Gaussian Regimes Research Articles

Energy level statistics of quantum dots

We investigate the charging energy level statistics of disordered interacting electrons inquantum dots by numerical calculations using the Hartree approximation. The aim is toobtain a global picture of the statistics as a function of disorder and interaction strengths.We find Poisson statistics at very strong disorder, Wigner–Dyson statistics for weakdisorder and interactions, and a Gaussian intermediate regime. These regimes are asexpected from previous studies and fundamental considerations, but we also find interestingand rather broad crossover regimes. In particular, intermediate between the Gaussian andPoisson regimes we find a two-sided exponential distribution for the energy level spacings.In comparing with experiment, we find that this distribution may be realized in somequantum dots.

Pairing and coherence transition in La1.82Sr0.18CuO4 strongly two-dimensional superconductor

We report conductivity fluctuation measurements in the La1.82Sr0.18CuO4 high temperature superconducting material. The conductivity fluctuation analysis was performed by utilizing the concept of the logarithmic derivative of the conductivity excess. Close and above the critical temperature Tc, we experimentally determine the occurrence of Gaussian and critical fluctuation regimes. Systematic measurements of conductivity as a function of temperature were performed for several values of transport current j. Fluctuation analysis close to the zero resistivity temperature Tc0 was performed and we clearly identified a characteristic exponent, which is analyzed by the dynamical scaling theory and considering a percolation-like transition in a frustrated and disordered system. The observation of a glass-like behavior in our experiments permits to interpret our results as corresponding to a vortex-glass regime.

FLUCTUATION CONDUCTIVITY OF POLYCRYSTALLINEY1-xTbxBa2Cu3O7-δSUPERCONDUCTORS

We studied the effect of superconducting fluctuations on the electrical conductivity of granular samples of Y1-xTbxBa2Cu3O7-δsuperconductors. For all samples we observed that the transition proceeds in two stages. Above the critical temperature, the Gaussian and critical regimes were observed, independently of the terbium concentration. In the regime of approach to the zero resistance state, and for low concentrations of terbium, an occurrence of a coherence transition was observed. For high concentrations of Tb , the results show a strong disorder at mesoscopic levels.

Non-Gaussian statistics of optical near-fields

Optical fields in the proximity of random media can be modeled as a superposition of waves with random phases. We demonstrate that, depending on the experimental geometry, both Gaussian and non-Gaussian regimes can be established for the statistics of scattered intensity. In a reflection-emission configuration, the first-order statistics of the scattered light is non-Gaussian and it can be used to retrieve information about the physical interface.

Dynamic bond portfolio choice in a model with Gaussian diffusion regimes

This paper studies bond prices, intertemporal consumption and portfolio choice in a simple two-factor continuous-time regime-switching term structure model. The real interest rate and the expected inflation are modelled as an “extended” Ornstein–Uhlenbeck process, whose mean and variance shift randomly within a high–low Markovian regime. The prices of nominal and indexed bonds, the nominal and real term premia and the consumption-portfolio choice of a typical risk-averse investor are studied in the case in which the regime is observed.

Effects of pressure on the fluctuation conductivity ofYBa2Cu3O7

The effects of hydrostatic pressure up to $1.11\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ on the in-plane fluctuation conductivity of $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}d}$ are investigated. The experiments are focused on the asymptotic region closely above ${T}_{c}$ where a three-dimensional Gaussian and genuine critical regimes are identified. From the analysis of the Gaussian critical amplitude one deduces that the off-plane coherence length ${\ensuremath{\xi}}_{c}(0)$ does not change significantly with pressure in the studied range. At low applied pressures the asymptotic critical exponent indicates the occurrence of a scaling beyond three-dimensional $XY$. However, at the highest studied pressure, this exponent assumes a value consistent with the predictions of the full-dynamic three-dimensional $XY$ universality class. The width of the critical regime, as measured by the Ginzburg criterium, increases significantly with pressure. This result is related to a pressure-induced reduction of the in-plane coherence length ${\ensuremath{\xi}}_{ab}(0)$.

Fluctuation conductivity in melt-textured REBa2Cu3O7−δ superconductors

Abstract We have studied fluctuations on the electrical conductivity in melt-textured REBa 2 Cu 3 O 7− δ superconductors, where RE corresponds to a natural mixture of rare earth elements extracted from xenotime mineral. For this study, melt processed samples were prepared using the top seeding growth technique. To identify power-law divergences of the conductivity, the results were analyzed in terms of the temperature derivative of the resistivity and of the logarithmic temperature derivative of the conductivity. The data revealed the occurrence of a two-stage intragranular–intergranular transition. In the normal phase, different Gaussian and critical regimes were clearly observed to each current direction. Such an observation reveals that there is an evidence for anisotropies effects in studied conductivity regimes. Finally, the results obtained showed that the fluctuation conductivity in melt-textured samples of REBa 2 Cu 3 O 7− δ is very similar to those observed in YBa 2 Cu 3 O 7− δ .

Effects of Zn and Mg in Cu sites ofYBa2Cu3O7−δsingle crystals on the resistive transition, fluctuation conductivity, and magnetic irreversibilities

We report on the resistive transition and fluctuation conductivity of an ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{2.97}{\mathrm{Zn}}_{0.03}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal and on the magnetic irreversibilities of this compound in two different oxygen states and another ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal in which (1 at. %) of Cu was substituted by Mg. Our measurements show a very drastic decrease of the superconducting transition temperature and the growth of granularity effects already in this low dopand concentration. In the temperature region immediately above ${T}_{c}$ our results of fluctuation conductivity reveal the occurrence of critical and Gaussian regimes. The resistive transition of the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{2.97}{\mathrm{Zn}}_{0.03}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ single crystal occurs in two steps. First superconductivity sets in within the grains and at somewhat lower temperature long-range superconducting order takes place over the whole sample. Between the zero resistance temperature ${T}_{c0}(H)$ and the pairing transition temperature ${T}_{c}(H)$ lays the magnetic irreversibility line ${T}_{\mathrm{irr}}(H),$ which follows the power law predicted by the flux creep theories in most of the high field range. However, in a low field region, dominated by Josephson flux dynamics, the irreversibility line exhibits two different regimes dominated by disorder and frustration and characterized by AT (de Almeida-Thouless) and GT (Gabay-Toulouse) power law behaviors. This Josephson flux dynamics is squeezed into a considerably smaller field region than in other granular ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ systems. We attribute the origin of the observed stepwise resistive transition and low field magnetic irreversibility regimes mainly to the granularity of the superconducting state, which is induced by the impurities at the Cu sites and increased by shortage of oxygen.

Experimental measurement of the statistics of the scattered intensity from particles on surfaces

We analyze the statistics of the co-polarized and cross-polarized scattered intensity from a flat substrate contaminated with spherical particles including multiple scattering between them. Both Gaussian and non-Gaussian regimes are considered. In particular, we focus on both the cross-polarized component and the probability of detecting zeros in the cross-polarized intensity, P(Icross=0). As it is shown, the latter gives information about particle interaction and can be measured with higher accuracy than other statistical parameters. A theoretical model for P(Icross=0) is presented for spherical Rayleigh scatterers. An scattering experiment was carried out to verify this model.

HALL CONDUCTIVITY FLUCTUATIONS IN EPITAXIAL YBa2Cu3O7-δ THIN FILMS

We present systematic measurements of the longitudinal and Hall resistivities in YBa2Cu3O7-δ epitaxial thin films. Above the critical temperature, T c , the longitudinal resistivity, ρxx(T), increases linearly with temperature, whereas the Hall resistivity, ρxy(T), varies inversely proportional to T. Consequently, the cotangent of the Hall angle shows quadratic temperature dependence. The fluctuation contributions to both the longitudinal and Hall conductivities in the normal phase are studied. In the case of the longitudinal conductivity, 2D and 3D Gaussian regimes are observed. In addition, a genuine 3D-XY critical regime is discerned closely above T c in experiments performed at low applied fields. The value of the corresponding critical exponent, λ C =0.33, indicates that the dynamic universality class for the superconducting transition in the analyzed system is given by the Model E of Hohenberg and Halperin. The analysis of the Hall conductivity fluctuations above T c reveals the occurrence of 2D and 3D Gaussian regimes which are consistent with those identified in the longitudinal conductivity results. Below T c the Hall resistivity shows a sign reversal before attaining the zero resistance state.

Kubo number and magnetic field line diffusion coefficient for anisotropic magnetic turbulence.

The magnetic field line diffusion coefficients Dx and D(y) are obtained by numerical simulations in the case that all the magnetic turbulence correlation lengths l(x), l(y), and l(z) are different. We find that the variety of numerical results can be organized in terms of the Kubo number, the definition of which is extended from R=(deltaB/B(0))(l(parallel)/l(perpendicular)) to R=(deltaB/B(0))(l(z)/l(x)), for l(x) > or = l(y). Here, l(parallel) (l(perpendicular)) is the correlation length along (perpendicular to) the average field B(0)=B(0)ê(z). We have anomalous, non-Gaussian transport for R less, similar 0.1, in which case the mean square deviation scales nonlinearly with time. For R greater, similar 1 we have several Gaussian regimes: an almost quasilinear regime for 0.1 less, similar R less, similar 1, an intermediate, transition regime for 1 less, similar R less, similar 10, and a percolative regime for R greater, similar 10. An analytical form of the diffusion coefficient is proposed, D(i)=D(deltaBl(z)/B(0)l(x))(mu)(l(i)/l(x))(nu)l(2)(x)/l(z), which well describes the numerical simulation results in the quasilinear, intermediate, and percolative regimes.

Gaussian and Three-Dimensional-XY Scalings and Effects of Disorder in the Fluctuation Magnetoconductivity of Polycrystalline DyBa2Cu3O7-δ

Systematic measurements of the fluctuation magnetoconductivity in granular DyBa2Cu3O7–δ in magnetic fields up to 50 kOe are reported. Gaussian and critical scalings are observed in the normal state. In the Gaussian regimes, large intervals corresponding to low-dimensional fluctuations are evidenced. Below Tc, in the regime describing the approach to the zero-resistivity state, the fluctuation conductivity diverges as expected in the coherence transition of mesoscopic granular superconductors in low magnetic fields.

Anomalous and Gaussian transport regimes in anisotropic three-dimensional magnetic turbulence

Anomalous and Gaussian transport regimes in anisotropic three-dimensional magnetic turbulence

The Hartree approximation in dynamics of polymeric manifolds in the melt

The Martin–Siggia–Rose functional integral technique is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds. The integration over the collective variables of the melt can be simply implemented in the framework of the dynamical random phase approximation. The resulting effective action functional of the test manifold is treated by making use of the self-consistent Hartree approximation. As an outcome the generalized Rouse equation of the test manifold is derived and its static and dynamic properties are studied. It was found that the static upper critical dimension, duc=2D/(2−D), discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, d̃uc=2duc, distinguishes between the simple Rouse and the renormalized Rouse behavior. We have argued that the Rouse mode correlation function has a stretched exponential form. The subdiffusional exponents for this regime are calculated explicitly. The special case of linear chains, D=1, shows good agreement with Monte-Carlo simulations.

Dynamics of polymeric manifolds in melts: the Hartree approximation

The Martin-Siggia-Rose functional technique and the self-consistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds.The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension discriminate between Gaussian and non-Gaussian regimes, whereas its dynamic counterpart discriminates between Rouse- and renormalized-Rouse behavior. The dynamic exponents are calculated explicitly. The special case of linear chains shows agreement with MD- and MC-simulations.

Little-Parks effect for arbitrary geometry: fluctuations of the magnetic moment of mesoscopic loops

The Little-Parks effect is analytically deduced for a cylinder of an arbitrary section. A detailed analysis is performed for a case of elliptic sections with various eccentricities. Fluctuations of the magnetic moment are calculated for a loop of an arbitrary shape in the critical and Gaussian regimes.

Off-lattice reconstruction of porous media: critical evaluation, geometrical confinement and molecular transport

Disordered porous solids are examples of interfacial systems where an internal surface partitions and fills the space in a complex way. These media play an important role in industrial processes. One challenging problem deals with the ability to describe the morphology and the topology of disordered porous media. Quantitative knowledge of the three-dimensional pore (3D) network is important in order to understand the role of geometric confinement in adsorption, condensation, transport and reaction processes. In this paper, we first describe a simple way to build `off-lattice' reconstructed porous media with or without periodic boundaries, based on Gaussian random fields. The possibility of having a continuous and analytical description of the internal interface avoids finite size effects and is highly suitable for studying gas kinetics, molecular dynamics or adsorption process within the representative elementary volume. Critical evaluation of these computer models and comparison with experiments are performed for different types of geometrical disorder (cement pastes, soils, Vycor glass, symmetrical sponge phase, mass or surface fractals). In the second part of this work, we analyse one the most basic transport types in disordered porous media, i.e. the gas diffusion in the Knudsen or molecular regime. We first discuss how geometric confinement influences this transport through its self-diffusion propagator. Available experimental data, such as the tortuosity factor, and numerical simulations on 3D off-lattice reconstructed porous media are directly compared. Finally, we focus more especially on the Knudsen diffusion. We show that this transport process can be analysed in term of a continuous time random walk formalism (CTRW) and strongly depends on the analytical shape of the pore chord distribution function, f p( r). Different no Gaussian regimes are observed when f p( r) follows an algebraic law with an exponent μ*. For 1<μ*<3, the Knudsen diffusion is a Levy walk. Analytical properties of this Levy walk are given for 1<μ*<2 (mass or surface fractal). Comparison with numerical simulations conducted inside some 3D off-lattice reconstructions conclude this paper.

Contributions of critical and Gaussian fluctuations to the specific heat in and in under a magnetic field

The mean-field electronic specific heat of a superconductor in the presence of a magnetic field is first calculated. The model contains the following as ingredients: an energy spectrum presenting saddle points in the band structure, a Josephson coupling between CuO planes and a gap symmetry. Superconductivity fluctuations are next extracted from published data on the specific heat of a and of an single crystal. Critical XY and Gaussian regimes are deduced from mean-field calculations. Magnetic field cross-overs are evaluated and physical parameters such as the Ginzburg-Landau number and the distance between CuO planes are calculated as tests.

Fluctuation conductivity and microscopic granularity in Bi-based high-temperature superconductors

Systematic conductivity measurements near ${T}_{c}$ in granular (Bi,Pb)-Sr-Ca-Cu-O superconductors are presented, and focus is given on the interplay between thermal fluctuations and disorder at micro- and mesoscopic levels. Experiments show that the resistive transition is a two-step process. In the normal phase, Gaussian and critical fluctuation conductivity regimes were identified. Both are affected by local disorder. Particularly, the critical regime is characterized by a power law with exponent ${\ensuremath{\lambda}}_{\mathrm{cr}}\ensuremath{\sim}3,$ which we interpret as resulting from microscopic granularity. Below ${T}_{c}$ and in the regime describing the approach to the zero-resistance state, fluctuation conductivity diverges as expected in a paracoherent-coherent transition of a mesoscopic granular superconductor. The results show that, instead of trivially rounding the transition, disorder at micro- and mesoscopic levels preserves a true critical phenomenology in granular superconductors.

Gaussian, three-dimensional-XY,and lowest-Landau-level scalings in the low-field fluctuation magnetoconductivity ofBi2Sr2CaCu2O8

Systematic measurements of low-field fluctuation magnetoconductivity in a single crystal of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ are reported. Gaussian, critical, and lowest-Landau-level scalings are observed. In the Gaussian regimes, large intervals corresponding to low-dimensional fluctuations are evidenced. Far above ${T}_{c},$ effects of disorder produces a fluctuation spectrum characterized by a fractal topology. Decreasing the temperature, at first a homogeneous two-dimensional behavior is observed. Then, near ${T}_{c}$ a crossover occurs to a narrow three-dimensional (3D) mean-field regime. Still closer to ${T}_{c},$ a scaling consistent with the predictions of the full dynamic 3D-$\mathrm{XY}$ universality class is clearly evidenced. This genuine critical regime is destroyed upon the application of magnetic fields above a few mT. For fields above a certain limit and in large temperature intervals, fluctuation magnetoconductivity scales as predicted by the lowest-Landau-level approximation of the Ginzburg-Landau theory.