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Thuillier et al. (Solar Phys. 290, 1581, 2015) article compares ATLAS-3 reference composite solar spectral irradiance (SSI) with more recent spatial measurements, as well as ground-based ones, including IRSPERAD. With respect to the IRSPERAD spectrum of Bolsee et al. (Solar Phys. 289, 2433, 2014), Thuillier et al. (2015) presents an analysis based on a set of meteorological parameters retrieved at the moment of the respective ground-based campaign. This comment is intended to give a new insight to the said analysis which is based upon revised values of the meteorological parameters incorrectly used in Thuillier et al. (2015).

We investigate, experimentally and theoretically, polarization rotation effects in dilute photonic crystals with transverse permittivity inhomogeneity perpendicular to the traveling direction of waves. A capsize, namely a drastic change of polarization to the perpendicular direction is observed in a one-dimensional photonic crystal in the frequency range $10\div 140$ GHz. To gain more insights into the rotational mechanism, we have developed a theoretical model of dilute photonic crystal, based on Maxwell's equations with a spatially dependent two dimensional inhomogeneous dielectric permittivity. We show that the polarization's rotation can be explained by an optical splitting parameter appearing naturally in Maxwell's equations for magnetic or electric fields components. This parameter is an optical analogous of Rashba like spin-orbit interaction parameter present in quantum waves, introduces a correction to the band structure of the two-dimensional Bloch states, creates the dynamical phase shift between the waves propagating in the orthogonal directions and finally leads to capsizing of the initial polarization. Excellent agreement between theory and experiment is found., Comment: 11pages,6figures

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 pages

We describe an instrument dedicated to measuring the top of atmosphere (TOA) solar spectral irradiance (SSI) in the near-infrared (NIR) between 600 nm and 2300 nm at a resolution of 10 nm. Ground-based measurements are performed through atmospheric NIR windows and the TOA SSI values are extrapolated using the Bouguer–Langley technique. The interest in this spectral range arises because it plays a main role in the Earth’s radiative budget and also because it is employed to validate models used in solar physics. Moreover, some differences were observed between recent ground-based and space-based instruments that take measurements in the NIR and the reference SOLSPEC(ATLAS3) spectrum. In the 1.6 μm region, the deviations vary from 6 % to 10 %. Our measuring system named IRSPERAD has been designed by Bentham (UK) and has been radiometrically characterized and absolutely calibrated against a blackbody at the Belgian Institute for Space Aeronomy and at the Physikalisch-Technische Bundesanstalt (Germany), respectively. A four-month measurement campaign was carried out at the Izana Atmospheric Observatory (Canary Islands, 2367 m a.s.l.). A set of top-quality solar measurements was processed to obtain the TOA SSI in the NIR windows. We obtained an average standard uncertainty of 1 % for 0.8 μm

We have provided a complete description of the electron localization length (LL) in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. Presented analytical expressions for LL are in excellent agreement with numerical calculations, exact up to order W2 (W being the disorder strength), and valid for an arbitrary number of propagating and evanescent channels. We have calculated the average conductance in Q1D systems, establish relationship between various lengths and show that it basically differs from 1D case.

A 1-year intercomparison of classical and modern radiation and sunshine duration instruments has been performed at Izaña Atmospheric Observatory (IZO) located in Tenerife (Canary Islands, Spain) starting on July 17, 2014. We compare global solar radiation (GSR) records measured with a CM-21 pyranometer Kipp & Zonen, taken in the framework of the Baseline Surface Radiation Network, with those measured with a Multifilter Rotating Shadowband Radiometer (MFRSR), and a bimetallic pyranometer (PYR), and GSR estimated from sunshine duration performed by a Campbell-Stokes sunshine recorder (CS) and a Kipp & Zonen sunshine duration sensor (CSD). Given the GSR BSRN records are subject of strict quality controls (based on principles of physical limits and comparison with the LibRadtran model), they have been used as reference in the intercomparison study. We obtain an overall root mean square error (RMSE) of ~0.9 MJm2 (4 %) for GSR PYR and GSR MFRSR, 1.9 MJm2 (7 %) and 1.2 MJm2 (5 %) for GSR CS and GSR CSD, respectively. Factors such as temperature, fraction of the clear sky, relative humidity and the solar zenith angle have shown to moderately affect the GSR observations. As application of the methodology developed in this work, we have re-evaluated the GSR time series between 1977 and 1991 obtained with two PYRs at IZO. By comparing with coincident GSR estimates from SD observations, we probe the high consistency of those measurements and their temporal stability. These results demonstrate that 1) the continuous-basis intercomparison of different GSR techniques offers important diagnostics for identifying inconsistencies between GSR data records, and 2) the GSR measurements performed with classical and more simple instruments are consistent with more modern techniques and, thus, valid to recover GSR time series and complete worldwide distributed GSR data. The intercomparison and quality assessment of these different techniques have allowed to obtain a complete and consistent long-term global solar radiation series (1977–2015) at Izaña.

A seasonal distribution of the Lidar Ratio (LR, extinction-to-backscattering coefficient ratio) for pure Saharan dust particles has been achieved. Simultaneous MPLNET/Micro Pulse lidar measurements in synergy with AERONET sun-photometer data were collected in the Tenerife area, a Saharan dust-influenced region, from June 2007 to November 2009. Dusty cases were mostly observed in summertime (71.4 % of total dusty cases). No differences were found among the LR values derived for spring, summertime and autumn times (a rather consistent seasonally averaged LR value of 57 sr is found). In wintertime, however, a higher mean LR is derived (65 sr), associated likely with a potential contamination from fine biomass burning particles coming from Sahel area during wintertime deforestation fires period. Results, obtained from a free-tropospheric pristine station (AEMET/Izana Observatory) under Saharan dust intrusion occurrence, provide a more realistic perspective about LR values to be used in elastic lidar-derived AOD inversion for Saharan pure dust particles, and hence in improving CALIPSO AOD retrievals.

We combine numerical diagonalization with a semi-analytical calculations to prove the existence of the intermediate non-ergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized population dynamics that is able to detect the violation of ergodicity of the delocalized states within the Abou-Chakra, Anderson and Thouless recursive scheme. This result is supplemented by statistics of random wave functions extracted from exact diagonalization of the Anderson model on ensemble of disordered Random Regular Graphs (RRG) of N sites with the connectivity K=2. By extrapolation of the results of both approaches to N->infinity we obtain the fractal dimensions D_{1}(W) and D_{2}(W) as well as the population dynamic exponent D(W) with the accuracy sufficient to claim that they are non-trivial in the broad interval of disorder strength W_{E}10^{5} reveals a singularity in D_{1,2}(W)-dependencies which provides a clear evidence for the first order transition between the two delocalized phases on RRG at W_{E}\approx 10.0. We discuss the implications of these results for quantum and classical non-integrable and many-body systems., Comment: 4 pages paper with 5 figures + Supplementary Material with 5 figures

El volumen 119 de 2016 de la revista EPJ Web of Conferences recoge las ponencias del 27th International Laser Radar Conference (ILRC 27) This work presents a first comparative study of the Lidar Ratio (LR) values obtained for dust particles in two singular dust-influenced regions: the Canary Islands (Spain, close to the African coast in the North Atlantic Ocean), frequently affected by Saharan dust intrusions, and the Kuwait area (Arabian Peninsula) as usually influenced by Arabian dust storms. Synergetic lidar and sun-photometry measurements are carried out in two stations located in these particular regions for that purpose. Several dusty cases were observed during 2014 in both stations and, just for illustration, two specific dusty case studies have been selected and analyzed to be shown in this work. In general, mean LR values of 54 sr and 40 sr were obtained in these studies cases for Saharan and Arabian dust particles, respectively. Indeed, these results are in agreement with other studies performed for dust particles arriving from similar desert areas. In particular, the disparity found in Saharan and Arabian dust LR values can be based on the singular composition of the suspended dust aerosols over each station. These results can be useful for CALIPSO extinction retrievals, where a single LR value (40 sr) is assumed for pure dust particles independently on the dust source region. This work has been supported by both the Spanish Ministerio de Economía y Competitividad (MINECO) under grant CGL2011-24891 (AMISOC project) and the Kuwait Foundation for the Advancement of Sciences under project 2011- 1401-01.

We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is located in the region of localized states not so far from the Anderson mobility edge $E_c$. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model. Our theoretical analysis is based on the analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems. We identify three distinct phases: 'critical' superconductive state formed at $E_F=E_c$, superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at $E_F$ still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap $\Delta$, that is due to many-body correlations and a new "pseudogap" energy scale $\Delta_P$ which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive $T_c$. Two gap nature of the "pseudo-gaped superconductor" is shown to lead to a number of unusual physical properties., Comment: 110 pages, 39 figures. The revised version corrects a number of typos, adds references and discussion of recent results

Light transport in a metal with two-dimensional hole arrays is considered. Analytical expression for a transmission coefficient in periodic, isolated and disordered cases are derived, assuming the existence of waveguide modes transverse tunneling in two-dimensional plane perpendicular to traveling direction of light. The one dimensional case of periodic holes, due to its simplicity, is investigated in detail. In the dilute metal regime, when metal fraction is small, our numerical study of the transmission coefficient of central diffracted wave indicates the existence of a minimum which is completely independent of an incident wavelength. Further increasing of metal fraction leads to the unusual monotonic increasing of central diffracted wave transmission. The role of the surface plasmons is discussed., 14pages, 2figures

Motivated by the problem of Many-Body Localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two localization transitions as the parameter $\gamma$ of the model varies from 0 to $\infty$. One of them is the Anderson transition from the localized to the extended states that happens at $\gamma=2$. The other one at $\gamma=1$ is the transition from the extended non-ergodic (multifractal) states to the extended ergodic states similar to the eigenstates of the Gaussian Orthogonal Ensemble. We computed the two-level spectral correlation function, the spectrum of multifractality $f(\alpha)$ and the wave function overlap which all show the transitions at $\gamma=1$ and $\gamma=2$., Comment: 8 pages, 9 figures (main text) + 7 pages, 4 figures (supplementary materials)

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., 4 two-column pages, 3 eps figures, RevTeX, new results added

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. B

Departamento de Fi´sica, Universidad de Murcia, E-30080 Murcia, Spain~Received 12 May 1997!A model of three-dimensional quantum chaotic billiards is used to investigate global quantum fluctuations inmetallic particles. The quantum system is described by means of a tight-binding Hamiltonian in which theenergies of the orbitals at the surface sites are chosen at random in the range (2W/2,W/2). The results indicatethat for reasonable values of W ~on the order of half the bandwidth! the energy fluctuations of the highestoccupied level are much larger than the corresponding average interlevel spacing. This provides a naturalexplanation for autoionization effects in granular metals. @S0163-1829~97!51436-6#

We studied by computer simulation the effects of Coulomb interactions on the properties of strongly localized Anderson insulators. We took full account of many-body effects by considering the many-electron configurations of the system rather than single-particle states. We developed an algorithm to obtain the configurations and energies of the low-lying system states, and from there the conductivity. At low-temperatures T, we found that the conductivity was proportional to exp({minus}T{sub 0}/T){sup 1/2}. Many-electron transitions were seen to be important at very low temperatures. In this regime, T{sub 0}{approx}0.61, which is much smaller than predicted by one-electron theory. Experimental results which use the predicted T{sub 0} to obtain localization radii must therefore be reinterpreted. {copyright} {ital 1997} {ital The American Physical Society}

We derive general expressions for the transmission coefficient and the traversal time in waveguides periodically loaded with dielectric slabs. We apply the results to resonant tunneling between two regions below cut-off, with exponentially decaying modes. At the resonant frequencies, we found a relationship between the traversal time and the lifetime. We also study the photonic band gap in a periodic quarter wavelength structure. As in several experiments, we found superluminal velocities.

We found the asymptotic solutions at low and high temperatures of the partition function of a general one-dimensional binary alloy. As a particular application, we considered the thermodynamic properties of quasiperiodic Fibonacci lattices. We showed that, at low temperatures, the quasiperiodicity produces an extra peak in the specific heat when plotted versus temperature.

We have carried out a Monte Carlo simulation of the conductivity of a two-dimensional strongly localized interacting system. A plot of dlog sigma /dlogT versus T, on a double logarithmic scale, clearly shows two distinct regimes, one activated at high T and a non-activated one at low T. The conductivity exponent in this later regime is close to 1/2 , in agreement with Efros and Shklovskii's predictions (1984), although the characteristic temperature T0'; is about a factor of two smaller than predicted.

The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. Although small quantum systems with discrete energy levels are noiseless and stay coherent forever in the absence of any coupling to external world, most large-scale quantum systems are able to produce a thermal bath and excitation decay. This intrinsic decoherence is manifested by a broadening of energy levels, which aquire a finite width. The important question is: what is the driving force and the mechanism of transition(s) between these two types of many-body systems - with and without intrinsic decoherence? Here we address this question via the numerical study of energy-level statistics of a system of interacting spin-1/2 with random transverse fields. We present the first evidence for a well-defined quantum phase transition between domains of discrete and continous many-body spectra in such spin models, implying the appearance of novel insulating phases in the vicinity of the superconductor-insulator transition in InO(x) and similar materials.

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., 6 pages

We consider a simple model of quantum disorder in two dimensions, characterized by a long-range site-to-site hopping. The system undergoes a metal-insulator transition -- its eigenfunctions change from being extended to being localized. We demonstrate that at the point of the transition the eigenfunctions do not become fractal. Their density moments do not scale as a power of the system size. Instead, in one of the considered limits our result suggests a power of the logarithm of the system size. In this regard, the transition differs from a similar one in the one-dimensional version of the same system, as well as from the conventional Anderson transition in more than two dimensions., Comment: 4 pages, 2 figures

The dynamical scaling for statistics of critical multifractal eigenstates proposed by Chalker is analytically verified for the critical random matrix ensemble in the limit of strong multifractality controlled by the small parameter $b\ll 1$. The power law behavior of the quantum return probability $P_{N}(\tau)$ as a function of the matrix size $N$ or time $\tau$ is confirmed in the limits $\tau/N\rightarrow\infty$ and $N/\tau\rightarrow\infty$, respectively, and it is shown that the exponents characterizing these power laws are equal to each other up to the order $b^{2}$. The corresponding analytical expression for the fractal dimension $d_{2}$ is found.

We have studied numerically the density of states of one-dimensional and two-dimensional systems with localized states interacting via the electronectron Coulomb interaction. The results can explain tunnelling conductance measurements on granular A1 wires and films in terms of the Coulomb gap. We have considered the effects of a finite localization length, and of screening by a metallic electrode, on the Coulomb gap.

We develop a supersymmetric virial expansion for two point correlation functions of almost diagonal Gaussian Random Matrix Ensembles (ADRMT) of the orthogonal symmetry. These ensembles have multiple applications in physics and can be used to study universal properties of time-reversal invariant disordered systems which are either insulators or close to the Anderson localization transition. We derive a two-level contribution to the correlation functions of the generic ADRMT and apply these results to the critical (multifractal) power law banded ADRMT. Analytical results are compared with numerical ones., 13 pages, 1 figure

We provide evidence that as a general rule Anderson localization effects become weaker as the degree of differentiability of the disordered potential increases. In one dimension a band of metallic states exists provided that the disordered potential is sufficiently correlated and has some minimum degree of differentiability. Several examples are studied in detail. In agreement with the one parameter scaling theory the motion in the metallic region is ballistic if the spectral density is smooth. Finally, we study the most promising settings to observe these results in the context of cold atoms., Comment: 5 pages, 3 figures, journal version

We consider the correlation of two single-particle probability densities $|\Psi_{E}({\bf r})|^{2}$ at coinciding points ${\bf r}$ as a function of the energy separation $\omega=|E-E'|$ for disordered tight-binding lattice models (the Anderson models) and certain random matrix ensembles. We focus on the models in the parameter range where they are close but not exactly at the Anderson localization transition. We show that even far away from the critical point the eigenfunction correlation show the remnant of multifractality which is characteristic of the critical states. By a combination of the numerical results on the Anderson model and analytical and numerical results for the relevant random matrix theories we were able to identify the Gaussian random matrix ensembles that describe the multifractal features in the metal and insulator phases. In particular those random matrix ensembles describe new phenomena of eigenfunction correlation we discovered from simulations on the Anderson model. These are the eigenfunction mutual avoiding at large energy separations and the logarithmic enhancement of eigenfunction correlations at small energy separations in the two-dimensional (2D) and the three-dimensional (3D) Anderson insulator. For both phenomena a simple and general physical picture is suggested., Comment: 16 pages, 18 figures

We study the dependence on the spatial dimensionality of different quantities relevant in the description of the Anderson transition by combining numerical calculations in a $3 \leq d \leq 6$ disordered tight binding model with theoretical arguments. Our results indicate that, in agreement with the one parameter scaling theory, the upper critical dimension for localization is infinity. Typical properties of the spectral correlations at the Anderson transition such as level repulsion or a linear number variance are still present in higher dimensions though eigenvalues correlations get weaker as the dimensionality of the space increases. It is argued that such a critical behavior can be traced back to the exponential decay of the two-level correlation function in a certain range of eigenvalue separations. We also discuss to what extent different effective random matrix models proposed in the literature to describe the Anderson transition provide an accurate picture of this phenomenon. Finally, we study the effect of a random flux in our results., RevTex4, 8 two-column pages, 5 .eps figures

The two-level correlation function $R_{d,\beta}(s)$ of $d$-dimensional disordered models ($d=1$, 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal ($\beta=1$) or unitary ($\beta=2$) symmetry in the strong ($b^d \ll 1$) coupling regime, where the parameter $b^{-d}$ plays the role of the coupling constant of the model. It is found that $R_{d,\beta}(s)$ is of the form $R_{d,\beta}(s)=1+\delta(s)-F_{\beta}(s^{\beta}/b^{d\beta})$, where $F_{1}(x)=\text{erfc}(a_{d,\beta} x)$ and $F_{2}(x)=\exp (-a_{d,\beta} x^2)$, with $a_{d,\beta}$ being a numerical coefficient depending on the dimensionality and the universality class. Finally, the level number variance and the spectral compressibility are also considerded., Comment: RevTex4, 7 two-column pages, 6 .eps figures, 1 table. A new section devoted to the spectral compressibility added. To be published in Phys. Rev. B

We calculate the dwell times for incident particles comming from both the right and from the left of an asymmetric one-dimensional barrier. We prove that these times have a common contribution proportional to the density of states and an asymmetric contribution that depends on the reflection amplitudes from the right and from the left, which cancels in the symmetric case.

The system size dependence of the multifractal spectrum $f(\alpha)$ and its singularity strength $\alpha$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that $f(\alpha)$ is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, $f(\alpha)$ strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength., Comment: RevTex4, 6 two-column pages, 4 .eps figures, new results added, updated references, to be published in Phys. Rev. B

Finite-size effects in the generalized fractal dimensions $d_q$ are investigated numerically. We concentrate on a one-dimensional disordered model with long-range random hopping amplitudes in both the strong- and the weak-coupling regime. At the macroscopic limit, a linear dependence of $d_q$ on $q$ is found in both regimes for values of $q \alt 4g^{-1}$, where $g$ is the coupling constant of the model., RevTex4, 5 two-column pages, 5 .eps figures, to be published in Phys. Rev. B

We investigate numerically the inverse participation ratio, $P_2$, of the 3D Anderson model and of the power-law random banded matrix (PRBM) model at criticality. We found that the variance of $\ln P_2$ scales with system size $L$ as $\sigma^2(L)=\sigma^2(\infty)-A L^{-D_2/2d}$, being $D_2$ the correlation dimension and $d$ the system dimension. Therefore the concept of a correlation dimension is well defined in the two models considered. The 3D Anderson transition and the PRBM transition for $b=0.3$ (see the text for the definition of $b$) are fairly similar with respect to all critical magnitudes studied., Comment: RevTex, 5 pages, 4 eps figures, to be published in Phys. Rev. Lett

We study the decay properties of correlation functions in quantum billiards with surface or bulk disorder. The quantum system is modeled by means of a tight-binding Hamiltonian with diagonal disorder, solved on LxL clusters of the square lattice. The correlation function is calculated by launching the system at t=0 into a wave function of the regular (clean) system and following its time evolution. The results show that the correlation function decays exponentially with a characteristic correlation time (inverse of the Lyapunov exponent lambda). For small enough disorder the Lyapunov exponent is approximately given by the imaginary part of the self-energy induced by disorder. On the other hand, if the scaling of the Lyapunov exponent with L is investigated by keeping constant l/L, where l is the mean free path, the results show that lambda is proportional to 1/L.

We show by a numerical procedure that a short-range interaction $u$ induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by an scaling analysis of the renormalized decay length of the bars. For $u=1$, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected., Comment: 4 two-column pages, 4 eps figures, Revtex, to be published in Europhys. Lett

We derive a general expression for the tunneling time in layered systems based on the Larmor-clock approach. We show that our results are equivalent to those obtained by the Feynman path-integral technique. We establish a relation between functional derivatives of the barrier potential and partial derivatives with respect to the incident energy. In application, we computed the tunneling time and the reflection time for a rectangular barrier, for a double rectangular barrier, and for a Gaussian potential.

We have studied electron-electron and electron-hole correlations of two-dimensional models of highly localized interacting electrons, exhibiting a Coulomb gap. Electrons close to the Fermi level try to cluster together. The probability of finding two electrons very close to the Fermi level in two nearest-neighbor sites is more than 20 times greater than in two far apart positions. Low-energy electrons are, on average, more distant from low-energy holes than would be implied by the constraint that their transition energy has to be positive

We argue that for granular metals a sizable fraction of the grains becomes charged because the energy fluctuation of the highest-occupied level of each grain, as predicted by random matrix theory, is larger than the charging energy. We have computed the ground state density of states and the degree of ionization of granular metals. The density of states shows a Coulomb gap around the Fermi energy, produced by the long-range part of the Coulomb interactions, which should dominate transport properties at low temperatures

We calculate numerically the energy level distributions of the two-dimensional Anderson model in the nearly clean, ballistic, diffusive and strongly localized regimes. The Poisson statistics governs nearest level spacings in the clean (in the absence of degeneracies due to the geometry) and localized regimes, whereas in the ballistic and diffusive regimes the level statistics follows the Wigner-Dyson distribution. In the diffusive and ballistic regimes, we study the critical energy , defined as the maximum energy up to which level fluctuations follow the logarithmic behaviour characteristic of random-matrix theory (RMT). A reasonably accurate determination of the ballistic-diffusive transition is achieved through the behaviour of the critical energies. We show how the level statistic is an adequate tool for characterizing the different regimes of disordered systems, and how the results obtained are in qualitative agreement with theoretical estimates. We finally analyse the behaviour of as a function of the energy within the band.

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., RevTex, 4 pages, 4 eps figures. Final version to be published in Phys. Rev. Lett

The conductance of quantum dots with ballistic point contacts supporting a single channel and placed at arbitrary sites on their perimeters has been numerically computed. The results indicate that whenever the contacts break the dot symmetry, the statistics of the conductance closely follow the circular orthogonal ensemble result, no matter whether the shape of the quantum dot is itself regular or not and independently of its size. On the other hand, the statistics of adjacent resonances ~a property closely related to the level statistics of the isolated quantum dot! follows the Wigner-Dyson distribution only for small systems. @S0163-1829~98!50540-1# Recent developments in nanostructuring techniques have made possible the fabrication of ballistic two-dimensional microstructures in which scattering by bulk impurities can be neglected and only scattering from the boundary of the conducting region is relevant. 1 This has allowed the study of the behavior of devices having either regular or chaotic classical dynamics. 2‐4 The main aim of these works was finding clear signatures that differentiate the quantum behavior of both types of billiards allowing the characterization of ‘‘quantum chaos.’’ In particular, conductance and magnetoconductance measurements have been carried out on quantum dots of different shapes. 1‐4 In most of the theoretical and experimental studies either the shape of the quantum dot or the position of the leads was chosen so as to reduce transmission via direct trajectories. 2‐8 Apart from this precaution, however, in none of these works was a possible dependence of the conductance on the position of the leads explicitly mentioned. In this paper, we present concluding evidence for the strong dependence of the dot conductance on the position of the leads. It is shown that the distribution of conductances 7‐11 of quantum dots of shapes leading to regular or chaotic classical dynamics may become indistinguishable if the leads are placed so as to break the symmetry of the system. The effect is maximum in the quantum limit, i.e., for point contacts having a single channel, which is, on the other hand, the most interesting case. We also investigate the statistics of the energy spacing between resonances. Our results indicate that symmetry-breaking leads give a distribution of resonance spacings according to Wigner-Dyson statistics 12 only for small systems. As the system size increases, the variance of the distribution of adjacent levels of a cluster with a vacancy ~which perturbs the system in a manner similar to the leads! moves from its Wigner-Dyson value ~0.286! towards ;0.7. Quantum dots are described by means of a tight-binding Hamiltonian with a single atomic level per lattice site and nearest-neighbor hopping. Calculations were carried out on L3M clusters of the square lattice. Regular billiards are, thus, perfect rectangles, whereas chaotic billiards are simulated not by an irregular surface shape but randomly choosing the energies of the atomic levels at the surface sites S. 13