynamically which allows us to approximate the observables to
arbitrary high order in a self--consistent and fully gauge invariant manner.
Methods to compute these observables are given. The question of backreaction
effects of inhomogeneities onto a homogeneous and isotropic background can be
addressed in this framework. We illustrate the latter by considering
homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a
homogeneous and isotropic sector.Comment: 39 pages, 1 figur
Regge calculus from a new angle
In Regge calculus space time is usually approximated by a triangulation with
flat simplices. We present a formulation using simplices with constant
sectional curvature adjusted to the presence of a cosmological constant. As we
will show such a formulation allows to replace the length variables by 3d or 4d
dihedral angles as basic variables. Moreover we will introduce a first order
formulation, which in contrast to using flat simplices, does not require any
constraints. These considerations could be useful for the construction of
quantum gravity models with a cosmological constant.Comment: 8 page
Note About Hamiltonian Formalism of Healthy Extended Horava-Lifshitz Gravity
In this paper we continue the study of the Hamiltonian formalism of the
healthy extended Horava-Lifshitz gravity. We find the constraint structure of
given theory and argue that this is the theory with the second class
constraints. Then we discuss physical consequence of this result. We also apply
the Batalin-Tyutin formalism of the conversion of the system with the second
class constraints to the system with the first class constraints to the case of
the healthy extended Horava-Lifshitz theory. As a result we find new theory of
gravity with structure that is different from the standard formulation of
Horava-Lifshitz gravity or General Relativity.Comment: 17 pages, v.2. references added, v.3. typos corrected, references
adde
- …