Effects of Isotope Substitution on Local Heating and Inelastic current in Hydrogen Molecular Junctions

Using first principle approaches, we investigate the effects of isotope substitution on the inelastic features in the hydrogen molecular junction. We observe thatlocal heating and inelastic current have significant isotope-substitution effects. Due to the contact characters, the energies of excited molecular vibrationsare inverse proportional to the square root of the mass. The heavier the molecule, the smaller the onset bias. In the $H_{2}$ and $D_{2}$ junctions, the heavier molecule has a smaller magnitude of electron-vibration interaction. Consequently, there is a crossing in the local temperature around $80 K$. In the HD junction, the electron-vibration interaction is enhanced by asymmetric distribution in mass. It leads to the largest discontinuity in the differential conductance and the most prominent heating in the HD junction. We predict that the junction instability is relevant to isotope substitution. The HD junction has the smallest breakdown voltage compared with the $H_{2}$ and $D_{2}$ junction

Sharp benefit-to-cost rules for the evolution of cooperation on regular graphs

We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman and Nowak [Nature 441 (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then we present a first-order approximation for fixation probabilities of general voter model perturbations on finite graphs subject to small perturbation in terms of the voter model fixation probabilities. In the context of regular graphs, we obtain algebraically explicit first-order approximations for the fixation probabilities of cooperators distributed as certain uniform distributions. These approximations lead to a rigorous proof that both of the rules of Ohtsuki et al. are valid and are sharp.Comment: Published in at http://dx.doi.org/10.1214/12-AAP849 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Seebeck coefficient of thermoelectric moleculat junction: First-principles calculations

A first-principles approach is presented for the thermoelectricity in molecular junctions formed by a single molecule contact. The study investigates the Seebeck coefficient considering the source-drain electrodes with distinct temperatures and chemical potentials in a three-terminal geometry junction. We compare the Seebeck coefficient in the amino-substituted and unsubstituted butanethiol junction and observe interesting thermoelectric properties in the amino-substituted junction. Due to the novel states around the Fermi levels introduced by the amino-substitution, the Seebeck coefficient could be easily modulated by using gate voltages and biases. When the temperature in one of the electrodes is fixed, the Seebeck coefficient varies significantly with the temperature in the other electrode, and such dependence could be modulated by varying the gate voltages. As the biases increase, richer features in the Seebeck coefficient are observed, which are closely related to the transmission functions in the vicinity of the left and right Fermi levels.Comment: 4 pages; 2 figure