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

Photoassociation adiabatic passage of ultracold Rb atoms to form ultracold Rb_2 molecules

We theoretically explore photoassociation by Adiabatic Passage of two colliding cold ^{85}Rb atoms in an atomic trap to form an ultracold Rb_2 molecule. We consider the incoherent thermal nature of the scattering process in a trap and show that coherent manipulations of the atomic ensemble, such as adiabatic passage, are feasible if performed within the coherence time window dictated by the temperature, which is relatively long for cold atoms. We show that a sequence of ~2*10^7 pulses of moderate intensities, each lasting ~750 ns, can photoassociate a large fraction of the atomic ensemble at temperature of 100 microkelvin and density of 10^{11} atoms/cm^3. Use of multiple pulse sequences makes it possible to populate the ground vibrational state. Employing spontaneous decay from a selected excited state, one can accumulate the molecules in a narrow distribution of vibrational states in the ground electronic potential. Alternatively, by removing the created molecules from the beam path between pulse sets, one can create a low-density ensemble of molecules in their ground ro-vibrational state.Comment: RevTex, 23 pages, 9 figure