35,575 research outputs found
Automatic structures, rational growth and geometrically finite hyperbolic groups
We show that the set of equivalence classes of synchronously
automatic structures on a geometrically finite hyperbolic group is dense in
the product of the sets over all maximal parabolic subgroups . The
set of equivalence classes of biautomatic structures on is
isomorphic to the product of the sets over the cusps (conjugacy
classes of maximal parabolic subgroups) of . Each maximal parabolic is a
virtually abelian group, so and were computed in ``Equivalent
automatic structures and their boundaries'' by M.Shapiro and W.Neumann, Intern.
J. of Alg. Comp. 2 (1992) We show that any geometrically finite hyperbolic
group has a generating set for which the full language of geodesics for is
regular. Moreover, the growth function of with respect to this generating
set is rational. We also determine which automatic structures on such a group
are equivalent to geodesic ones. Not all are, though all biautomatic structures
are.Comment: Plain Tex, 26 pages, no figure
Two-mode heterodyne phase detection
We present an experimental scheme that achieves ideal phase detection on a
two-mode field. The two modes and are the signal and image band modes
of an heterodyne detector, with the field approaching an eigenstate of the
photocurrent . The field is obtained by means of a
high-gain phase-insensitive amplifier followed by a high-transmissivity
beam-splitter with a strong local oscillator at the frequency of one of the two
modes.Comment: 3 pages, 1 figur
Laser-induced currents along molecular wire junctions
The treatment of the previous paper is extended to molecular wires.
Specifically, the effect of electron-vibrational interactions on the electronic
transport induced by femtosecond laser fields along unbiased
molecular nanojunctions is investigated. For this, the photoinduced vibronic
dynamics of trans-polyacetylene oligomers coupled to macroscopic metallic leads
is followed in a mean-field mixed quantum-classical approximation. A reduced
description of the dynamics is obtained by introducing projective lead-molecule
couplings and deriving an effective Schr\"odinger equation satisfied by the
orbitals in the molecular region. Two possible rectification mechanisms are
identified and investigated. The first one relies on near-resonance
photon-absorption and is shown to be fragile to the ultrafast electronic
decoherence processes introduced by the wire's vibrations. The second one
employs the dynamic Stark effect and is demonstrated to be highly efficient and
robust to electron-vibrational interactions.Comment: 14 pages, 10 figures. Accepted in J. Chem. Phy
Thin-Slice Forecasts of Gubernatorial Elections
We showed 10-second, silent video clips of unfamiliar gubernatorial debates to a group of experimental participants and asked them to predict the election outcomes. The participants' predictions explain more than 20 percent of the variation in the actual two-party vote share across the 58 elections in our study, and their importance survives a range of controls, including state fixed effects. In a horse race of alternative forecasting models, participants' visual forecasts significantly outperform economic variables in predicting vote shares, and are comparable in predictive power to a measure of incumbency status. Adding policy information to the video clips by turning on the sound tends, if anything, to worsen participants' accuracy, suggesting that naïveté may be an asset in some forecasting tasks.
Time-Optimal Transfer of Coherence
We provide exact analytical solutions for the problem of time-optimal
transfer of coherence from one spin polarization to a three-fold coherence in a
trilinear Ising chain with a fixed energy available and subject to local
controls with a non negligible time cost. The time of transfer is optimal and
consistent with a previous numerical result obtained assuming instantaneous
local controls.Comment: Published version (with typos in eqs. (25)-(27) corrected
Vacuum effective action and inflation
We consider vacuum quantum effects in the Early Universe, which may lead to
inflation. The inflation is a direct consequence of the supposition that, at
high energies, all the particles can be described by the weakly interacting,
massless, conformally invariant fields. We discuss, from the effective field
theory point of view, the stability of inflation, transition to the FRW
solution, and also possibility to study metric and density perturbations.Comment: 6 pages, LaTeX, no figures. Contribution to the Proceedings of the X
Jorge Andre Swieca school in Particles and Fields. To be published in World
Scientifi
Quantum Noise in the Collective Abstraction Reaction A+B AB+B
We demonstrate theoretically that the collective abstraction reaction A+B AB+B can be realized efficiently with degenerate bosonic or fermionic
matter waves. We show that this is dominated by quantum fluctuations, which are
critical in triggering its initial stages with the appearance of macroscopic
non-classical correlations of the atomic and molecular fields as a result. This
study opens up a promising new regime of quantum degenerate matter-wave
chemistry.Comment: 4 pages, 3 figures, publishe
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