Automatic structures, rational growth and geometrically finite hyperbolic groups

We show that the set $SA(G)$ of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic group $G$ is dense in the product of the sets $SA(P)$ over all maximal parabolic subgroups $P$. The set $BSA(G)$ of equivalence classes of biautomatic structures on $G$ is isomorphic to the product of the sets $BSA(P)$ over the cusps (conjugacy classes of maximal parabolic subgroups) of $G$. Each maximal parabolic $P$ is a virtually abelian group, so $SA(P)$ and $BSA(P)$ 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 $G$ is regular. Moreover, the growth function of $G$ 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 $a$ and $b$ are the signal and image band modes of an heterodyne detector, with the field approaching an eigenstate of the photocurrent $\hat{Z}=a+b^{\dag}$. 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 $\omega+2\omega$ 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