Neutral triplet Collective Mode as a new decay channel in Graphite

In an earlier work we predicted the existence of a neutral triplet collective mode in undoped graphene and graphite [Phys. Rev. Lett. {\bf 89} (2002) 16402]. In this work we study a phenomenological Hamiltonian describing the interaction of tight-binding electrons on honeycomb lattice with such a dispersive neutral triplet boson. Our Hamiltonian is a generalization of the Holstein polaron problem to the case of triplet bosons with non-trivial dispersion all over the Brillouin zone. This collective mode constitutes an important excitation branch which can contribute to the decay rate of the electronic excitations. The presence of such collective mode, modifies the spectral properties of electrons in graphite and undoped graphene. In particular such collective mode, as will be shown in this paper, can account for some part of the missing decay rate in a time-domain measurement done on graphite

On the Approximability and Hardness of the Minimum Connected Dominating Set with Routing Cost Constraint

In the problem of minimum connected dominating set with routing cost constraint, we are given a graph $G=(V,E)$, and the goal is to find the smallest connected dominating set $D$ of $G$ such that, for any two non-adjacent vertices $u$ and $v$ in $G$, the number of internal nodes on the shortest path between $u$ and $v$ in the subgraph of $G$ induced by $D \cup \{u,v\}$ is at most $\alpha$ times that in $G$. For general graphs, the only known previous approximability result is an $O(\log n)$-approximation algorithm ($n=|V|$) for $\alpha = 1$ by Ding et al. For any constant $\alpha > 1$, we give an $O(n^{1-\frac{1}{\alpha}}(\log n)^{\frac{1}{\alpha}})$-approximation algorithm. When $\alpha \geq 5$, we give an $O(\sqrt{n}\log n)$-approximation algorithm. Finally, we prove that, when $\alpha =2$, unless $NP \subseteq DTIME(n^{poly\log n})$, for any constant $\epsilon > 0$, the problem admits no polynomial-time $2^{\log^{1-\epsilon}n}$-approximation algorithm, improving upon the $\Omega(\log n)$ bound by Du et al. (albeit under a stronger hardness assumption)

Uniqueness of Nash equilibria in quantum Cournot duopoly game

A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.Comment: 7 pages, 2 figure

CP Violating Rate Difference Relations for B→PPB\to PP and B→PVB \to PV in Broken SU(3)

Within the standard model there exist certain relations between CP violating rate differences in B decays in the SU(3) limit. We study SU(3) breaking corrections to these relations in the case of charmless, hadronic, two body $B$ decays using the improved factorization model of Ref.\cite{3}. We consider the cases $B \to PP$ and $B \to PV$ for both $B_d$ and $B_s$ mesons. We present an estimate for $A_{CP}(\pi^- \pi^+)$ in terms of $A_{CP}(K^- \pi^+)$.Comment: Latex 13 pages, no figure