10 research outputs found
Non-perturbative probability distribution function for cosmological counts in cells
We present a non-perturbative calculation of the 1-point probability
distribution function (PDF) for the spherically-averaged matter density field.
The PDF is represented as a path integral and is evaluated using the
saddle-point method. It factorizes into an exponent given by a spherically
symmetric saddle-point solution and a prefactor produced by fluctuations. The
exponent encodes the leading sensitivity of the PDF to the dynamics of
gravitational clustering and statistics of the initial conditions. In contrast,
the prefactor has only a weak dependence on cosmology. It splits into a
monopole contribution which is evaluated exactly, and a factor corresponding to
aspherical fluctuations. The latter is crucial for the consistency of the
calculation: neglecting it would make the PDF incompatible with translational
invariance. We compute the aspherical prefactor using a combination of analytic
and numerical techniques. We demonstrate the factorization of spurious enhanced
contributions of large bulk flows and their cancellation due the equivalence
principle. We also identify the sensitivity to the short-scale physics and
argue that it must be properly renormalized. The uncertainty associated with
the renormalization procedure gives an estimate of the theoretical error. For
zero redshift, the precision varies from sub percent for moderate density
contrasts to tens of percent at the tails of the distribution. It improves at
higher redshifts. We compare our results with N-body simulation data and find
an excellent agreement.Comment: 85 pages, 21 figures, minor correction
Towards a Unified Theory of Massless Superfields of All Superspins
We describe the ``universal'' action for massless superfields of all
superspins in N = 1, D = 4 anti-de Sitter superspace as a gauge theory of
unconstrained superfields taking their values in the commutative algebra of
analytic functions over a one-sheeted hyperboloid in . The action is
invariant under N = 2 supersymmetry transformations which form a closed algebra
off the mass-shell.Comment: 12 pages, LaTe
Automatic code generation for many-body electronic structure methods: the tensor contraction engine‡‡
Synthesis of High-Performance Parallel Programs for a Class of Ab Initio Quantum Chemistry Models
Invited Paper This paper provides an overview of a program synthesis system for a class of quantum chemistry computations. These computations are expressible as a set of tensor contractions and arise in electronic structure modeling. The input to the system is a a high-level specification of the computation, from which the system can synthesize high-performance parallel code tailored to the characteristics of th