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If the gauge quantum chiral anomaly predicts chiral effects related to chemical potentials, then the gravitational chiral anomaly is responsible for the effects of temperature. The prediction of the gravitational anomaly for the temperature term in the chiral vortical effect coincides with the prediction of statistical calculations by the Kubo formula for spin 1/2, but two predictions disagree already for spin 1. A solution to this problem related to the features of infrared regularization is described. Also the thermodynamic instability in systems with acceleration, which occurs at temperatures below the Unruh temperature and the transition through the Unruh temperature are discussed.

The effect due to doping by B, Si, N atoms on the magneto-transport properties of graphene is investigated using the generalized tight-binding model in conjunction with the Kubo formula. The crucial electronic and transport properties are greatly diversified by different types of dopant and doping concentrations. The effect of these guest atoms includes opening a band gap, thereby giving rise to rich Landau level energy spectra and consequently a unique quantum-Hall conductivity. The Fermi-energy dependent quantum-Hall effect appears as a step structure having both integer and half-integer plateaus. Doping with Si leads to an occurrence of a zero quantum-Hall conductivity, unlike the plateau sequence for pristine graphene. The predicted dopant- and concentration-enriched quantum-Hall effect for doped graphene can provide useful information for magneto-transport measurements, possible technological and even metrology applications.

The properties of the electric transport in the neighbourhood of the topological transition is investigated in some topological insulators models such as the Qi-Wu-Zhang model or Chern insulator with aim to verify the behavior of the AC and DC currents employing the Kubo formula of linear response theory. The system describes electrons hopping in one- and two-dimensional chains, in case of one-dimensional model with staggered hopping amplitudes. Our results show a strong effect of the sudden variation of the topological charge Q on conductivity for the two-dimensional Chern insulator case. For the one-dimensional model, we obtain an ideal conductor behavior for the DC current.

Electronic properties of gapped graphene structure taking into account the effects of interaction between electrons and Einstein phonons have been addressed. Specially we study the temperature dependence of electrical conductivity and density of states of the structure. The effects of gap parameter, magnetic field and electron doping on electrical conductivity of the system have been studied. Gap parameter is defined as the on-site energy difference of atoms on two different sublattices of honeycomb structure. Green’s function method has been implemented to obtain electronic density of states of the system in the context of Holstein model Hamiltonian. One loop electronic self-energy of the model Hamiltonian has been obtained in order to find interacting electronic Green’s function. The electrical conductivity of graphene structure in the presence of electron-phonon coupling can be readily found using interacting Green’s function based on Kubo formula. We present the numerical results of energy dependence of density of states for different values of gap parameter and magnetic field in the presence of Holstein phonons. Finally the temperature dependence of electrical conductivity of gapped graphene structure due to electron phonon interaction and magnetic has been investigated. Our results show turning on magnetic field leads to appear double van Hov singularity for each value of electron phonon coupling.

A theoretical formulation is obtained for a chiral filled waveguide formed by two parallel graphene layers. The thin graphene layers are extended infinitesimally and Kubo formula is used for surface conductivity. The fields expressions in the model are obtained using Maxwell’s equations. It is shown that a chiral filled graphene parallel-plate waveguide can guide hybrid mode instead of quasi-transverse electromagnetic modes. The influence of chirality and or chemical potential on the properties of electromagnetic wave propagation in a planar graphene-chiral-graphene waveguide is discovered under realistic material parameters. A dispersion expression is derived, which covers the achiral graphene-chiral-graphene case. It is observed that when the chirality is raised to certain value the propagating mode is vanished. It is also revealed that chirality and chemical potential might modulate the propagation mode in the waveguide. This work may enrich the electromagnetic theory which is of great importance for Electronic devices. The presented results are compared with published under special cases.

The study on the electronic especially optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) in an antiferromagnetic state has been rarely involved. Here we theoretically study the electronic and optical properties of a ZPNR with N chains ( N -ZPNR) modulated by a vertical electric field (VEF). Within the Hubbard model Hamiltonian combined with the self-consistent calculation, and by adopting the Green’s function method, we obtain the band structure and corresponding conductance for the system. The corresponding optical absorption spectrum is further obtained based on the Kubo formula. It is interesting to find that there is an even–odd effect on the electronic and optical properties of N -ZPNR induced by the VEF, which may fundamentally originate from the parity of the wavefunctions. The VEF lifts the degeneracy of the two edge bands for 12-ZPNR, but it only bends and shifts the two edge bands without lifting the spin degeneracy for 13-ZPNR. We further present the spatial distribution of the corresponding wavefunction to understand this even–odd effect more intuitively. As expected, the VEF can separate the spin-up and -down optical absorption for 12-ZPNR, but it does not break the spin degeneracy of the optical absorption for 13-ZPNR. Our results may provide a further understanding on the electronic and optical properties of N -ZPNR with an antiferromagnetic state, and may be useful to identify the even–odd property of ZPNR samples by detecting the optical absorption in experiment.

Using the WIEN2k code, we perform ab-initio calculations of the electronic structure and the permittivity tensor of bcc Fe with magnetization along the [001] and [011] directions. The electronic structure is calculated with various numbers of k -points in the full Brillouin zone and the convergence of the calculated data is being studied. Two exchange-correlation potentials are employed, namely LDA and GGA, and their effect on the outcoming spectra is shown. The permittivity tensor is obtained from the electronic structure by the Kubo formula. From the permittivity tensor the complex spectra of linear ( K ) and quadratic ( G s , 2 G 44 ) magneto-optical parameters are extracted. The spectra are compared to the literature.

I study spin transport on the anisotropic ferromagnetic checkerboard lattice with a Dzyaloshinskii -Moriya interaction and an easy-axis anisotropy term. I show that by fine-tuning the parameters, we can get a flat band. The transverse and longitudinal dynamical spin conductivities are calculated using a Kubo formula. The Drude weight was also calculated as a function of temperature. The Drude weight vanishes at T = 0 but is finite for T > 0. A finite Drude weight indicates an ideal conductor, which we refer to as ballistic transport.

The Kubo formula is used to extract the electrical conductivity (EC) of different diameters of doped zigzag carbon nanotubes and their corresponding unzipped armchair graphene nanoribbons, as a function of temperature and chemical potential, within the tight-binding Hamiltonian model and Green's functions approach. The results reveal more sensitivity to temperature for semiconducting systems in addition to a decrease in EC of all systems with increasing cross-sections.

In this work, we investigate the longitudinal continuum spin conductivity of the spin-1 Heisenberg model with biquadratic interaction (the θ parameter controls the ratio of the biquadratic and exchange couplings). The calculations were performed for the model on square lattice in the Neel and ferroquadrupolar phases using spin wave theory and Schwinger boson formalism. In the antiferromagnetic phase that corresponds to range: - π θ 0 or ( sin θ 0 ), we use the Dyson-Maleev representation to calculate the spin conductivity at T = 0 finding the AC spin conductivity diverging at DC limit, ω = 0 . Evidencing so, that the system is an ideal spin conductor in this limit. In the ferroquadrupolar phase ( sin θ > 0 ), we find a different behavior for the spin conductivity which changes abruptly from a scalar to a tensor in the Green-Kubo formula: 〈 J 〉 = σ ∇ h , where σ is the conductivity, and also, in this case, a superconductor behavior for spin current at DC limit.

The present study tries to evaluate the fluctuation electrical conductivity in a granular s-wave superconductor at the temperature near to the critical temperature. The evaluation is conducted under the condition of limited tunneling conductance between the grains and small impurity concentration. All the first order fluctuation corrections, involving the nonlocal scattered electron in a granular s-wave superconductor, are calculated in three dimensions and in the limit of clean. Using Green's function theory initially, the Cooperon (impurity vertex), λ ( q , e 1 , e 2 ) , and the fluctuation propagator, L k ( q , Ω k ) , are calculated in the presence of impurities. Then, the three distinct contributions of Aslamazov-Larkin, Maki-Thompson, and Density of states are calculated by means of the Kubo formula. Analysis shows that the terms of Aslamazov-Larkin and anomalous Maki-Thompson have positive contributions to the conductivity in the clean limit, whereas the terms of Density of state and the regular Maki-Thompson have negative signs, leading to the reduction of total fluctuation conductivity.

We investigate thermal transport in a granular s-wave dirty superconductor at nanometer-scale in 3 d in the limit of large tunneling conductance, J T ≫ 1 at near and far from the critical temperature. Calculations is carried out by using Green's function, we obtain the impurity vertex (Cooperon) and fluctuations propagator in the presence of impurities. Then, by concerning Kubo formula we evaluate the three distinct contributions of the Aslamazov-Larkin (AL), Maki-Thompson (MT) and density of states (DOS). The distinctive contributions to fluctuations conductivity depend differently on the tunneling because of their different natures. Therefore, we will show that in the limit of e ≪ J T η/ T c , where η is the mean level spacing in a grain and ϵ = l n T T c ≃ ( T − T c ) / T c is the reduced temperature, the tunneling is effective also there is a crossover to the specific behavior of a homogeneous system, as T → T c , from the point of view of the fluctuating Cooper pairs. In the limit of e ≫ J T η/ T c , the tunneling is not effective, and the system behaves as an ensemble of real zero-dimensional grains.

We compute the optical conductivity of gapped graphene taking into account the effects of interaction between electrons and Einstein phonons beyond the usual Dirac-cone approximation. Our study is based on the Kubo formula that is established upon the retarded self-energy. Specially we report the frequency dependence of optical absorption of the structure. We find numerical results for frequency dependence of optical absorption for different values of gap parameter in the presence of Holstein phonons. We have also studied the effects of electron-phonon coupling strength and electronic concentration on the behavior of optical absorption of the gapped graphene structure. Our results show the increase of electronic chemical potential in doped case leads to appear optical band gap in the structure. This optical gap arises from Pauli blocking of vertical transitions when conduction band is doped. Electron-phonon coupling broadens the peak in the optical spectral and decreases the intensity of optical absorption. However the frequency position of the peak is not considerably affected by electron-phonon coupling.

In computing electric conductivity based on the Kubo formula, the vertex corrections describe such effects as anisotropic scattering and quantum interference and are important to quantum transport properties. These vertex corrections are obtained by solving Bethe-Salpeter equations, which can become numerically intractable when a large number of k-points and multiple bands are involved. We introduce a non-iterative approach to the vertex correction based on rank factorization of the impurity vertices, which significantly alleviate the computational burden. We demonstrate that this method can be implemented along with effective Hamiltonians extracted from electronic structure calculations on perfect crystals, thereby enabling quantitative analysis of quantum effects in electron conduction for real materials., Comment: 22 pages, 6 figures

The band structure, density of states (DOS), and electrical conductivity (EC) of different configurations of a double-strand poly-GC-poly-AT DNA-like nanowire are investigated within the tight-binding Hamiltonian model and the Green's function formalism. Three different configurations of the double-strand DNA-like nanowire were considered: infinite, finite, and cyclic. The change of behavior in the band structure due to the introduction of dimerization effects of the longitudinal hopping terms was studied. Without dimerization, the DNA-like nanowire behaves as a conductor and with dimerization, a semiconductor behavior was observed. This behavior change was also verified through the calculation of the DOS via the Green's function formalism. The effects of the finite size of the DNA-like nanowire and also the effect of length increase on the EC of the system were studied using Kubo formula. There exists a direct relationship between EC and length of DNA-like nanowire. As length increases, so does the EC of the DNA-like nanowire. This information can be useful in both theoretical research and experimental development of DNA-based molecular electronics.

We determine the classical diffusion of two dimensional Dirac-like quasiparticles, in the presence of conserving spin disorder (scattering off electric impurities) and non-conserving spin disorder (scattering off magnetic impurities). We use the Kubo formula for the conductivity tensor and employ diagrammatic perturbation theory to calculate the vertex correction and the renormalisation of the current operator for both electric and magnetic scattering. Scattering off electric impurities is isotropic and the current operator renormalised to two times the bare current operator irrespective of the direction of the dynamics, as usual for Dirac-like fermions. For magnetic scattering the renormalisation of the current operator depends on the direction of the dynamics and on the polarisation of the magnetic impurities, making the system anisotropic. We calculate the anisotropic magnetoresistance (AMR) and analyse it as a function of the ratio of the strength of the electric to the magnetic scattering potentials, for short range Gaussian correlation.

We conducted a theoretical study on magneto-optical (MO) properties of cylindrical metallic nanowires. The MO conductivity was calculated using the Kubo formula. Results show that in contrast to parabolically confined quantum wires realized from low-dimensional semiconductor systems, the features of MO absorption and the retard effect of the MO response by cylindrical metallic nanowires depend sensitively on the polarization of the radiation field due to corresponding selection rules. The frequencies of resonant absorption induced by inter-subband MO transition channels are within the terahertz (THz) bandwidth and can be tuned effectively by adjusting the radius of the nanowire and/or varying the strength of the magnetic field. This study is pertinent to the potential application of metallic nanowires as frequency-tunable THz optoelectronic devices.

Calculations of renormalized perpendicular conductivity within Kubo formula employing single particle temperature dependent Green's function formalism for bilayer graphene has been attempted. On the basis of numerical analysis, perpendicular conductivity as a function of temperature, interlayer coupling, onsite Coulomb interaction and carrier concentration per site has been analyzed for both AA- and AB-stacked bilayer graphene. It is found that perpendicular conductivity increases with interlayer coupling and also with temperature at low temperatures while at higher temperatures, there is saturation in perpendicular conductivity. Influences of onsite Coulomb interaction and carrier concentration per site on perpendicular conductivity is just opposite to each other while onsite Coulomb energy suppresses the rate of increase of σ ⊥ / σ ⊥0 with temperature, on the other hand increase in carrier density per site enhance this rate significantly. Finally, theoretically obtained results on temperature dependent perpendicular conductivity are viewed in terms of electronic transport data as well as recent theoretical works available in bilayer graphene.

We calculate the electrical conductivity of a metallic sample under the effects of distributed impurities and a random distribution of grain boundaries by means of a quantum mechanical procedure based on Kubo formula. Grain boundaries are represented either by a one-dimensional regular array of Dirac delta potentials (Mayadas and Shatzkes model) or by its three-dimensional extension (Szczyrbowski and Schmalzbauer model). We give formulas expressing the conductivity of bulk samples, thin films and thin wires of rectangular cross-sections in the case when the samples are bounded by perfectly flat surfaces. We find that, even in the absence of surface roughness, the conductivity in thin samples is reduced from its bulk value. If there are too many grain boundaries per unit length, or their scattering strength is high enough, there is a critical value R c of the reflectivity R of an individual boundary such that the electrical conductivity vanishes for R > R c . Also, the conductivity of thin wires shows a stepwise dependence on R . The effect of weak random variations in the strength or separation of the grain boundaries is computed by means of the method of correlation length. Finally, the resistivity of nanometric polycrystalline tungsten films reported in Choi et al. J. Appl. Phys. (2014) 115 104308 is tentatively analyzed by means of the present formalism.

We study a weakly disordered 2D electron gas with two bands and a spectral node within the weak-localization approach and compare its results with those of Gaussian fluctuations around the self-consistent Born approximation. The appearance of diffusive modes depends on the type of disorder. In particular, we find for a random gap a diffusive mode only from ladder contributions, whereas for a random scalar potential the diffusive mode is created by ladder and by maximally crossed contributions. The ladder (maximally crossed) contributions correspond to fermionic (bosonic) Gaussian fluctuations. We calculate the conductivity corrections from the density--density Kubo formula and find a good agreement with the experimentally observed V-shape conductivity of graphene., 10 pages, 2 figures

A non-contact method is proposed to characterize graphene at microwave frequency by combining Raman spectroscopy and Amphenol Precision Connector (APC-7). The CVD-grown graphene is transferred to the ring-shape Teflon substrate and characterized by Raman spectroscopy to estimate its doping density and the related Fermi energy. The graphene is then sandwiched between two APC-7 coaxial connectors and S parameters under transverse electromagnetic (TEM) mode normal incident waves are measured to extract the surface conductivity through transmission matrix, in which the de-embedding process can be avoided. By combing the Kubo formula with our proposed circuit model, the scattering rate of graphene on Teflon substrate is obtained and analyzed.

Kubo formula was obtained for conductivity tensor of electron gas on the surface of nanotube with superlattice in magnetic field. The high-frequency conductivity tensor components were calculated for quantum and quasiclassical cases. Electromagnetic wave Landau damping areas in the tube were determined. The conductivity tensor components show Aharonov–Bohm type oscillations and de Haas–van Alphen ones. When Fermi energy exceeds the miniband width, beatings are observed in the plot of conductivity vs. the tube parameters. Otherwise, the beatings are absent.

It is well known that future information technology relies upon electronic states other than charge, through the feasibility of constructing spintronic and valleytronic devices. The main challenge in such applications is the generation and control of the corresponding state currents. The present paper is thus concerned with charge, spin and valley currents which intrinsically develop in armchair silicene nanoribbons (ASNs). In pursuing this consideration the well established Kubo formula is employed. Taking the symmetries of the ASN into account, we analyze the structure of total Hamiltonian and demonstrate how the matrix elements along with the summations involved in the suitably adopted Kubo formula, may be analytically calculated. The results so-obtained along with the corresponding figures reveal that all three currents develop in a step-wise manner. The heights, indicating a jump in the current, and the plateaus, indicating a constant current, are shown to be tunable by adjusting the width and/or the buckled effect. Moreover, we demonstrate that for particular (critical) widths an inversion in band gaps may occur, giving rise to quantum phase transitions. More practical result of this paper, as we show, is the fact that the ASN can generate pure spin or valley current under specific conditions placed on the width, buckled effect and Fermi energy. The material presented in this paper thus provides novel means of generation and control of the charge, spin and valley currents.

The electric field-induced optical activity of monolayer phosphorene within the framework of effective anisotropic tight-binding model and the linear response theory is studied. The optical conductivity tensor is derived using the Kubo formula and an incident circular electromagnetic wave is applied perpendicularly to the phosphorene’s plane. By dividing the optical frequency into three regimes, beneath, near and above the band gap, the electric-field-dependent measurement of the stretching and rotation angle of the polarization ellipse is investigated in details. Beneath the band gap, both reflected and transmitted lights are almost polarized linearly independent of the gate voltage, however, the polarization can be tuned via the electric field for the frequencies near and above the band gap. Our results show that, at certain electric fields, rotation angle 180° of the polarization ellipse belongs only to the frequencies above the band gap. Additionally, the absorption in phosphorene is possible up to a few percents, confirming the transparency of monolayer phosphorene. The findings here pave the way for setting up the real applications in optoelectronics.

We present electric field effects on the optical field-dependent dielectric function of phosphorene. We use a two-band model and the Kubo formula to obtain refractive index and absorption coefficient. From our findings, the refraction (absorption) along the armchair direction is smaller (larger) than the zigzag direction for the optical energies close to and larger than the band gap. Moreover, we find that for frequencies beneath the band gap, dynamical dielectric function decreases with the electric field independent of the orientation, whereas there is a strong anisotropic treatment above the band gap.

Using the Kubo formula approach and Green's function method, the temperature dependence of the transmittance and effective surface resistance of high quality MgB2 film are calculated in the framework of the two-band model. For large interval of temperatures below TC our results are in agreement with experimental data. We show a single-gap model based on BCS theory, which is insufficient to understand such quantities, but a two-band model with different symmetries can describes the experimental data rather well. In the two-gap model we consider that the transmittance and effective surface resistance are a weighted sum of the contributions from σ and π bonds and hybridization between them is negligible.

It is proved that the Kubo formula for the conductivity σ ( ω ) is valid at real frequencies ω. On this basis, an exact relation is derived for the static conductivity σ st of the Coulomb system. It is shown that the static conductivity is determined by the time correlation function in the limit t → ∞ . It is proved that the permittivity e ( ω ) satisfies the Kramers–Kronig relations which take into account a singularity associated with static conductivity.

The thermal conductivity of ZnTe with zinc-blende structure has been computed by equilibrium molecular dynamics method based on Green–Kubo formalism. A Tersoff's potential is adopted in the simulation to model the atomic interactions. The calculations are performed as a function of temperature up to 800 K. The calculated thermal conductivities are in agreement with the experimental values between 150 K and 300 K, while the results above the room temperature are comparable with the Slack's equation.

We study the Anderson model on a two-dimensional square lattice with an applied weak magnetic field B which causes the hopping matrix elements to have Peierls phase factors. The recursion method is applied and B dependent conductivity σ(B) is calculated from the Kubo formula for different system sizes N and degree of disorder W. For large W there is no appreciable change of σ(B) with B, but its system size dependence is first an increasing and then a decreasing behavior.

In this contribution, we present a numerical study of quantum transport in carbon nanotubes based materials. After a brief presentation of the computational approach used to investigate the transport coefficient (Kubo method), the scaling properties of quantum conductance in ballistic regime as well as in the diffusive regimes are illustrated. The impact of elastic (impurities) and dynamical disorders (phonon vibrations) are analyzed separately, with the extraction of main transport length scales (mean free path and localization length), as well as the temperature dependence of the nanotube resistance. The results are found in very good agreement with both analytical results and experimental data, demonstrating the predictability efficiency of our computational strategy. To cite this article: H. Ishii et al., C. R. Physique 10 (2009).

In this paper, we study spin currents, generated by a magnetic field gradient, in the two-dimensional XY model with single-ion anisotropy and coupled to phonons in the large D phase. The spin conductivity is calculated, at zero temperature, using the Kubo formula.

Based on the Kubo–Greenwood formula, a novel renormalization plus convolution method is developed to investigate impurity effects on the electrical conductivity of periodic and aperiodic systems. This method combines the convolution theorem with the real-space renormalization technique, being able to address multidimensional quasiperiodic systems with defects. In this paper, the electronic transport in mirror Fibonacci systems with site impurity is investigated in detail. The results show that the mirror symmetry in quasiperiodic systems induces a large number of transparent states in the dc conductivity spectra. Moreover, the introduction of symmetrically located impurities in mirror Fibonacci chains preserves many of these transparent states. Finally, impurity effects on the ac conductivity of quasiperiodic nanowires are also analyzed.

We investigated the phonon scattering effects on the transport properties of carbon nanotube devices with micron-order lengths at room temperature, using the time-dependent wave-packet approach based on the Kubo formula within a tight-binding approximation. We studied the scattering effects of both the longitudinal acoustic and the optical phonons on the transport properties. The conductance of semiconducting nanotubes is decreased by the acoustic phonon, instead of the optical phonon. Furthermore, we clarified how the electron mobilities of the devices are affected by the acoustic phonon.

By applying the numerical tensor analysis proposed by Yoneda and Kubo [Simultaneous determination of mean pressure and deviatoric stress based on numerical tensor analysis: a case study for polycrystalline X-ray diffraction of gold enclosed in a methanol–ethanol mixture. J. Phys.: Condens. Matter 18(2006)S979], we have determined deviatoric stress and mean pressure of polycrystalline MgO compressed in the Kawai-type apparatus. After the compression at room temperature, the mean pressure and the deviatoric stress in MgO were determined as 34.5 and 3.2 GPa, respectively. The mean pressure is significantly lower than the nominal pressure of 37.2 GPa determined by the conventional pressure determination method. By heating the sample to 1850 K with the constant press load, the deviatoric stress dramatically decreased to 0.1 GPa with a mean pressure of 34.2 GPa at room temperature after the heating. These results show both the importance of stress analysis to determine pressure more accurately and the effectiveness of annealing to reduce deviatoric stress in the sample.

The general formulae of the dynamic susceptibility are derived using the relaxation method and the TCLE method for the linear response by introducing the renormalized hat-operator in terms of thermo-field dynamics (TFD). In the former method, the Kubo formula is calculated for systems with no external driving fields, while in the latter method the admittance is directly calculated from time-convolutionless equations with external driving terms. The relation between the two methods is analytically investigated, and also the fluctuation–dissipation theorem is examined for the two methods in terms of TFD. The TCLE method is applied to an interacting spin system, and a formula of the transverse magnetic susceptibility is derived for such a system. The transverse magnetic susceptibility of an interacting spin system with S = 1 / 2 spins is obtained up to the first order in powers of the spin–spin interaction.

It is well-known that liquid caesium shows some unusual properties at low densities. We used supercell technique within linear muffin-tin orbital method to investigate this phenomenon. Electronic structure of liquid caesium for different temperatures from the melting point up to critical point was obtained. The atomic structure was simulated for a cluster of 2000 atoms by the Reatto method on the base of experimental structure factors of Cs obtained by Winter and co-workers for different temperatures (from 323 K up to 1923 K). The Kubo-Greenwood formula was applied for the calculations of melts conductivity. The received results indicate that metal-nonmetal transition in liquid cesium is connected not to the gap at Fermi energy in density of electronic states, but more likely with electrons localization on some kind of atomic clusters. © 2007 Elsevier B.V. All rights reserved.

We are interested in the behavior with respect to the small parameter ϵ > 0 of solutions ρ ϵ of the conservative transport(-diffusion) equation ∂ t ρ ϵ + ∇ x ( ρ ϵ u ϵ ) = η Δ x ρ ϵ , with η ⩾ 0 , driven by a large random velocity field: | u ϵ | = O ( 1 / ϵ ) . Assuming that the velocity does not have long-time memory we justify the convergence of the expectation E ρ ϵ to the solution of a diffusion equation. This question has been widely investigated; here we present a simple proof which only relies on PDE tools.

The resistivities of liquid alkali metals are investigated using Ziman formula and the alternative expression based on Kubo formula suggested by Unal and Alkan [B. Unal, B. Alkan, J. Phys. Soc. Jpn. 62 (1993) 2425]. As the input pseudopotential, the individual version of the electron-ion potential proposed by Fioalhais and coworkers which was originally developed for solid state is used and static structure factors are derived from the solution of Ornstein–Zernike integral equation with Rogers–Young closure. Good agreement with experiment is found for liquid Na and K using both formulas. For Li, Rb and Cs the agreement between the calculated values using Ziman formula and experimental data is less satisfactory. From present investigations, it is shown that the formula based on Kubo formula suggested by Unal and Alkan is the better chose for the resistivity calculations of liquid Li, Rb and Cs metals.

Nonequilibrium steady states (NESS) and current fluctuations are investigated for a noninteracting system consisting of a single-level quantum dot (QD) embedded in an Aharonov–Bohm (AB) ring. With the aid of asymptotic incoming fields, NESS are explicitly constructed. In terms of current fluctuations, the interplay between particle-like and wave-like behaviors of electrons is investigated. The current–current correlation function is found to be related to the differential conductance (an extension of the Kubo formula) and a relative entropy production is shown to be nonnegative at NESS.

By obtaining Kubo formula type and using nonequilibrium Green’s functions, we calculate the shear viscosity of a trapped Bose-condensed gas below and above the Bose–Einstein condensation temperature (TBEC). The contributions of the interactions between condensate and noncondensate atoms and between noncondensate atoms take into account to the viscous relaxation time, by evaluating second order self-energies in Beliaev approximation.

We report novel features of angular dependent magnetoresistance oscillations (AMROs) observed in strong magnetic fields where only a few Landau levels are occupied. In order to realize this “near-quantum-limit” in real Q2D systems, we have chosen GaAs/AlGaAs semiconductor superlattices for AMRO experiments. Near the quantum limit, the peak position of AMRO slightly depends on field strength, and it jumps synchronizing Shubnikov-de Haas peaks. AMRO disappears when the parallel field component exceeds a certain value which gives a broad local minimum of interlayer resistance. The observed features are hardly expected from the conventional picture based on the semiclassical Fermi surface topological effect ignoring Landau quantization. We have successfully explained these new features by the quantum mechanical picture which evaluates interlayer conductivity from magnetic eigen states using the Kubo formula. This quantum picture gives the most general and complete description of AMRO in Q2D conductors.

Thermal conductivity of GaN was investigated by molecular dynamics simulation. We used Stillinger–Weber potentials, and Green-Kubo's formula was employed to calculate thermal conductivity. The results showed that the thermal conductivity of GaN at 300 K was in the range of 310 λ 380 W / mK , which is higher than the reported experimental values. We also investigated the temperature dependence of thermal conductivity in the temperature range of 300–1200 K.

The real part of the optical conductivity is calculated by using the Kubo formula approach, and in the framework of the two-bands model. It is shown that a single-gap model is insufficient to describe the optical behavior of superconductor MgB 2 film, but the two-gap model with different symmetries is sufficient to explain the experimental results.

Pumping of charge (Q) in a closed ring geometry is not quantized even in the strict adiabatic limit. The deviation form exact quantization can be related to the Thouless conductance. We use Kubo formalism as a starting point for the calculation of both the dissipative and the adiabatic contributions to Q. As an application we bring examples for classical dissipative pumping, classical adiabatic pumping, and in particular we make an explicit calculation for quantum pumping in case of the simplest pumping device, which is a 3 site lattice model., 5 pages, 3 figures. The long published version is cond-mat/0307619. This is the short unpublished version

The localization and transport properties in quasiperiodic systems are quite different from those in crystalline and in disordered materials. In this work, we study the electrical conduction in macroscopic Fibonacci lattices by using the Kubo–Greenwood formula and a single-band tight-binding model. This study is carried out by means of the convolution technique and a novel renormalization method, which allows iterative evaluation of the products of the Green’s function in an exact way. The results of the spectrally averaged conductance show a power-law decay as the length of the quasiperiodic systems increases along the applied electric field. This fact reveals the critical localization nature in quasicrystalline materials, contrary to the constant and exponencial decay behaviors found in the periodic and randomly disordered systems, respectively.

The thermal conductivity of a trapped Bose condensed gas is calculated by using the Kubo formula approach. By evaluating the appropriate self-energies of the system the thermal relaxation time is calculated. Below the Bose–Einstein condensation temperature in addition to the relaxation time due to collision between non-condensate atoms ( τ 22 ) we include the contribution from the interaction between condensate and non-condensate atoms ( τ 12 ) in the thermal relaxation time. In a trapped Bose gas the contribution of the relaxation time ( τ 12 ) is always important, since the condensate density at the central region of a trap is much larger than the density of the thermal cloud even at temperatures near the transition temperature. Above the Bose–Einstein condensation temperature the only term present is τ 22 and the normal thermal conductivity coefficient is obtained.

The far-infrared absorption in two-dimensional electron layers subject to magnetic field of general orientation was studied theoretically. The Kubo formula is employed to derive diagonal components of the magneto-conductivity tensor of two-dimensional electron single-layers and double-layers. The parabolic quantum well is used to model a simple single-layer system. Both single-layer and double-layer systems can be realized in a pair of tunnel-coupled, strictly two-dimensional quantum wells. Obtained results are compared to experimental data., Comment: 4 pages, 6 figures, elsart/PHYEAUTH macros; presented on the EP2DS-15 Conference in Nara, Japan. To be published in Physica E

We present ab initio calculations of the electronic transport properties of a hypothetical monoatomic quasiperiodic system, decagonal aluminum (d-Al). Our aim is to study the influence of quasiperiodicity on the transport properties in an example system that is sufficiently realistic to represent real Al-based quasicrystals, but does not involve the additional complexity of a strong s,p–d hybridization, which determines the properties of many crystalline and quasicrystalline Al-transition metal alloys. The investigation of the transport properties of a series of quasiperiodic approximants with increasing linear dimensions is based on a calculation of the electronic eigenstates and the Kubo–Greenwood formula. A scaling analysis demonstrates small deviations of the eigenstates from extended behavior and shows that the transport properties belong to the sub-ballistic regime, with a scaling exponent of the electronic diffusivity of β∼0.66 that is somewhat larger than the quantum-diffusion limit (β=0.5), but distinctly smaller than for ballistic transport (β=1). In this sub-ballistic or over-diffusive regime the conductivity diverges in the thermodynamic limit, leading to metallic behavior.

By an improved scaling analysis, we suggest that there may appear two possibilities concerning the electronic localization in two-dimensional random media. The first is that all electronic states are localized in two dimensions, as conjectured previously. The second possibility is that electronic behaviors in two- and three-dimensional random systems are similar, in agreement with a recent calculation based on a direct calculation of the conductance with the use of the Kubo formula. In this case, non-localized states are possible in two dimensions, and have some peculiar properties. A few predictions are proposed. Moreover, the present analysis accommodates results from the previous scaling analysis.

The electronic transport at zero degrees in quasiperiodic systems is investigated by using the Kubo–Greenwood formula and a novel renormalization method, which allows an evaluation in an exact way of the products of the Green’s function in macroscopic Fibonacci chains. The analysis of transport properties in two-dimensional Fibonacci superlattices and in double quasiperiodic lattices is carried out by means of the convolution technique. The spectrally averaged conductance shows a linear dependence with the width of the system and a power-law decay as its length increases along the applied electric field.