Dielectric response of Anderson and pseudogapped insulators

Using a combination of analytic and numerical methods, we study the polarizability of a (non-interacting) Anderson insulator in one, two, and three dimensions and demonstrate that, in a wide range of parameters, it scales proportionally to the square of the localization length, contrary to earlier claims based on the effective-medium approximation. We further analyze the effect of electron-electron interactions on the dielectric constant in quasi-1D, quasi-2D and 3D materials with large localization length, including both Coulomb repulsion and phonon-mediated attraction. The phonon-mediated attraction (in the pseudogapped state on the insulating side of the Superconductor-Insulator Transition) produces a correction to the dielectric constant, which may be detected from a linear response of a dielectric constant to an external magnetic field.Comment: 9 page

Conduction Channels of One-Atom Zinc Contacts

We have determined the transmission coefficients of atomic-sized Zn contacts using a new type of breakjunction which contains a whisker as a central bridge. We find that in the last conductance plateau the transport is unexpectedly dominated by a well-transmitting single conduction channel. We explain the experimental findings with the help of a tight-binding model which shows that in an one-atom Zn contact the current proceeds through the 4s and 4p orbitals of the central atom.Comment: revtex4, 5 pages, 5 figure

Anomalously large critical regions in power-law random matrix ensembles

We investigate numerically the power-law random matrix ensembles. Wavefunctions are fractal up to a characteristic length whose logarithm diverges asymmetrically with different exponents, 1 in the localized phase and 0.5 in the extended phase. The characteristic length is so anomalously large that for macroscopic samples there exists a finite critical region, in which this length is larger than the system size. The Green's functions decrease with distance as a power law with an exponent related to the correlation dimension.Comment: RevTex, 4 pages, 4 eps figures. Final version to be published in Phys. Rev. Let

Single-channel transmission in gold one-atom contacts and chains

We induce superconductivity by proximity effect in thin layers of gold and study the number of conduction channels which contribute to the current in one-atom contacts and atomic wires. The atomic contacts and wires are fabricated with a Scanning Tunneling Microscope. The set of transmission probabilities of the conduction channels is obtained from the analysis of the $I(V)$ characteristic curve which is highly non-linear due to multiple Andreev reflections. In agreement with theoretical calculations we find that there is only one channel which is almost completely open.Comment: 4 pages, 2 figures. To be published in Phys. Rev. B, Rapid Communications (2003

Not Hydro: Using Neural Networks to estimate galaxy properties on a Dark-Matter-Only simulation

Using data from TNG300-2, we train a neural network (NN) to recreate the stellar mass ($M^*$) and star formation rate (SFR) of central galaxies in a dark-matter-only simulation. We consider 12 input properties from the halo and sub-halo hosting the galaxy and the near environment. $M^*$ predictions are robust, but the machine does not fully reproduce its scatter. The same happens for SFR, but the predictions are not as good as for $M^*$. We chained neural networks, improving the predictions on SFR to some extent. For SFR, we time-averaged this value between $z=0$ and $z=0.1$, which improved results for $z=0$. Predictions of both variables have trouble reproducing values at lower and higher ends. We also study the impact of each input variable in the performance of the predictions using a leave-one-covariate-out approach, which led to insights about the physical and statistical relation between input variables. In terms of metrics, our machine outperforms similar studies, but the main discoveries in this work are not linked with the quality of the predictions themselves, but to how the predictions relate to the input variables. We find that previously studied relations between physical variables are meaningful to the machine. We also find that some merger tree properties strongly impact the performance of the machine. %We highlight the value of machine learning (ML) methods in helping understand the information contained in different variables, since with its help we were able to obtain useful insights resulting from studying the impact of input variables on the resulting behaviour of galaxy properties. We conclude that ML models are useful tools to understand the significance of physical different properties and their impact on target characteristics, as well as strong candidates for potential simulation methods.Comment: 17 pages, 16 figures, to be published in MNRA

Mean Free Path and Energy Fluctuations in Quantum Chaotic Billiards

The elastic mean free path of carriers in a recently introduced model of quantum chaotic billiards in two and three dimensions is calculated. The model incorporates surface roughness at a microscopic scale by randomly choosing the atomic levels at the surface sites between -W/2 and W/2. Surface roughness yields a mean free path l that decreases as L/W^2 as W increases, L being the linear size of the system. But this diminution ceases when the surface layer begins to decouple from the bulk for large enough values of W, leaving more or less unperturbed states on the bulk. Consequently, the mean free path shows a minimum of about L/2 for W of the order of the band width. Energy fluctuations reflect the behavior of the mean free path. At small energy scales, strong level correlations manifest themselves by small values of the number of levels variance Sigma^2(E) that are close to Random Matrix Theory (RMT) in all cases. At larger energy scales, fluctuations are below the logarithmic behavior of RMT for l > L, and above RMT value when l < L.Comment: 8 twocolumn pages, seven figures, revtex and epsf macros. To be published in Physical Review B

Computation of the Euler Number of a Binary Image Composed of Hexagonal Cells

ABSTRACTMost of the proposals to compute the Euler number of a binary image have been designed to work with imagescomposed of squared cells. Only a few of these methods (in the case of images composed of hexagonal cells) havebeen reported in literature, although it is known that images composed of hexagonal cells do not suffer from theproblems of connectivity frequently found in the case of images composed of squared cells. In this paper, a new wayto compute the Euler number (E) of a binary image composed of hexagonal cells is presented. For this, the perimeterP of the isolated regions in the image, their contact perimeter c P and the type T of a cell are used to obtain thisimportant invariant. The proposal can be used alone or in combination with other features to describe any binaryplanar shape composed of hexagonal pixels for its further recognition

Critical spectral statistics in two-dimensional interacting disordered systems

The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the critical nearest level-spacing distribution $P(s)$ allows one to find a delocalization transition at a critical disorder $W_{\rm c}$ for any non-zero value of the interaction strength. At the critical point the spacings distribution has a small-$s$ behavior $P_c(s)\propto s$, and a Poisson-like decay at large spacings.Comment: 4 two-column pages, 3 eps figures, RevTeX, new results adde