First steps towards total reality of meromorphic functions

It was earlier conjectured by the second and the third authors that any rational curve $g:{\mathbb C}P^1\to {\mathbb C}P^n$ such that the inverse images of all its flattening points lie on the real line ${\mathbb R}P^1\subset {\mathbb C}P^1$ is real algebraic up to a linear fractional transformation of the image ${\mathbb C}P^n$. (By a flattening point $p$ on $g$ we mean a point at which the Frenet $n$-frame $(g',g'',...,g^{(n)})$ is degenerate.) Below we extend this conjecture to the case of meromorphic functions on real algebraic curves of higher genera and settle it for meromorphic functions of degrees $2,3$ and several other cases.Comment: 10 pages, 1 figur

Robust ultrafast currents in molecular wires through Stark shifts

A novel way to induce ultrafast currents in molecular wires using two incident laser frequencies, $\omega$ and $2\omega$, is demonstrated. The mechanism relies on Stark shifts, instead of photon absorption, to transfer population to the excited states and exploits the temporal profile of the field to generate phase controllable transport. Calculations in a \emph{trans}-polyacetylene oligomer coupled to metallic leads indicate that the mechanism is highly efficient and robust to ultrafast electronic dephasing processes induced by vibronic couplings.Comment: 4 pages, 2 figures, accepted to Physical Review Letter

Do supernovae of type 1 paly a role in cosmic-ray production?

A model of cosmic-ray origin is suggested which aims to account for some salient features of the composition. Relative to solar abundances, the Galactic cosmic rays (GCR) are deficient in hydrogen and helim (H and He) by an order of magnitude when the two compositions are normalized at iron. Our conjectural model implicates supernovae of Type I (SN-I) as sources of some of the GCR. SN-I occur approximately as often as SN-II, through their genesis is thought to be different. Recent studies of nucleosynthesis in SN-I based on accreting white dwarfs, find that the elements from Si to Fe are produced copiously. On the other hand, SN-I are virtually devoid of hydrogen, and upper limits deduced for He are low. If SN-I contribute significantly to the pool of GCR by injecting energetic particles into the interstellar medium (ISM), then this could explain why the resulting GCR is relatively deficient in H and He. A test of the model is proposed, and difficulties are discussed

On total reality of meromorphic functions

We show that if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points then it is conjugate to a real meromorphic function after a suitable projective automorphism of the image.Comment: 13 page

Cluster algebras and Poisson geometry

We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of connected components of refined open Bruhat cells in Grassmanians G(k,n) over real numbers.Comment: minor change