A fast version of the k-means classification algorithm for astronomical applications

Context. K-means is a clustering algorithm that has been used to classify large datasets in astronomical databases. It is an unsupervised method, able to cope very different types of problems. Aims. We check whether a variant of the algorithm called single-pass k-means can be used as a fast alternative to the traditional k-means. Methods. The execution time of the two algorithms are compared when classifying subsets drawn from the SDSS-DR7 catalog of galaxy spectra. Results. Single-pass k-means turn out to be between 20 % and 40 % faster than k-means and provide statistically equivalent classifications. This conclusion can be scaled up to other larger databases because the execution time of both algorithms increases linearly with the number of objects. Conclusions. Single-pass k-means can be safely used as a fast alternative to k-means

Single magnetic adsorbates on s-wave superconductors

In superconductors, magnetic impurities induce a pair-breaking potential for Cooper pairs, which locally affects the Bogoliubov quasiparticles and gives rise to Yu-Shiba-Rusinov (YSR or Shiba, in short) bound states in the density of states (DoS). These states carry information on the magnetic coupling strength of the impurity with the superconductor, which determines the many-body ground state properties of the system. Recently, the interest in Shiba physics was boosted by the prediction of topological superconductivity and Majorana modes in magnetically coupled chains and arrays of Shiba impurities. Here, we review the physical insights obtained by scanning tunneling microscopy into single magnetic adsorbates on the $s$-wave superconductor lead (Pb). We explore the tunneling processes into Shiba states, show how magnetic anisotropy affects many-body excitations, and determine the crossing of the many-body groundstate through a quantum phase transition. Finally, we discuss the coupling of impurities into dimers and chains and their relation to Majorana physics.Comment: 18 pages, 17 figures, revie

Long-range repulsive interaction between TTF molecules on a metal surface induced by charge transfer

The low-coverage adsorption of a molecular electron donor, tetrathiafulvalene, on Au(111) is characterized by the spontaneous formation of superlattice of monomers, whose spacing exceeds the equilibrium distance of non-covalent interactions and depends on coverage. The origin of this peculiar growth mode is due to a long-range repulsive interaction between molecules. The analysis of molecular-pair distributions obtained by scanning tunneling microscopy measurements permits us to determine that the nature of TTF intermolecular interactions on Au (111) is electrostatic. A repulsion between molecules is caused by the accumulation of charge due to electron donation into the metal surface, as pictured through density functional theory calculations

Tuning the magnetic anisotropy of single molecules

The magnetism of single atoms and molecules is governed by the atomic scale environment. In general, the reduced symmetry of the surrounding splits the $d$ states and aligns the magnetic moment along certain favorable directions. Here, we show that we can reversibly modify the magnetocrystalline anisotropy by manipulating the environment of single iron(II) porphyrin molecules adsorbed on Pb(111) with the tip of a scanning tunneling microscope. When we decrease the tip--molecule distance, we first observe a small increase followed by an exponential decrease of the axial anisotropy on the molecules. This is in contrast to the monotonous increase observed earlier for the same molecule with an additional axial Cl ligand. We ascribe the changes in the anisotropy of both species to a deformation of the molecules in the presence of the attractive force of the tip, which leads to a change in the $d$ level alignment. These experiments demonstrate the feasibility of a precise tuning of the magnetic anisotropy of an individual molecule by mechanical control.Comment: 16 pages, 5 figures; online at Nano Letters (2015

Optimal generalized quantum measurements for arbitrary spin systems

Positive operator valued measurements on a finite number of N identically prepared systems of arbitrary spin J are discussed. Pure states are characterized in terms of Bloch-like vectors restricted by a SU(2 J+1) covariant constraint. This representation allows for a simple description of the equations to be fulfilled by optimal measurements. We explicitly find the minimal POVM for the N=2 case, a rigorous bound for N=3 and set up the analysis for arbitrary N.Comment: LateX, 12 page

Magnetic anisotropy in Shiba bound states across a quantum phase transition

The exchange coupling between magnetic adsorbates and a superconducting substrate leads to Shiba states inside the superconducting energy gap and a Kondo resonance outside the gap. The exchange coupling strength determines whether the quantum many-body ground state is a Kondo singlet or a singlet of the paired superconducting quasiparticles. Here, we use scanning tunneling spectroscopy to identify the different quantum ground states of Manganese phthalocyanine on Pb(111). We observe Shiba states, which are split into triplets by magnetocrystalline anisotropy. Their characteristic spectral weight yields an unambiguous proof of the nature of the quantum ground state.Comment: 6 pages, 4 figure