Symplectic reduction and topology for applications in classical molecular dynamics

This paper aims to introduce readers with backgrounds in classical molecular dynamics to some ideas in geometric mechanics that may be useful. This is done through some simple but specific examples: (i) the separation of the rotational and internal energies in an arbitrarily floppy N-body system and (ii) the reduction of the phase space accompanying the change from the laboratory coordinate system to the center of mass coordinate system relevant to molecular collision dynamics. For the case of two-body molecular systems constrained to a plane, symplectic reduction is employed to demonstrate explicitly the separation of translational, rotational, and internal energies and the corresponding reductions of the phase space describing the dynamics for Hamiltonian systems with symmetry. Further, by examining the topology of the energy-momentum map, a unified treatment is presented of the reduction results for the description of (i) the classical dynamics of rotating and vibrating diatomic molecules, which correspond to bound trajectories and (ii) the classical dynamics of atom–atom collisions, which correspond to scattering trajectories. This provides a framework for the treatment of the dynamics of larger N-body systems, including the dynamics of larger rotating and vibrating polyatomic molecular systems and the dynamics of molecule–molecule collisions

Pricing under innovation

We study pricing when firms introduce process and product innovations over time. We set up a model of endogenous productivity and markup under imperfect competition and dynamic pricing. We estimate it using output price indices reported by an unbalanced panel of 2,300 Spanish manufacturing firms during 1990-2006. Markups turn out to be procyclical and change with the introduction of innovations. Firms use innovation to increase margins, but product innovators are careful to raise prices on new or improved goods. Process innovations tend to leave prices unchanged, product innovations tend to raise prices and firms that introduce both tend to decrease them

Observation of strong electron dephasing in disordered Cu93_{93}Ge4_4Au3_3 thin films

We report the observation of strong electron dephasing in a series of disordered Cu$_{93}$Ge$_4$Au$_3$ thin films. A very short electron dephasing time possessing very weak temperature dependence around 6 K, followed by an upturn with further decrease in temperature below 4 K, is found. The upturn is progressively more pronounced in more disordered samples. Moreover, a ln$T$ dependent, but high-magnetic-field-insensitive, resistance rise persisting from above 10 K down to 30 mK is observed in the films. These results suggest a nonmagnetic dephasing process which is stronger than any known mechanism and may originate from the coupling of conduction electrons to dynamic defects.Comment: to appear in Phys. Rev. Let

Telomere length as a predictor of response to Pioglitazone in patients with unremitted depression: a preliminary study.

We studied peripheral leukocyte telomere length (LTL) as a predictor of antidepressant response to PPAR-γ agonist in patients with unremitted depression. In addition we examined correlation between LTL and the insulin resistance (IR) status in these subjects. Forty-two medically stable men and women ages 23-71 with non-remitted depression participated in double-blind placebo-controlled add-on of Pioglitazone to treatment-as-usual. Oral glucose tolerance tests were administered at baseline and at 12 weeks. Diagnostic evaluation of psychiatric disorders was performed at baseline and mood severity was followed weekly throughout the duration of the trial. At baseline, no differences in LTL were detected by depression severity, duration or chronicity. LTL was also not significantly different between insulin-resistant and insulin-sensitive subjects at baseline. Subjects with longer telomeres exhibited greater declines in depression severity in the active arm, but not in a placebo arm, P=0.005, r=-0.63, 95% confidence interval (95% CI)=(-0.84,-0.21). In addition, LTL predicted improvement in insulin sensitivity in the group overall and did not differ between intervention arms, P=0.036, r=-0.44, 95% CI=(-0.74,0.02) for the active arm, and P=0.026, r=-0.50, 95% CI=(-0.78,-0.03) for the placebo arm. LTL may emerge as a viable predictor of antidepressant response. An association between insulin sensitization and LTL regardless of the baseline IR status points to potential role of LTL as a non-specific moderator of metabolic improvement in these patients

Neutrino scattering in supernovae and spin correlations of a unitary gas

Core collapse supernova simulations can be sensitive to neutrino interactions near the neutrinosphere. This is the surface of last scattering. We model the neutrinosphere region as a warm unitary gas of neutrons. A unitary gas is a low density system of particles with large scattering lengths. We calculate modifications to neutrino scattering cross sections because of the universal spin and density correlations of a unitary gas. These correlations can be studied in laboratory cold atom experiments. We find significant reductions in cross sections, compared to free space interactions, even at relatively low densities. These reductions could reduce the delay time from core bounce to successful explosion in multidimensional supernova simulations.Comment: 5 pages, 2 figures, minor corrections in response to referee, Phys. Rev. C in pres

The metal insulator transition in cluster dynamical mean field theory: intersite correlation, cluster size, interaction strength, and the location of the transition line

To gain insight into the physics of the metal insulator transition and the effectiveness of cluster dynamical mean field theory (DMFT) we have used one, two and four site dynamical mean field theory to solve a polaron model of electrons coupled to a classical phonon field. The cluster size dependence of the metal to polaronic insulator phase boundary is determined along with electron spectral functions and cluster correlation functions. Pronounced cluster size effects start to occur in the intermediate coupling region in which the cluster calculation leads to a gap and the single-site approximation does not. Differences (in particular a sharper band edge) persist in the strong coupling regime. A partial density of states is defined encoding a generalized nesting property of the band structure; variations in this density of states account for differences between the dynamical cluster approximation and the cellular-DMFT implementations of cluster DMFT, and for differences in behavior between the single band models appropriate for cuprates and the multiband models appropriate for manganites. A pole or strong resonance in the self energy is associated with insulating states; the momentum dependence of the pole is found to distinguish between Slater-like and Mott-like mechanisms for metal insulator transition. Implications for the theoretical treatment of doped manganites are discussed.Comment: 28 pages (single column, double space) 15 figure