Pushing NRQCD to the limit

Lattice NRQCD has proven successful in describing the physics of the upsilon system and B-mesons, though some concerns arise when it is used in simulations of charm quarks. It is certainly possible that the NRQCD expansion is not converging fast enough at this scale. We present some preliminary results on the low-mass breakdown of NRQCD, in particular the behaviour of heavy quarkonium and heavy-light meson spectra as the bare heavy quark mass is decreased well below 1, with the aim of understanding more about the manifestation of this breakdown.Comment: Lattice 99 submission, 3 Pages, 3 eps figure

A generalization of Ostrowski inequality on time scales for k points

In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.Comment: 10 page

The biased odd cycle game

In this paper we consider biased Maker-Breaker games played on the edge set of a given graph $G$. We prove that for every $\delta>0$ and large enough $n$, there exists a constant $k$ for which if $\delta(G)\geq \delta n$ and $\chi(G)\geq k$, then Maker can build an odd cycle in the $(1:b)$ game for $b=O(\frac{n}{\log^2 n})$. We also consider the analogous game where Maker and Breaker claim vertices instead of edges. This is a special case of the following well known and notoriously difficult problem due to Duffus, {\L}uczak and R\"{o}dl: is it true that for any positive constants $t$ and $b$, there exists an integer $k$ such that for every graph $G$, if $\chi(G)\geq k$, then Maker can build a graph which is not $t$-colorable, in the $(1:b)$ Maker-Breaker game played on the vertices of $G$?Comment: 10 page

Signatures of Majorana Kramers pairs in superconductor-Luttinger liquid and superconductor-quantum dot-normal lead junctions

Time-reversal invariant topological superconductors are characterized by the presence of Majorana Kramers pairs localized at defects. One of the transport signatures of Majorana Kramers pairs is the quantized differential conductance of $4e^2/h$ when such a one-dimensional superconductor is coupled to a normal-metal lead. The resonant Andreev reflection, responsible for this phenomenon, can be understood as the boundary condition change for lead electrons at low energies. In this paper, we study the stability of the Andreev reflection fixed point with respect to electron-electron interactions in the Luttinger liquid. We first calculate the phase diagram for the Luttinger liquid-Majorana Kramers pair junction and show that its low-energy properties are determined by Andreev reflection scattering processes in the spin-triplet channel, i.e. the corresponding Andreev boundary conditions are similar to that in a spin-triplet superconductor - normal lead junction. We also study here a quantum dot coupled to a normal lead and a Majorana Kramers pair and investigate the effect of local repulsive interactions leading to an interplay between Kondo and Majorana correlations. Using a combination of renormalization group analysis and slave-boson mean-field theory, we show that the system flows to a new fixed point which is controlled by the Majorana interaction rather than the Kondo coupling. This Majorana fixed point is characterized by correlations between the localized spin and the fermion parity of each spin sector of the topological superconductor. We investigate the stability of the Majorana phase with respect to Gaussian fluctuations.Comment: 26 pages, 8 figure

Identification of single nucleotides in MoS2 nanopores

Ultrathin membranes have drawn much attention due to their unprecedented spatial resolution for DNA nanopore sequencing. However, the high translocation velocity (3000-50000 nt/ms) of DNA molecules moving across such membranes limits their usability. To this end, we have introduced a viscosity gradient system based on room-temperature ionic liquids (RTILs) to control the dynamics of DNA translocation through a nanometer-size pore fabricated in an atomically thin MoS2 membrane. This allows us for the first time to statistically identify all four types of nucleotides with solid state nanopores. Nucleotides are identified according to the current signatures recorded during their transient residence in the narrow orifice of the atomically thin MoS2 nanopore. In this novel architecture that exploits high viscosity of RTIL, we demonstrate single-nucleotide translocation velocity that is an optimal speed (1-50 nt/ms) for DNA sequencing, while keeping the signal to noise ratio (SNR) higher than 10. Our findings pave the way for future low-cost and rapid DNA sequencing using solid-state nanopores.Comment: Manuscript 24 pages, 4 Figures Supporting Information 24 pages, 12 Figures, 2 Tables Manuscript in review Nature Nanotechnology since May 27th 201

Two Open Universes Connected by a Wormhole: Exact Solutions

In this paper I present a spacetime of two open universes connected by a Lorentzian wormhole. The spacetime has the following features: (1) It can exactly solve the Einstein equations; (2) The weak energy condition is satisfied everywhere; (3) It has a topology of R^2\times T_g (g\ge 2); (4) It has no event horizons.Comment: 10 pages, late