848 research outputs found
Spinodal Backreaction During Inflation and Initial Conditions
We investigate how long wavelength inflationary fluctuations can cause the
background field to deviate from classical dynamics. For generic potentials, we
show that, in the Hartree approximation, the long wavelength dynamics can be
encapsulated by a two-field model operating in an effective potential. The
latter is given by a simple Gaussian integral transformation of the original
inflationary potential. We use this new expression to study backreaction
effects in quadratic, hilltop, flattened, and axion monodromy potentials. We
find that the net result of the altered dynamics is to slightly modify the
spectral tilt, drastically decrease the tensor-to-scalar ratio, and to
effectively smooth over any features of the potential, with the size of these
deviations set by the initial value of power in large scale modes and the shape
of the potential during the entire evolution.Comment: 30 pages, 8 figure
Trapping and Cooling a mirror to its quantum mechanical ground state
We propose a technique aimed at cooling a harmonically oscillating mirror to
its quantum mechanical ground state starting from room temperature. Our method,
which involves the two-sided irradiation of the vibrating mirror inside an
optical cavity, combines several advantages over the two-mirror arrangements
being used currently. For comparable parameters the three-mirror configuration
provides a stiffer trap for the oscillating mirror. Furthermore it prevents
bistability from limiting the use of higher laser powers for mirror trapping,
and also partially does so for mirror cooling. Lastly, it improves the
isolation of the mirror from classical noise so that its dynamics are perturbed
mostly by the vacuum fluctuations of the optical fields. These improvements are
expected to bring the task of achieving ground state occupation for the mirror
closer to completion.Comment: 5 pages, 1 figur
A Linear Approximation for the Excitation Energies of single and double analog states in the f_{7/2} shell
We find that the excitation energies of single analog states for odd-even
nuclei in the f shell with J=j=7/2 and the J=0 double
analog states in the even-even nuclei are well described by the formulas
and ,respectively,
where is usually the ground state isospin. It is remarkable
to note that the parameter X accounts for the departures from the symmetry
energy based predictions.Comment: 8 pages and no figure
Using a Laguerre-Gaussian beam to trap and cool the rotational motion of a mirror
We show theoretically that it is possible to trap and cool the rotational
motion of a macroscopic mirror made of a perfectly reflecting spiral phase
element using orbital angular momentum transfer from a Laguerre-Gaussian
optical field. This technique offers a promising route to the placement of the
rotor in its quantum mechanical ground state in the presence of thermal noise.
It also opens up the possibility of simultaneously cooling a vibrational mode
of the same mirror. Lastly, the proposed design may serve as a sensitive
torsional balance in the quantum regime.Comment: New cavity design, reworked title; to appear in Phys. Rev. Let
Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei
In the single j shell there is a two to one relationship between the spectra
of certain even-even and neighbouring odd mass nuclei e.g. the calculated
energy levels of J=0^+ states in ^{44}Ti are at twice the energies of
corresponding levels in ^{43}Ti(^{43}Sc) with J=j=7/2. Here an approximate
extension of the relationship is made by adopting a truncated seniority scheme
i.e. for ^{46}Ti and ^{45}Sc we get the relationship if we do not allow the
seniority v=4 states to mix with the v=0 and v=2 states. Better than that, we
get very close to the two to one relationship if seniority v=4 states are
admixed perturbatively. In addition, it is shown that the higher isospin states
do not contain seniority 4 admixtures.Comment: 11 pages, RevTex file and no figures, typos added, references changed
and changed content
The Origin of Power-Law Emergent Scaling in Large Binary Networks
In this paper we study the macroscopic conduction properties of large but
finite binary networks with conducting bonds. By taking a combination of a
spectral and an averaging based approach we derive asymptotic formulae for the
conduction in terms of the component proportions p and the total number of
components N. These formulae correctly identify both the percolation limits and
also the emergent power law behaviour between the percolation limits and show
the interplay between the size of the network and the deviation of the
proportion from the critical value of p = 1/2. The results compare excellently
with a large number of numerical simulations
Multi-parameter models of innovation diffusion on complex networks
A model, applicable to a range of innovation diffusion applications with a
strong peer to peer component, is developed and studied, along with methods for
its investigation and analysis. A particular application is to individual
households deciding whether to install an energy efficiency measure in their
home. The model represents these individuals as nodes on a network, each with a
variable representing their current state of adoption of the innovation. The
motivation to adopt is composed of three terms, representing personal
preference, an average of each individual's network neighbours' states and a
system average, which is a measure of the current social trend. The adoption
state of a node changes if a weighted linear combination of these factors
exceeds some threshold. Numerical simulations have been carried out, computing
the average uptake after a sufficient number of time-steps over many
realisations at a range of model parameter values, on various network
topologies, including random (Erdos-Renyi), small world (Watts-Strogatz) and
(Newman's) highly clustered, community-based networks. An analytical and
probabilistic approach has been developed to account for the observed
behaviour, which explains the results of the numerical calculations
Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations
The effects of setting all T=0 two body interaction matrix elements equal to
a constant (or zero) in shell model calculations (designated as ) are
investigated. Despite the apparent severity of such a procedure, one gets
fairly reasonable spectra. We find that using in single j shell
calculations degeneracies appear e.g. the and
states in Sc are at the same excitation energies; likewise the
I=,,9 and 10 states in Ti. The
above degeneracies involve the vanishing of certain 6j and 9j symbols. The
symmetry relations of Regge are used to explain why these vanishings are not
accidental. Thus for these states the actual deviation from degeneracy are good
indicators of the effects of the T=0 matrix elements. A further indicator of
the effects of the T=0 interaction in an even - even nucleus is to compare the
energies of states with odd angular momentum with those that are even
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