52,911 research outputs found
The anamorphic universe
We introduce "anamorphic" cosmology, an approach for explaining the
smoothness and flatness of the universe on large scales and the generation of a
nearly scale-invariant spectrum of adiabatic density perturbations. The
defining feature is a smoothing phase that acts like a contracting universe
based on some Weyl frame-invariant criteria and an expanding universe based on
other frame-invariant criteria. An advantage of the contracting aspects is that
it is possible to avoid the multiverse and measure problems that arise in
inflationary models. Unlike ekpyrotic models, anamorphic models can be
constructed using only a single field and can generate a nearly scale-invariant
spectrum of tensor perturbations. Anamorphic models also differ from pre-big
bang and matter bounce models that do not explain the smoothness. We present
some examples of cosmological models that incorporate an anamorphic smoothing
phase.Comment: 35 pages, 3 figures, 1 tabl
Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes
The renormalization group (RG) method as a powerful tool for reduction of
evolution equations is formulated in terms of the notion of invariant
manifolds. We start with derivation of an exact RG equation which is analogous
to the Wilsonian RG equations in statistical physics and quantum field theory.
It is clarified that the perturbative RG method constructs invariant manifolds
successively as the initial value of evolution equations, thereby the meaning
to set is naturally understood where is the arbitrary initial
time. We show that the integral constants in the unperturbative solution
constitutes natural coordinates of the invariant manifold when the linear
operator in the evolution equation has no Jordan cell; when has a
Jordan cell, a slight modification is necessary because the dimension of the
invariant manifold is increased by the perturbation. The RG equation determines
the slow motion of the would-be integral constants in the unperturbative
solution on the invariant manifold. We present the mechanical procedure to
construct the perturbative solutions hence the initial values with which the RG
equation gives meaningful results. The underlying structure of the reduction by
the RG method as formulated in the present work turns out to completely fit to
the universal one elucidated by Kuramoto some years ago. We indicate that the
reduction procedure of evolution equations has a good correspondence with the
renormalization procedure in quantum field theory; the counter part of the
universal structure of reduction elucidated by Kuramoto may be the Polchinski's
theorem for renormalizable field theories. We apply the method to interface
dynamics such as kink-anti-kink and soliton-soliton interactions in the latter
of which a linear operator having a Jordan-cell structure appears.Comment: 67 pages. No figures. v2: Additional discussions on the unstable
motion in the the double-well potential are given in the text and the
appendix added. Some references are also added. Introduction is somewhat
reshape
Spectral properties of zero temperature dynamics in a model of a compacting granular column
The compacting of a column of grains has been studied using a one-dimensional
Ising model with long range directed interactions in which down and up spins
represent orientations of the grain having or not having an associated void.
When the column is not shaken (zero 'temperature') the motion becomes highly
constrained and under most circumstances we find that the generator of the
stochastic dynamics assumes an unusual form: many eigenvalues become
degenerate, but the associated multi-dimensional invariant spaces have but a
single eigenvector. There is no spectral expansion and a Jordan form must be
used. Many properties of the dynamics are established here analytically; some
are not. General issues associated with the Jordan form are also taken up.Comment: 34 pages, 4 figures, 3 table
Diffusion-annihilation dynamics in one spatial dimension
We discuss a reaction-diffusion model in one dimension subjected to an
external driving force. Each lattice site may be occupied by at most one
particle. The particles hop with asymmetric rates (the sum of which is one) to
the right or left nearest neighbour site if it is vacant, and annihilate with
rate one if it is occupied.
We compute the long time behaviour of the space dependent average density in
states where the initial density profiles are step functions. We also compute
the exact time dependence of the particle density for uncorrelated random
initial conditions. The representation of the uncorrelated random initial state
and also of the step function profile in terms of free fermions allows the
calculation of time-dependent higher order correlation functions. We outline
the procedure using a field theoretic approach.Comment: 26 pages, 1 Postscript figure, uses epsf.st
Are there really conformal frames? Uniqueness of affine inflation
Here we concisely review the nonminimal coupling dynamics of a single scalar
field in the context of purely affine gravity and extend the study to
multifield dynamics. The coupling is performed via an affine connection and its
associated curvature without referring to any metric tensor. The latter arises
a posteriori and it may gain an emergent character like the scale of gravity.
What is remarkable in affine gravity is the transition from nonminimal to
minimal couplings which is realized by only field redefinition of the scalar
fields. Consequently, the inflationary models gain a unique description in this
context where the observed parameters, like the scalar tilt and the
tensor-to-scalar ratio, are invariant under field reparametrization. Overall,
gravity in its affine approach is expected to reveal interesting and rich
phenomenology in cosmology and astroparticle physics.Comment: Review Article: matches the published version in IJMPD, 44 pages, 1
table and 2 figure
The Modulation of Multiple Phases Leading to the Modified KdV Equation
This paper seeks to derive the modified KdV (mKdV) equation using a novel
approach from systems generated from abstract Lagrangians that possess a
two-parameter symmetry group. The method to do uses a modified modulation
approach, which results in the mKdV emerging with coefficients related to the
conservation laws possessed by the original Lagrangian system. Alongside this,
an adaptation of the method of Kuramoto is developed, providing a simpler
mechanism to determine the coefficients of the nonlinear term. The theory is
illustrated using two examples of physical interest, one in stratified
hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to
illustrate how the criterion for the mKdV equation to emerge may be assessed
and its coefficients generated.Comment: 35 pages, 5 figure
Conjugates, Filters and Quantum Mechanics
The Jordan structure of finite-dimensional quantum theory is derived, in a
conspicuously easy way, from a few simple postulates concerning abstract
probabilistic models (each defined by a set of basic measurements and a convex
set of states). The key assumption is that each system A can be paired with an
isomorphic system, , by means of a
non-signaling bipartite state perfectly and uniformly correlating each
basic measurement on A with its counterpart on . In the case of a
quantum-mechanical system associated with a complex Hilbert space ,
the conjugate system is that associated with the conjugate Hilbert space
, and corresponds to the standard maximally
entangled EPR state on . A second
ingredient is the notion of a , that is, a
probabilistically reversible process that independently attenuates the
sensitivity of detectors associated with a measurement. In addition to offering
more flexibility than most existing reconstructions of finite-dimensional
quantum theory, the approach taken here has the advantage of not relying on any
form of the "no restriction" hypothesis. That is, it is not assumed that
arbitrary effects are physically measurable, nor that arbitrary families of
physically measurable effects summing to the unit effect, represent physically
accessible observables. An appendix shows how a version of Hardy's "subspace
axiom" can replace several assumptions native to this paper, although at the
cost of disallowing superselection rules.Comment: 33 pp. Minor corrections throughout; some revision of Appendix
Consistent perturbations in an imperfect fluid
We present a new prescription for analysing cosmological perturbations in a
more-general class of scalar-field dark-energy models where the energy-momentum
tensor has an imperfect-fluid form. This class includes Brans-Dicke models,
f(R) gravity, theories with kinetic gravity braiding and generalised galileons.
We employ the intuitive language of fluids, allowing us to explicitly maintain
a dependence on physical and potentially measurable properties. We demonstrate
that hydrodynamics is not always a valid description for describing
cosmological perturbations in general scalar-field theories and present a
consistent alternative that nonetheless utilises the fluid language. We apply
this approach explicitly to a worked example: k-essence non-minimally coupled
to gravity. This is the simplest case which captures the essential new features
of these imperfect-fluid models. We demonstrate the generic existence of a new
scale separating regimes where the fluid is perfect and imperfect. We obtain
the equations for the evolution of dark-energy density perturbations in both
these regimes. The model also features two other known scales: the Compton
scale related to the breaking of shift symmetry and the Jeans scale which we
show is determined by the speed of propagation of small scalar-field
perturbations, i.e. causality, as opposed to the frequently used definition of
the ratio of the pressure and energy-density perturbations.Comment: 40 pages plus appendices. v2 reflects version accepted for
publication in JCAP (new summary of notation, extra commentary on choice of
gauge and frame, extra references to literature
The Octonions
The octonions are the largest of the four normed division algebras. While
somewhat neglected due to their nonassociativity, they stand at the crossroads
of many interesting fields of mathematics. Here we describe them and their
relation to Clifford algebras and spinors, Bott periodicity, projective and
Lorentzian geometry, Jordan algebras, and the exceptional Lie groups. We also
touch upon their applications in quantum logic, special relativity and
supersymmetry.Comment: 56 pages LaTeX, 11 Postscript Figures, some small correction
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