10,482 research outputs found
Topological Frequency Conversion in a Driven Dissipative Quantum Cavity
Recent work (PRX 7, 041008) has shown that a spin coupled to two externally
supplied circularly-polarized electromagnetic modes can effectuate a
topological, quantized transfer of photons from one mode to the other. Here we
study the effect in the case when only one of the modes is externally provided,
while the other is a dynamical quantum mechanical cavity mode. Focusing on the
signatures and stability under experimentally accessible conditions, we show
that the effect persists down to the few-photon quantum limit and that it can
be used to generate highly entangled "cat states" of cavity and spin. By tuning
the strength of the external drive to a "sweet spot", the quantized pumping can
arise starting from an empty (zero photon) cavity state. We also find that
inclusion of external noise and dissipation does not suppress but rather
stabilizes the conversion effect, even after multiple cavity modes are taken
into account.Comment: 12 pages, 6 figure
Successive minima of toric height functions
Given a toric metrized R-divisor on a toric variety over a global field, we
give a formula for the essential minimum of the associated height function.
Under suitable positivity conditions, we also give formulae for all the
successive minima. We apply these results to the study, in the toric setting,
of the relation between the successive minima and other arithmetic invariants
like the height and the arithmetic volume. We also apply our formulae to
compute the successive minima for several families of examples, including
weighted projective spaces, toric bundles and translates of subtori.Comment: To appear in Annales de l'Institut Fourier (Grenoble), 40 pages, 5
figure
Pseudoriemannian metrics on spaces of bilinear structures
The space of all non degenerate bilinear structures on a manifold carries
a one parameter family of pseudo Riemannian metrics. We determine the geodesic
equation, covariant derivative, curvature, and we solve the geodesic equation
explicitly. Each space of pseudo Riemannian metrics with fixed signature is a
geodesically closed submanifold. The space of non degenerate 2-forms is also a
geodesically closed submanifold. Then we show that, if we fix a distribution on
, the space of all Riemannia metrics splits as the product of three spaces
which are everywhere mutually orthogonal, for the usual metric. We investigate
this situation in detail
The theory of parametrically amplified electron-phonon superconductivity
The ultrafast optical manipulation of ordered phases in strongly correlated
materials is a topic of significant theoretical, experimental, and
technological interest. Inspired by a recent experiment on light-induced
superconductivity in fullerenes [Mitrano et al., Nature 530, 2016], we develop
a comprehensive theory of light-induced superconductivity in driven
electron-phonon systems with lattice nonlinearities. In analogy with the
operation of parametric amplifiers, we show how the interplay between the
external drive and lattice nonlinearities lead to significantly enhanced
effective electron-phonon couplings. We provide a detailed and unbiased study
of the nonequilibrium dynamics of the driven system using the real-time Green's
function technique. To this end, we develop a Floquet generalization of the
Migdal-Eliashberg theory and derive a numerically tractable set of quantum
Floquet-Boltzmann kinetic equations for the coupled electron-phonon system. We
study the role of parametric phonon generation and electronic heating in
destroying the transient superconducting state. Finally, we predict the
transient formation of electronic Floquet bands in time- and angle-resolved
photo-emission spectroscopy experiments as a consequence of the proposed
mechanism.Comment: 42 pages, 17 figure
Trans-Planckian Dark Energy?
It has recently been proposed by Mersini et al. 01, Bastero-Gil and Mersini
02 that the dark energy could be attributed to the cosmological properties of a
scalar field with a non-standard dispersion relation that decreases
exponentially at wave-numbers larger than Planck scale (k_phys > M_Planck). In
this scenario, the energy density stored in the modes of trans-Planckian
wave-numbers but sub-Hubble frequencies produced by amplification of the vacuum
quantum fluctuations would account naturally for the dark energy. The present
article examines this model in detail and shows step by step that it does not
work. In particular, we show that this model cannot make definite predictions
since there is no well-defined vacuum state in the region of wave-numbers
considered, hence the initial data cannot be specified unambiguously. We also
show that for most choices of initial data this scenario implies the production
of a large amount of energy density (of order M_Planck^4) for modes with
momenta of order M_Planck, far in excess of the background energy density. We
evaluate the amount of fine-tuning in the initial data necessary to avoid this
back-reaction problem and find it is of order H/M_Planck. We also argue that
the equation of state of the trans-Planckian modes is not vacuum-like.
Therefore this model does not provide a suitable explanation for the dark
energy.Comment: RevTeX - 15 pages, 7 figures: final version to appear in PRD, minor
changes, 1 figure adde
Fine-Tuning Constraints on Supergravity Models
We discuss fine-tuning constraints on supergravity models. The tightest
constraints come from the experimental mass limits on two key particles: the
lightest CP even Higgs boson and the gluino. We also include the lightest
chargino which is relevant when universal gaugino masses are assumed. For each
of these particles we show how fine-tuning increases with the experimental mass
limit, for four types of supergravity model: minimal supergravity, no-scale
supergravity (relaxing the universal gaugino mass assumption), D-brane models
and anomaly mediated supersymmetry breaking models. Among these models, the
D-brane model is less fine tuned.The experimental propects for an early
discovery of Higgs and supersymmetry at LEP and the Tevatron are discussed in
this framework.Comment: 17 pages, Latex, including 5 eps figure
Social Security and Democracy
Many political economic theories use and emphasize the process of voting in their explanation of the growth of Social Security, government spending, and other public policies. But is there an empirical connection between democracy and Social Security program size or design? Using some new international data sets to produce both country-panel econometric estimates as well as case studies of South American and southern European countries, we find that Social Security policy varies according to economic and demographic factors, but that very different political histories can result in the same Social Security policy. We find little partial effect of democracy on the size of Social Security budgets, on how those budgets are allocated, or how economic and demographic factors affect Social Security. If there is any observed difference, democracies spend a little less of their GDP on Social Security, grow their budgets a bit more slowly, and cap their payroll tax more often, than do economically and demographically similar nondemocracies. Democracies and nondemocracies are equally likely to have benefit formulas inducing retirement and, conditional on GDP per capita, equally likely to induce retirement with a retirement test vs. an earnings test.
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