2,586 research outputs found
String Inflation After Planck 2013
We briefly summarize the impact of the recent Planck measurements for string
inflationary models, and outline what might be expected to be learned in the
near future from the expected improvement in sensitivity to the primordial
tensor-to-scalar ratio. We comment on whether these models provide sufficient
added value to compensate for their complexity, and ask how they fare in the
face of the new constraints on non-gaussianity and dark radiation. We argue
that as a group the predictions made before Planck agree well with what has
been seen, and draw conclusions from this about what is likely to mean as
sensitivity to primordial gravitational waves improves.Comment: LaTeX, 21 pages plus references; slight modification of the
discussion of inflection point inflation, references added and typos
correcte
Maximum Hands-Off Control: A Paradigm of Control Effort Minimization
In this paper, we propose a new paradigm of control, called a maximum
hands-off control. A hands-off control is defined as a control that has a short
support per unit time. The maximum hands-off control is the minimum support (or
sparsest) per unit time among all controls that achieve control objectives. For
finite horizon control, we show the equivalence between the maximum hands-off
control and L1-optimal control under a uniqueness assumption called normality.
This result rationalizes the use of L1 optimality in computing a maximum
hands-off control. We also propose an L1/L2-optimal control to obtain a smooth
hands-off control. Furthermore, we give a self-triggered feedback control
algorithm for linear time-invariant systems, which achieves a given sparsity
rate and practical stability in the case of plant disturbances. An example is
included to illustrate the effectiveness of the proposed control.Comment: IEEE Transactions on Automatic Control, 2015 (to appear
Inflating with Large Effective Fields
We re-examine large scalar fields within effective field theory, in
particular focussing on the issues raised by their use in inflationary models
(as suggested by BICEP2 to obtain primordial tensor modes). We argue that when
the large-field and low-energy regimes coincide the scalar dynamics is most
effectively described in terms of an asymptotic large-field expansion whose
form can be dictated by approximate symmetries, which also help control the
size of quantum corrections. We discuss several possible symmetries that can
achieve this, including pseudo-Goldstone inflatons characterized by a coset
(based on abelian and non-abelian, compact and non-compact symmetries),
as well as symmetries that are intrinsically higher dimensional. Besides the
usual trigonometric potentials of Natural Inflation we also find in this way
simple {\em large-field} power laws (like ) and exponential
potentials, . Both of these can
describe the data well and give slow-roll inflation for large fields without
the need for a precise balancing of terms in the potential. The exponential
potentials achieve large through the limit and so
predict ; consequently gives but not much larger (and so could be ruled out as measurements on
and improve). We examine the naturalness issues for these models and
give simple examples where symmetries protect these forms, using both
pseudo-Goldstone inflatons (with non-abelian non-compact shift symmetries
following familiar techniques from chiral perturbation theory) and
extra-dimensional models.Comment: 21 pages + appendices, 3 figure
String Theory Realizations of the Nilpotent Goldstino
We describe in detail how the spectrum of a single anti-D3-brane in
four-dimensional orientifolded IIB string models reproduces precisely the field
content of a nilpotent chiral superfield with the only physical component
corresponding to the fermionic goldstino. In particular we explicitly consider
a single anti-D3-brane on top of an O3-plane in warped throats, induced by
fluxes. More general systems including several anti-branes and other
orientifold planes are also discussed. This provides further evidence to the
claim that non-linearly realized supersymmetry due to the presence of
antibranes in string theory can be described by supersymmetric theories
including nilpotent superfields. Implications to the KKLT and related scenarios
of de Sitter moduli stabilization, to cosmology and to the structure of soft
SUSY-breaking terms are briefly discussed.Comment: 33 pages, 8 figures. v2: reference added, minor change
Statistical thermodynamics of economic systems
We formulate thermodynamics of economic systems in terms of an arbitrary
probability distribution for a conserved economic quantity. As in statistical
physics, thermodynamic macroeconomic variables emerge as the mean value of
microeconomic variables and their determination is reduced to the computation
of the partition function, starting from an arbitrary function. Explicit
hypothetical examples are given which include linear and nonlinear economic
systems, as well as multiplicative systems such as those dominated by a Pareto
law distribution. We propose to use the formalism of phase transitions to study
severe changes of macroeconomic variables.Comment: Discussions added, typos correcte
Orbital stability of the restricted three body problem in General Relativity
We consider the problem of orbital stability of the motion of a test particle
in the restricted three-body problem, by using the orbital moment and its time
derivative. We show that it is possible to get some insight into the stability
properties of the motion of test particles, without knowing the exact solutions
of the motion equations.Comment: 2 page
Normal Coordinates and Primitive Elements in the Hopf Algebra of Renormalization
We introduce normal coordinates on the infinite dimensional group
introduced by Connes and Kreimer in their analysis of the Hopf algebra of
rooted trees. We study the primitive elements of the algebra and show that they
are generated by a simple application of the inverse Poincar\'e lemma, given a
closed left invariant 1-form on . For the special case of the ladder
primitives, we find a second description that relates them to the Hopf algebra
of functionals on power series with the usual product. Either approach shows
that the ladder primitives are given by the Schur polynomials. The relevance of
the lower central series of the dual Lie algebra in the process of
renormalization is also discussed, leading to a natural concept of
-primitiveness, which is shown to be equivalent to the one already in the
literature.Comment: Latex, 24 pages. Submitted to Commun. Math. Phy
On the local Lorentz invariance in N=1 supergravity
We discuss the local Lorentz invariance in the context of N=1 supergravity
and show that a previous attempt to find explicit solutions to the Lorentz
constraint in terms of matrices is not correct. We improve that
solution by using a different representation of the Lorentz operators in terms
of the generators of the rotation group, and show its compatibility with the
matrix representation of the fermionic field. We find the most general wave
functional that satisfies the Lorentz constraint in this representation
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