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

Numerical study of relaxation in electron glasses

We perform a numerical simulation of energy relaxation in three-dimensional electron glasses in the strongly localized regime at finite temperatures. We consider systems with no interactions, with long-range Coulomb interactions and with short-range interactions, obtaining a power law relaxation with an exponent of 0.15, which is independent of the parameters of the problem and of the type of interaction. At very long times, we always find an exponential regime whose characteristic time strongly depends on temperature, system size, interaction type and localization radius. We extrapolate the longest relaxation time to macroscopic sizes and, for interacting samples, obtain values much larger than the measuring time. We finally study the number of electrons participating in the relaxation processes of very low energy configurations.Comment: 6 eps figures. To be published in Phys. Rev.

Impact of incomplete ionization of dopants on the electrical properties of compensated p-type silicon

This paper investigates the importance of incomplete ionization of dopants in compensated p-type Si and its impact on the majority-carrier density and mobility and thus on the resistivity. Both theoretical calculations and temperature-dependent Hall-effect measurements demonstrate that the carrier density is more strongly affected by incomplete ionization in compensated Si than in uncompensated Si with the same net doping. The previously suggested existence of a compensation-specific scattering mechanism to explain the reduction of mobility in compensated Si is shown not to be consistent with the T-dependence of the measuredcarrier mobility. The experiment also shows that, in the vicinity of 300 K, the resistivity of compensated Si has a much weaker dependence on temperature than that of uncompensated silicon

Resonant tunneling through a small quantum dot coupled to superconducting leads

We address the problem of non-linear transport through discrete electronic levels in a small quantum dot coupled to superconducting electrodes. In our approach the low temperature I-V characteristics can be calculated including all multiple quasi-particle and Andreev processes. The limit of very weak coupling to the leads and large charging energies is briefly analyzed comparing the calculated lineshapes of the I-V curves with recent experimental results. When the coupling to the leads increases and Coulomb blockade effects can be neglected, the combination of multiple Andreev processes and resonant transmission gives rise to a rich subgap structure which largely differs from the one found in the more studied S-N-S systems. We show how multiple processes can be included within a simple sequential tunneling picture qualitatively explaining the subgap structure. We suggest an experimental set-up where the predicted effects could be observed.Comment: 11 pages, 4 postscript figures, to be published in Phys. Rev. B (rapid communications

A first study of the galaxy HRG 2304 and its companion AM 1646-795 (NED01)

Aims. We report the first study of the peculiar ring-like galaxy HRG 2304 (NED02),which was previously classified as a ring galaxy with an elliptical smooth ring. This object was selected to prove that it is a candidate for the Solitaire-type ring galaxies in an early stage of ring formation. The main goal of this work is to provide the spectral characteristics of the current object and its companion AM 1646-795 (NED01). Methods. The study is based on spectroscopic observations in the optical band to highlight the characteristics of this interacting galaxy. To investigate the star formation history of HRG 2304 we used the stellar population synthesis code STARLIGHT. The direct V and B broad band images were used to enhance some fine structures. Results. Along the entire long-slit signal, the spectra of HRG 2304 and its companion resemble that of an early-type galaxy. We estimated a heliocentric systemic redshift of z = 0.0415, corresponding to heliocentric velocities of 12449 km s-1 for HRG 2304 (NED02) and 12430 km s-1 for AM1646-795 (NED01). The spatial variation in the contribution of the stellar population components for both objects are dominated by an old stellar population 2x10^9 < t < 13x10^9 yr. The observed radial-velocity distribution and the fine structures around HRG 2304 suggest an ongoing tidal interaction of both galaxies. Conclusions.The spectroscopic results and the morphological peculiarities of HRG 2304 can be adequately interpreted as an ongoing interaction with the companion galaxy. Both galaxies are early-type, the companion is elliptical, and the smooth distribution of the material around HRG 2304 and its off-center nucleus in the direction of AM1646-795 (NED01) characterize HRG 2304 as a Solitaire-type galaxy candidate in an early stage of ring formation.Comment: Accepted for publication in Astronomy and Astrophysics, 9 pages, 10 figures and 3 table

Quantum algorithms for classical lattice models

We give efficient quantum algorithms to estimate the partition function of (i) the six vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar graph, (iii) the Potts model on a quasi 2D square lattice, and (iv) the Z_2 lattice gauge theory on a three-dimensional square lattice. Moreover, we prove that these problems are BQP-complete, that is, that estimating these partition functions is as hard as simulating arbitrary quantum computation. The results are proven for a complex parameter regime of the models. The proofs are based on a mapping relating partition functions to quantum circuits introduced in [Van den Nest et al., Phys. Rev. A 80, 052334 (2009)] and extended here.Comment: 21 pages, 12 figure

Level number variance and spectral compressibility in a critical two-dimensional random matrix model

We study level number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b the level number variance behaves linearly, with the compressibility chi between 0 and 1, which is typical for critical systems. For large values of b, we derive that chi=0, as one would normally expect in the metallic phase. Using numerical simulations we determine the critical value of b at which the transition between these two phases occurs.Comment: 6 page