Applications of shuffle product to restricted decomposition formulas for multiple zeta values

In this paper we obtain a recursive formula for the shuffle product and apply it to derive two restricted decomposition formulas for multiple zeta values (MZVs). The first formula generalizes the decomposition formula of Euler and is similar to the restricted formula of Eie and Wei for MZVs with one strings of 1's. The second formula generalizes the previous results to the product of two MZVs with one and two strings of 1's respectively.Comment: 11 page

Vertical absorption edge and universal onset conductance in semi-hydrogenated graphene

We show that for graphene with any finite difference in the on-site energy between the two sub-lattices ($\Delta$), The optical absorption edge is determined by the $\Delta$. The universal conductance will be broken and the conductance near the band edge varies with frequency as $1/\omega^2$. Moreover, we have identified another universal conductance for such systems without inversion symmetry, i.e., the onset conductance at the band edge is $\sigma_c=2\sigma_0=\pi e^2/2h$, independent of the size of the band gap. The total integrated optical response is nearly conserved despite of the opening of the band gap.Comment: 4 pages, 4 figure

Driving dynamic colloidal assembly using eccentric self-propelled colloids

Designing protocols to dynamically direct the self-assembly of colloidal particles has become an important direction in soft matter physics because of the promising applications in fabrication of dynamic responsive functional materials. Here using computer simulations, we found that in the mixture of passive colloids and eccentric self-propelled active particles, when the eccentricity and self-propulsion of active particles are high enough, the eccentric active particles can push passive colloids to form a large dense dynamic cluster, and the system undergoes a novel dynamic demixing transition. Our simulations show that the dynamic demixing occurs when the eccentric active particles move much faster than the passive particles such that the dynamic trajectories of different active particles can overlap with each other while passive particles are depleted from the dynamic trajectories of active particles. Our results suggest that this is in analogy to the entropy driven demixing in colloid-polymer mixtures, in which polymer random coils can overlap with each other while deplete the colloids. More interestingly, we find that by fixing the passive colloid composition at certain value, with increasing the density, the system undergoes an intriguing re-entrant mixing, and the demixing only occurs within certain intermediate density range. This suggests a new way of designing active matter to drive the self-assembly of passive colloids and fabricate dynamic responsive materials.Comment: Accepted in Soft Matter. Supplementary information can found at https://www.dropbox.com/sh/xb3u5iaoucc2ild/AABFUyqjXips7ewaie2rFbj_a?dl=

Quantum transport through double-dot Aharonov-Bohm interferometry in Coulomb blockade regime

Transport through two quantum dots laterally embedded in Aharonov-Bohm interferometry with infinite intradot and arbitrary interdot Coulomb repulsion is analyzed in the weak coupling and Coulomb blockade regime. By employing the modified quantum rate equations and the slave-boson approach, we establish a general dc current formula at temperatures higher than the Kondo temperature for the case that the spin degenerate levels of two dots are close to each other. We examine two simple examples for identical dots - no doubly occupied states and no empty state. In the former, completely destructive coherent transport and phase locking appear at magnetic flux $\Phi=\Phi_{0}/2$ and $\Phi=0$ respectively; in the latter, partially coherent transport exhibits an oscillation with magnetic flux having a period of $\Phi_0$.Comment: 8 pages, 3 figure