On the stability of Hamiltonian relative equilibria with non-trivial isotropy

We consider Hamiltonian systems with symmetry, and relative equilibria with isotropy subgroup of positive dimension. The stability of such relative equilibria has been studied by Ortega and Ratiu and by Lerman and Singer. In both papers the authors give sufficient conditions for stability which require first determining a splitting of a subspace of the Lie algebra of the symmetry group, with different splittings giving different criteria. In this note we remove this splitting construction and so provide a more general and more easily computed criterion for stability. The result is also extended to apply to systems whose momentum map is not coadjoint equivariant

Dynamical phases and intermittency of the dissipative quantum Ising model

We employ the concept of a dynamical, activity order parameter to study the Ising model in a transverse magnetic field coupled to a Markovian bath. For a certain range of values of the spin-spin coupling, magnetic field and dissipation rate, we identify a first order dynamical phase transition between active and inactive {\em dynamical phases}. We demonstrate that dynamical phase-coexistence becomes manifest in an intermittent behavior of the bath quanta emission. Moreover, we establish the connection between the dynamical order parameter that quantifies the activity, and the longitudinal magnetization that serves as static order parameter. The system we consider can be implemented in current experiments with Rydberg atoms and trapped ions

Stability of relative equilibria with singular momentum values in simple mechanical systems

A method for testing $G_\mu$-stability of relative equilibria in Hamiltonian systems of the form "kinetic + potential energy" is presented. This method extends the Reduced Energy-Momentum Method of Simo et al. to the case of non-free group actions and singular momentum values. A normal form for the symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve

Universal time-evolution of a Rydberg lattice gas with perfect blockade

We investigate the dynamics of a strongly interacting spin system that is motivated by current experimental realizations of strongly interacting Rydberg gases in lattices. In particular we are interested in the temporal evolution of quantities such as the density of Rydberg atoms and density-density correlations when the system is initialized in a fully polarized state without Rydberg excitations. We show that in the thermodynamic limit the expectation values of these observables converge at least logarithmically to universal functions and outline a method to obtain these functions. We prove that a finite one-dimensional system follows this universal behavior up to a given time. The length of this universal time period depends on the actual system size. This shows that already the study of small systems allows to make precise predictions about the thermodynamic limit provided that the observation time is sufficiently short. We discuss this for various observables and for systems with different dimensions, interaction ranges and boundary conditions.Comment: 16 pages, 3 figure

Synthesis, Photochemical, and Redox Properties of Gold(I) and Gold(III) Pincer Complexes Incorporating a 2,2′:6′,2″-Terpyridine Ligand Framework

Reaction of [Au(C6F5)(tht)] (tht = tetrahydrothiophene) with 2,2′:6′,2″-terpyridine (terpy) leads to complex [Au(C6F5)(η1-terpy)] (1). The chemical oxidation of complex (1) with 2 equiv of [N(C6H4Br-4)3](PF6) or using electrosynthetic techniques affords the Au(III) complex [Au(C6F5)(η3-terpy)](PF6)2 (2). The X-ray diffraction study of complex 2 reveals that the terpyridine acts as tridentate chelate ligand, which leads to a slightly distorted square-planar geometry. Complex 1 displays fluorescence in the solid state at 77 K due to a metal (gold) to ligand (terpy) charge transfer transition, whereas complex 2 displays fluorescence in acetonitrile due to excimer or exciplex formation. Time-dependent density functional theory calculations match the experimental absorption spectra of the synthesized complexes. In order to further probe the frontier orbitals of both complexes and study their redox behavior, each compound was separately characterized using cyclic voltammetry. The bulk electrolysis of a solution of complex 1 was analyzed by spectroscopic methods confirming the electrochemical synthesis of complex 2

Cluster Transformation Coefficients for Structure and Dynamics Calculations in n-Particle Systems: Atoms, Nuclei, and Quarks

The structure and dynamics of an n-particle system are described with coupled nonlinear Heisenberg's commutator equations where the nonlinear terms are generated by the two-body interaction that excites the reference vacuum via particle-particle and particle-hole excitations. Nonperturbative solutions of the system are obtained with the use of dynamic linearization approximation and cluster transformation coefficients. The dynamic linearization approximation converts the commutator chain into an eigenvalue problem. The cluster coefficients factorize the matrix elements of the (n)-particles or particle-hole systems in terms of the matrix elements of the (n-1)-systems coupled to a particle-particle, particle-hole, and hole-hole boson. Group properties of the particle-particle, particle-hole, and hole-hole permutation groups simplify the calculation of these coefficients. The particle-particle vacuum-excitations generate superconductive diagrams in the dynamics of 3-quarks systems. Applications of the model to fermionic and bosonic systems are discussed.Comment: 13 pages, 5 figures, Wigner Proceedings for Conference Wigner Centenial Pecs, July 8-12, 200

Exclusive measurement of coherent eta photoproduction from the deuteron

Coherent photoproduction of eta mesons from the deuteron has been measured from threshold up to incident photon energies of 750 MeV using the photon spectrometer TAPS at the tagged photon facility at the Mainz microtron MAMI. For the first time, differential coherent cross sections have been deduced from the coincident detection of the eta meson and the recoil deuteron. A missing energy analysis was used for the suppression of background events so that a very clean identification of coherent eta-photoproduction was achieved. The resulting cross sections agree with previous experimental results except for angles around 90 deg in the photon-deuteron cm-system where they are smaller. They are compared to various model calculations.Comment: 4 pages, 4 figure

Quasi-free Compton Scattering and the Polarizabilities of the Neutron

Differential cross sections for quasi-free Compton scattering from the proton and neutron bound in the deuteron have been measured using the Glasgow/Mainz tagging spectrometer at the Mainz MAMI accelerator together with the Mainz 48 cm $\oslash$ $\times$ 64 cm NaI(Tl) photon detector and the G\"ottingen SENECA recoil detector. The data cover photon energies ranging from 200 MeV to 400 MeV at $\theta^{LAB}_\gamma=136.2^\circ$. Liquid deuterium and hydrogen targets allowed direct comparison of free and quasi-free scattering from the proton. The neutron detection efficiency of the SENECA detector was measured via the reaction $p(\gamma,\pi^+ n)$. The "free" proton Compton scattering cross sections extracted from the bound proton data are in reasonable agreement with those for the free proton which gives confidence in the method to extract the differential cross section for free scattering from quasi-free data. Differential cross sections on the free neutron have been extracted and the difference of the electromagnetic polarizabilities of the neutron have been obtained to be $\alpha-\beta= 9.8\pm 3.6(stat){}^{2.1}_1.1(syst)\pm 2.2(model)$ in units $10^{-4}fm^3$. In combination with the polarizability sum $\alpha +\beta=15.2\pm 0.5$ deduced from photoabsorption data, the neutron electric and magnetic polarizabilities, $\alpha_n=12.5\pm 1.8(stat){}^{+1.1}_{-0.6}\pm 1.1(model)$ and $\beta_n=2.7\mp 1.8(stat){}^{+0.6}_{-1.1}(syst)\mp 1.1(model)$ are obtained. The backward spin polarizability of the neutron was determined to be $\gamma^{(n)}_\pi=(58.6\pm 4.0)\times 10^{-4}fm^4$

Linking Spanish wine farmers to international markets: Is direct export better than indirect export in improving farm performance?

Selecting an appropriate export channel is one of farmers’ most important strategic decisions as it determines farm performance. Although direct and indirect exports are two important channels linking farmers to international markets, little is known about whether direct export is better than indirect export in improving farm performance. This study addresses this research gap by analyzing the impact of export channel choice on wine export farm performance, utilizing data collected from 479 wine-exporting farmers from Spain. An inverse probability-weighted regression adjustment estimator addresses the selection bias issue of export channel choice. The results show that the wine export price received by the direct exporters is significantly lower than that received by the indirect exports. Using domestic intermediaries for exportation (i.e. indirect export) can reduce information asymmetry and transaction costs, which enable indirect wine exporters to sell their products at higher prices. However, there are no significant differences between direct and indirect exporters in export volume, value, diversity, and satisfaction. The findings highlight that direct and indirect exports do not generate differentiated profits, and wine farmers should choose one of them that can facilitate their access to international markets

Neutron polarizabilities investigated by quasi-free Compton scattering from the deuteron

Measuring Compton scattered photons and recoil neutrons in coincidence, quasi-free Compton scattering by the neutron has been investigated at MAMI (Mainz) at $theta^{lab}_\gamma=136^o$ in an energy range from 200 to 400 MeV. From the data a polarizability difference of $\alpha_n - \beta_n = 9.8 \pm 3.6(stat)^{+2.1}_{-1.1}(syst)\pm 2.2(model)$ in units of $10^{-4}fm^3$ has been determined. In combination with the polarizability sum $\alpha_n+\beta_n= 15.2\pm 0.5$ deduced from photo absorption data, the neutron electric and magnetic polarizabilities, $\alpha_n=12.5\pm 1.8(stat)^{+1.1}_{-0.6}(syst)\pm 1.1(model)$ and $\beta_n = 2.7\mp 1.8(stat)^{+0.6}_{-1.1}(syst)\mp 1.1(model)$, are obtained