Quantum recurrences versus stability

Consequences of quantum recurrences on the stability of a broad class of dynamical systems is presented.Comment: to appear in Physics Lett.

Functionalization of carbon nanotubes with -CHn, -NHn fragments, -COOH and -OH groups

We present results of extensive theoretical studies concerning stability, morphology, and band structure of single wall carbon nanotubes (CNTs) covalently functionalized by -CHn(for n=2,3,4),-NHn(for n=1,2,3,4),-COOH and -OH groups. Our studies are based on ab initio calculations in the framework of the density functional theory. We determine the dependence of the binding energies on the concentration of the adsorbed molecules, critical densities of adsorbed molecules, global and local changes in the morphology, and electronic structure paying particular attention to the functionalization induced changes of the band gaps. These studies reveal physical mechanisms that determine stability and electronic structure of those systems and also provide valuable theoretical predictions relevant for application. Functionalization of CNTs causes generally their elongation and locally sp2 -> sp3 rehybridization in the neighborhood of chemisorbed groups. For adsorbants making particularly strong covalent bonds with the CNTs(-CH2), we observe formation of the 5/7 defects. In CNTs functionalized with -CH2,-NH4, and -OH, we determine critical density of molecules that could be covalently bound to CNTs. Functionalization of CNTs can be utilized for band gap engineering and also lead to changes in their metallic/semiconductor character. In semiconducting CNTs, adsorbants such as -CH3,-NH2,-OH and -COOH, introduce 'impurity' bands in the band gap of pristine CNTs. In the case of -CH3,-NH2, the induced band gaps are typically smaller than in the pure CNT and depend strongly on the concentration of adsorbants. However, functionalization of semiconducting CNTs with -OH leads to the metallization of CNTs. On the other hand, the functionalization of semi-metallic (9,0)CNT with -CH2 causes the increase of the band gap and induces semi-metal to semiconductor transition.Comment: accepted in Journal of Chemical Physic

On the structure of positive maps II: low dimensional matrix algebras

We use a new idea that emerged in the examination of exposed positive maps between matrix algebras to investigate in more detail the difference between positive maps on $M_2(C)$ and $M_3(C)$. Our main tool stems from classical Grothendieck theorem on tensor product of Banach spaces and is an older and more general version of Choi-Jamiolkowski isomorphism between positive maps and block positive Choi matrices. It takes into account the correct topology on the latter set that is induced by the uniform topology on positive maps. In this setting we show that in $M_2(C)$ case a large class of nice positive maps can be generated from the small set of maps represented by self-adjoint unitaries, $2 P_x$ with $x$ maximally entangled vector and $p\otimes 1$ with $p$ rank 1 projector. We show why this construction fails in $M_3(C)$ case. There are also similarities. In both $M_2(C)$ and $M_3(C)$ cases any unital positive map represented by self-adjoint unitary is unitarily equivalent to the transposition map. Consequently we obtain a large family of exposed maps. We also investigate a convex structure of the Choi map, the first example of non-decomposable map. As a result the nature of the Choi map will be explained. This gives an information on the origin of appearance of non-decomposable maps on $M_3(C)$.Comment: Lemma 5 (in previous version, false) is removed. We would be very grateful for any remar