Electron-Transport Properties of Na Nanowires under Applied Bias Voltages

We present first-principles calculations on electron transport through Na nanowires at finite bias voltages. The nanowire exhibits a nonlinear current-voltage characteristic and negative differential conductance. The latter is explained by the drastic suppression of the transmission peaks which is attributed to the electron transportability of the negatively biased plinth attached to the end of the nanowire. In addition, the finding that a voltage drop preferentially occurs on the negatively biased side of the nanowire is discussed in relation to the electronic structure and conduction.Comment: 4 pages, 6 figure

Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual

We study Vasiliev's system of higher spin gauge fields coupled to massive scalars in AdS_3, and compute the tree level two and three point functions. These are compared to the large N limit of the W_N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.Comment: 58 pages; typos corrected, references adde

On the Quantum Invariant for the Brieskorn Homology Spheres

We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres $\Sigma(p_1,p_2,p_3)$ by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit $\tau\to N \in \mathbb{Z}$. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern-Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.Comment: 26 pages, 2 figure

Arithmetical Congruence Preservation: from Finite to Infinite

Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational polynomials (taking only integral values) and the function giving the least common multiple of $1,2,\ldots,k$. The tool used to obtain these characterizations is "lifting": if $\pi\colon X\to Y$ is a surjective morphism, and $f$ a function on $Y$ a lifting of $f$ is a function $F$ on $X$ such that $\pi\circ F=f\circ\pi$. In this paper we relate the finite and infinite notions by proving that the finite case can be lifted to the infinite one. For $p$-adic and profinite integers we get similar characterizations via lifting. We also prove that lattices of recognizable subsets of $Z$ are stable under inverse image by congruence preserving functions

Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: The minimal dimension of a canonical measure)

In this paper, we formulate the geometric Bogomolov conjecture for abelian varieties, and give some partial answers to it. In fact, we insist in a main theorem that under some degeneracy condition, a closed subvariety of an abelian variety does not have a dense subset of small points if it is a non-special subvariety. The key of the proof is the study of the minimal dimension of the components of a canonical measure on the tropicalization of the closed subvariety. Then we can apply the tropical version of equidistribution theory due to Gubler. This article includes an appendix by Walter Gubler. He shows that the minimal dimension of the components of a canonical measure is equal to the dimension of the abelian part of the subvariety. We can apply this result to make a further contribution to the geometric Bogomolov conjecture.Comment: 30 page

Structure of a translocation signal domain mediating conjugative transfer by Type IV secretion systems

Relaxases are proteins responsible for the transfer of plasmid and chromosomal DNA from one bacterium to another during conjugation. They covalently react with a specific phosphodiester bond within DNA origin of transfer sequences, forming a nucleo-protein complex which is subsequently recruited for transport by a plasmid-encoded type IV secretion system. In previous work we identified the targeting translocation signals presented by the conjugative relaxase TraI of plasmid R1. Here we report the structure of TraI translocation signal TSA. In contrast to known translocation signals we show that TSA is an independent folding unit and thus forms a bona fide structural domain. This domain can be further divided into three sub-domains with striking structural homology with helicase sub-domains of the SF1B family. We also show that TSA is part of a larger vestigial helicase domain which has lost its helicase activity but not its single-stranded DNA binding capability. Finally, we further delineate the binding site responsible for translocation activity of TSA by targeting single residues for mutations. Overall, this study provides the first evidence that translocation signals can be part of larger structural scaffolds, overlapping with translocation-independent activities

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

The early part of the gravitational wave signal of binary neutron star inspirals can potentially yield robust information on the nuclear equation of state. The influence of a star's internal structure on the waveform is characterized by a single parameter: the tidal deformability lambda, which measures the star's quadrupole deformation in response to the companion's perturbing tidal field. We calculate lambda for a wide range of equations of state and find that the value of lambda spans an order of magnitude for the range of equation of state models considered. An analysis of the feasibility of discriminating between neutron star equations of state with gravitational wave observations of the early part of the inspiral reveals that the measurement error in lambda increases steeply with the total mass of the binary. Comparing the errors with the expected range of lambda, we find that Advanced LIGO observations of binaries at a distance of 100 Mpc will probe only unusually stiff equations of state, while the proposed Einstein Telescope is likely to see a clean tidal signature.Comment: 12 pages, submitted to PR

Effects of non-magnetic impurities on spin-fluctuations induced superconductivity

We study the effects of non-magnetic impurities on the phase diagram of a system of interacting electrons with a flat Fermi surface. The one-loop Wilsonian renormalization group flow of the angle dependent diffusion function $D(\theta_1,\theta_2,\theta_3)$ and interaction $U(\theta_1,\theta_2,\theta_3)$ determines the critical temperature and the nature of the low temperature state. As the imperfect nesting increases the critical temperature decreases and the low temperature phase changes from the spin-density wave (SDW) to the d-wave superconductivity (dSC) and finally, for bad nesting, to the random antiferromagnetic state (RAF). Both SDW and dSC phases are affected by disorder. The pair breaking depends on the imperfect nesting and is the most efficient when the critical temperature for superconductivity is maximal.Comment: 4 pages, 4 figures. Submitted to PR