3,578 research outputs found
Self-reproduction in k-inflation
We study cosmological self-reproduction in models of inflation driven by a
scalar field with a noncanonical kinetic term (-inflation). We
develop a general criterion for the existence of attractors and establish
conditions selecting a class of -inflation models that admit a unique
attractor solution. We then consider quantum fluctuations on the attractor
background. We show that the correlation length of the fluctuations is of order
, where is the speed of sound. By computing the magnitude
of field fluctuations, we determine the coefficients of Fokker-Planck equations
describing the probability distribution of the spatially averaged field .
The field fluctuations are generally large in the inflationary attractor
regime; hence, eternal self-reproduction is a generic feature of -inflation.
This is established more formally by demonstrating the existence of stationary
solutions of the relevant FP equations. We also show that there exists a
(model-dependent) range within which large
fluctuations are likely to drive the field towards the upper boundary
, where the semiclassical consideration breaks down. An exit
from inflation into reheating without reaching will occur almost
surely (with probability 1) only if the initial value of is below
. In this way, strong self-reproduction effects constrain models of
-inflation.Comment: RevTeX 4, 17 pages, 1 figur
Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
We present a numerical finite size scaling study of the localization length
in long cylinders near the integer quantum Hall transition (IQHT) employing the
Chalker-Coddington network model. Corrections to scaling that decay slowly with
increasing system size make this analysis a very challenging numerical problem.
In this work we develop a novel method of stability analysis that allows for a
better estimate of error bars. Applying the new method we find consistent
results when keeping second (or higher) order terms of the leading irrelevant
scaling field. The knowledge of the associated (negative) irrelevant exponent
is crucial for a precise determination of other critical exponents,
including multifractal spectra of wave functions. We estimate ,
which is considerably larger than most recently reported values. Within this
approach we obtain the localization length exponent confirming
recent results. Our stability analysis has broad applicability to other
observables at IQHT, as well as other critical points where corrections to
scaling are present.Comment: 6 pages and 3 figures, plus supplemental material
Sound attenuation apparatus
An apparatus is disclosed for reducing acoustic transmission from mechanical or acoustic sources by means of a double wall partition, within which an acoustic pressure field is generated by at least one secondary acoustic source. The secondary acoustic source is advantageously placed within the partition, around its edges, or it may be an integral part of a wall of the partition
Uncertainty of Governmental Relief and the Crowding out of Insurance
This paper discusses the problem of crowding out of insurance by co-existing governmental relief programs - so-called 'charity hazard' - in a context of different institutional schemes of governmental relief in Austria and Germany. We test empirically whether an assured partial relief scheme (as in Austria) drives a stronger crowding out of private insurance than a scheme promising full relief which is subject to ad hoc political decision making (as in Germany). Our general finding is that the institutional design of governmental relief programs significantly affects the demand for private natural hazard insurance.Insurance demand, governmental relief, natural hazards
Letter to J. Lamar Woodard regarding SEAALL membership dues, July 6, 1976
A letter from A. Ferdinand Engel to J. Lamar Woodard regarding the SEAALL membership renewal for the Tennessee State Library & Archives
Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition
We study the critical behavior near the integer quantum Hall plateau
transition by focusing on the multifractal (MF) exponents describing the
scaling of the disorder-average moments of the point contact conductance
between two points of the sample, within the Chalker-Coddington network model.
Past analytical work has related the exponents to the MF exponents
of the local density of states (LDOS). To verify this relation, we
numerically determine the exponents with high accuracy. We thereby
provide, at the same time, independent numerical results for the MF exponents
for the LDOS. The presence of subleading corrections to scaling
makes such determination directly from scaling of the moments of virtually
impossible. We overcome this difficulty by using two recent advances. First, we
construct pure scaling operators for the moments of which have precisely
the same leading scaling behavior, but no subleading contributions. Secondly,
we take into account corrections to scaling from irrelevant (in the
renormalization group sense) scaling fields by employing a numerical technique
("stability map") recently developed by us. We thereby numerically confirm the
relation between the two sets of exponents, (point contact conductances)
and (LDOS), and also determine the leading irrelevant (corrections
to scaling) exponent as well as other subleading exponents. Our results
suggest a way to access multifractality in an experimental setting.Comment: 7 pages and 4 figures, plus Supplemental materia
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