8,176 research outputs found
The Trispectrum in the Effective Field Theory of Large Scale Structure
We compute the connected four point correlation function (the trispectrum in
Fourier space) of cosmological density perturbations at one-loop order in
Standard Perturbation Theory (SPT) and the Effective Field Theory of Large
Scale Structure (EFT of LSS). This paper is a companion to our earlier work on
the non-Gaussian covariance of the matter power spectrum, which corresponds to
a particular wavenumber configuration of the trispectrum. In the present
calculation, we highlight and clarify some of the subtle aspects of the EFT
framework that arise at third order in perturbation theory for general
wavenumber configurations of the trispectrum. We consistently incorporate
vorticity and non-locality in time into the EFT counterterms and lay out a
complete basis of building blocks for the stress tensor. We show predictions
for the one-loop SPT trispectrum and the EFT contributions, focusing on
configurations which have particular relevance for using LSS to constrain
primordial non-Gaussianity.Comment: 25+3 pages, 7 figure
On the limits of spectral methods for frequency estimation
An algorithm is presented which generates pairs of oscillatory random time
series which have identical periodograms but differ in the number of
oscillations. This result indicate the intrinsic limitations of spectral
methods when it comes to the task of measuring frequencies. Other examples, one
from medicine and one from bifurcation theory, are given, which also exhibit
these limitations of spectral methods. For two methods of spectral estimation
it is verified that the particular way end points are treated, which is
specific to each method, is, for long enough time series, not relevant for the
main result.Comment: 18 pages, 6 figures (Referee did not like the previous title. Many
other changes
Complex plane representations and stationary states in cubic and quintic resonant systems
Weakly nonlinear energy transfer between normal modes of strongly resonant
PDEs is captured by the corresponding effective resonant systems. In a previous
article, we have constructed a large class of such resonant systems (with
specific representatives related to the physics of Bose-Einstein condensates
and Anti-de Sitter spacetime) that admit special analytic solutions and an
extra conserved quantity. Here, we develop and explore a complex plane
representation for these systems modelled on the related cubic Szego and LLL
equations. To demonstrate the power of this representation, we use it to give
simple closed form expressions for families of stationary states bifurcating
from all individual modes. The conservation laws, the complex plane
representation and the stationary states admit furthermore a natural
generalization from cubic to quintic nonlinearity. We demonstrate how two
concrete quintic PDEs of mathematical physics fit into this framework, and thus
directly benefit from the analytic structures we present: the quintic nonlinear
Schroedinger equation in a one-dimensional harmonic trap, studied in relation
to Bose-Einstein condensates, and the quintic conformally invariant wave
equation on a two-sphere, which is of interest for AdS/CFT-correspondence.Comment: v2: version accepted for publicatio
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