Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"

Comment on "Indispensable Finite Time Correlations for Fokker-Planck Equations from Time Series Data"Comment: 2 pages, 1 figur

Structure of self-assembled Mn atom chains on Si(001)

Mn has been found to self-assemble into atomic chains running perpendicular to the surface dimer reconstruction on Si(001). They differ from other atomic chains by a striking asymmetric appearance in filled state scanning tunneling microscopy (STM) images. This has prompted complicated structural models involving up to three Mn atoms per chain unit. Combining STM, atomic force microscopy and density functional theory we find that a simple necklace-like chain of single Mn atoms reproduces all their prominent features, including their asymmetry not captured by current models. The upshot is a remarkably simpler structure for modelling the electronic and magnetic properties of Mn atom chains on Si(001).Comment: 5 pages, 4 figure

Electronic coupling between Bi nanolines and the Si(001) substrate: An experimental and theoretical study

Atomic nanolines are one dimensional systems realized by assembling many atoms on a substrate into long arrays. The electronic properties of the nanolines depend on those of the substrate. Here, we demonstrate that to fully understand the electronic properties of Bi nanolines on clean Si(001) several different contributions must be accounted for. Scanning tunneling microscopy reveals a variety of different patterns along the nanolines as the imaging bias is varied. We observe an electronic phase shift of the Bi dimers, associated with imaging atomic p-orbitals, and an electronic coupling between the Bi nanoline and neighbouring Si dimers, which influences the appearance of both. Understanding the interplay between the Bi nanolines and Si substrate could open a novel route to modifying the electronic properties of the nanolines.Comment: 6 pages (main), 2 pages (SI), accepted by Phys. Rev.

Endotaxial Si nanolines in Si(001):H

We present a detailed study of the structural and electronic properties of a self-assembled silicon nanoline embedded in the H-terminated silicon (001) surface, known as the Haiku stripe. The nanoline is a perfectly straight and defect free endotaxial structure of huge aspect ratio; it can grow micrometre long at a constant width of exactly four Si dimers (1.54nm). Another remarkable property is its capacity to be exposed to air without suffering any degradation. The nanoline grows independently of any step edges at tunable densities, from isolated nanolines to a dense array of nanolines. In addition to these unique structural characteristics, scanning tunnelling microscopy and density functional theory reveal a one-dimensional state confined along the Haiku core. This nanoline is a promising candidate for the long sought after electronic solid-state one-dimensional model system to explore the fascinating quantum properties emerging in such reduced dimensionality.Comment: 8 pages, 6 figure

One dimensional Si-in-Si(001) template for single-atom wire growth

Single atom metallic wires of arbitrary length are of immense technological and scientific interest. We describe a novel silicon-only template enabling the self-organised growth of isolated micrometer long surface and subsurface single-atom chains. It consists of a one dimensional, defect-free reconstruction - the Haiku core, here revealed for the first time in details - self-assembled on hydrogenated Si(001) terraces, independent of any step edges. We discuss the potential of this Si-in-Si template as an appealing alternative to vicinal surfaces for nanoscale patterning.Comment: 3 pages, 2 figure

On low-sampling-rate Kramers-Moyal coefficients

We analyze the impact of the sampling interval on the estimation of Kramers-Moyal coefficients. We obtain the finite-time expressions of these coefficients for several standard processes. We also analyze extreme situations such as the independence and no-fluctuation limits that constitute useful references. Our results aim at aiding the proper extraction of information in data-driven analysis.Comment: 9 pages, 4 figure

A Quantum-Proof Non-Malleable Extractor, With Application to Privacy Amplification against Active Quantum Adversaries

In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret $X$ in order to establish a shared private key $K$ by exchanging messages over an insecure communication channel. If the channel is authenticated the task can be solved in a single round of communication using a strong randomness extractor; choosing a quantum-proof extractor allows one to establish security against quantum adversaries. In the case that the channel is not authenticated, Dodis and Wichs (STOC'09) showed that the problem can be solved in two rounds of communication using a non-malleable extractor, a stronger pseudo-random construction than a strong extractor. We give the first construction of a non-malleable extractor that is secure against quantum adversaries. The extractor is based on a construction by Li (FOCS'12), and is able to extract from source of min-entropy rates larger than $1/2$. Combining this construction with a quantum-proof variant of the reduction of Dodis and Wichs, shown by Cohen and Vidick (unpublished), we obtain the first privacy amplification protocol secure against active quantum adversaries

STM microscopy of the CDW in 1T-TiSe2 in the presence of single atom defects

We present a detailed low temperature scanning tunneling microscopy study of the commensurate charge density wave (CDW) in 1$T$-TiSe$_2$ in the presence of single atom defects. We find no significant modification of the CDW lattice in single crystals with native defects concentrations where some bulk probes already measure substantial reductions in the CDW phase transition signature. Systematic analysis of STM micrographs combined with density functional theory modelling of atomic defect patterns indicate that the observed CDW modulation lies in the Se surface layer. The defect patterns clearly show there are no 2$H$-polytype inclusions in the CDW phase, as previously found at room temperature [Titov A.N. et al, Phys. Sol. State 53, 1073 (2011). They further provide an alternative explanation for the chiral Friedel oscillations recently reported in this compound [J. Ishioka et al., Phys. Rev. B 84, 245125, (2011)].Comment: 5 pages, 4 figure