Quantum transport through anisotropic molecular magnets: Hubbard Green function approach

We extend the Green function approach to quantum transport through an anisotropic molecular magnet system with the help of Hubbard operators. Based on the single molecular magnet model, we reformulate the large spin and the total Hamiltonian in the language of Hubbard operators and obtain analytical expressions of the retarded Green function in sequential tunneling and Kondo regimes. In addition to this, we show the connection of our method to the master equation method in sequential regime and discuss a simple isotropic case in Kondo regime, in which we find a three-peak Kondo structure, a feature characterizing the isotropic exchange interaction between the localized electron and large spin.     

Green function solution of the Boltzmann transport equation for semiconducting thin film with rough boundaries

In this study the Green function solution of the Boltzmann transport equation on semiconducting thin film with irregular walls has been applied for the first time. The effects of electron scattering caused by these irregularities on the electrical conductivity have been investigated. First of all by using coordinate transformations, the irregularities on the walls have been transferred into the volume and in this way the both surfaces have been brought into flat forms. By taking two models, Gaussian and exponential, for random potential energy term contained in the transformed Hamiltonian as the perturbation, the resistivity results have been calculated and compared with the ones obtained from the methods widely known in the literature. The Boltzmann transport equation has been solved in relaxation time approximation for the irregular walled system in the case of no magnetic field.     

Special solutions of the Fokker-Planck transport equation for arbitrary band structures; Mobility and diffusivity in a uniform field of force

A Fokker-Planck equation can be derived from a transition-type transport equation if the transition rates are nearly local in momentum space compared with the inhomogeneity length of the distribution. It is a second-order differential equation, whose coefficients depend on the band structureE(k), the viscosity tensor (k), and the temperatureT. Classical solutions of the Fokker-Planck equation deal with the parabolic band structure of free Brownian particles in a field of force. Mobility and diffusivity are then independent of the applied field. Here the explicit solution for the stationary state and the time-integrated conditional probability will be given in one dimension. This suffices to determine mobility and diffusivity. Assuming = 1, these quantities become independent of the field and the band structure, if the latter is nonperiodic, though the distribution still depends on it. This property even holds in three dimensions fork-independent viscosity tensors. Field-dependent mobility and diffusivity are obtained for ak-dependent viscosity or = 1 and periodic band structures. The latter is demonstrated for the caseE-cosk, which is also related to the noise problem in Josephson junctions.     

An analytic and numerical solution with spectral Green's function method for transport equation in spherical geometry

Since in many cases curvilinear geometry is more appropriate than cartesian geometry for precise modeling of the complex systems for reactor calculation, we have developed the spectral Green's function (SGF) method which is employed to obtain angular and scalar flux distributions in heterogeneous sphere geometry with isotropic scattering. In this study, we showed that the neutron transport problems of homogeneous spheres could be reduced to the solution of plane geometry equation.Finally, some results are discussed and compared with those already obtained by diamond difference scheme to test the accuracy of the results. The agreement is satisfactory. SGF method is very suitable for the numerical solution of the neutron transport equation with isotropic scattering.     

Analytical evaluation of the plasma dispersion function for a Fermi—Dirac distribution

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.     

A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach

With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green’s function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach from two aspects. For the aspect of phonon transport, the phonon NEGF method is briefly introduced and its applications on thermal transport in mesoscopic systems including one-dimensional atomic chains, multi-terminal systems, and transient phonon transport are discussed. For the aspect of thermoelectric transport, the caloritronic effects in which the charge, spin, and valley degrees of freedom are manipulated by the temperature gradient are discussed. The time-dependent thermoelectric behavior is also presented in the transient regime within the partitioned scheme based on the NEGF method.     

Au-Si-Au结点电子输运性质的第一性原理计算

采用密度泛函理论和非平衡格林函数相结合的方法对Au(100)-Si-Au(100) 系统左侧对顶位、右侧对空位的纳米结点的电子输运性质进行了理论模拟计算, 结果得到纳米结点的电导随电极距离(d_z)增大而减小. 在d_z =9.72 Å时, 结点的结合能最低, 结构最稳定, 此时电导为1.227G₀ (G₀=2e²/h), 其电子输运通道主要是Si原子的p_x, p_y和 p_z轨道电子形成的最高占居轨道共振峰; 在外偏压下, 电流-电压曲线表现出线性特征; 随着外加正负电压的增大, 电导略有减小, 且表现出不对称性的变化. 关键词： 硅原子 电子输运 密度泛函理论 非平衡格林函数     

Model for anomalous transport of oxygen in nonstoichiometric perovskites: 1. General formulation of the problem

An attempt to explain the phenomenon of anomalous fast oxygen anion transport previously observed in the course of low temperatures topotactic oxidation of perovskite-related nonstoichiometric compounds has been made. According to the model developed the fast oxygen uptake relates to the high concentration of extended defects which exist in these compounds or can arise during oxidation. Experimentally observed specific kinetics has been described as being a result of fast oxygen transport taking place along the extended defects and followed by slow diffusion into undisturbed areas of the lattice.     

A general analytical method for evaluation of the thermodynamic properties of matters using virial coefficients with Morse potential at high temperature

In this paper, we established an analytical formula for the second virial coefficient (SVC) with Morse potential without using any numerical methods, and the obtained formula is applied to the calculation of the speed of sound of some matter at high temperature. This approach is based on the series expansion formula and special functions, which allows the exact evaluations of any thermodynamic properties of matter using the SVC. As an application, the obtained analytical formula is used for evaluation of the SVC with Morse potential for high‐temperature gas and the plasma region of the intermolecular interactions of neutral atom gases of B, Si, Zn, H₂, N₂, O₂, NO, CO, He, Ne, Ar, Kr , and Xe . Based on the obtained formula of SVC, the speed of sound for gases of N₂, Ar , and Zn are also determined analytically. A specific maximum temperature is chosen for every gas to ensure that there are still neutral atoms in the gas, and low temperatures are avoided due to quantum effects. The results are compared with numerical data and another analytical data from the literature. The new analytical solution is shown to be in good agreement with the compared data and is verified to supply proper thermodynamic data.     

New soliton solutions for a discrete electrical lattice using the Jacobi elliptical function method

This paper presents many new solutions of a modified Zakharov–Kuznetsov equation obtained by using the Jacobi elliptical function method. This equation is shown to model a two dimensional discrete electrical lattice. The solutions reported herein are of varied types and include hyperbolic and trigonometric solutions, as well as kink and bell-shaped solitons. The comparison of our results to well-known ones is done. The method used here is very simple and concise and can be also applied to other nonlinear partial differential equations. More importantly, the solutions found in this work can have significant applications in telecommunication systems where solitons are used to codify data.     

A Monte Carlo study of ionic transport in a simple cubic random alloy via the interstitialcy mechanism: effects of non-collinear and direct interstitial jumps

Self-diffusion and ionic conduction via the interstitialcy mechanism in a simple cubic, binary random alloy AB were investigated as a function of composition using Monte Carlo simulation. It was found that allowance for non-collinear jumps (partly) replacing concurrent collinear site exchanges leads to a reduction in diffusion correlation effects. This goes along with a shift of the diffusion percolation threshold to lower concentrations of the (more) mobile component B. Even stronger changes of mass and charge transport compared to an exclusively collinear interstitialcy scheme are observed for additional contributions of direct interstitial jumps. It is remarkable that for both extensions of interstitialcy mediated diffusion, the Haven ratio appears to be greater than unity in certain composition ranges poor in B. All results rely on the calculation of tracer and interstitialcy correlation factors in the simplest possible three-dimensional lattice structure. Yet they may have more general relevance to the interpretation of tracer self-diffusion data and ionic conductivity measurements on crystalline materials.     

Analytical approach to quantum phase transitions of ultracold Bose gases in bipartite optical lattices using the generalized Green’s function method

In order to investigate the quantum phase transitions and the time-of-flight absorption pictures analytically in a systematic way for ultracold Bose gases in bipartite optical lattices, we present a generalized Green’s function method. Utilizing this method, we study the quantum phase transitions of ultracold Bose gases in two types of bipartite optical lattices, i.e., a hexagonal lattice with normal Bose–Hubbard interaction and a d-dimensional hypercubic optical lattice with extended Bose–Hubbard interaction. Furthermore, the time-of-flight absorption pictures of ultracold Bose gases in these two types of lattices are also calculated analytically. In hexagonal lattice, the time-of-flight interference patterns of ultracold Bose gases obtained by our analytical method are in good qualitative agreement with the experimental results of Soltan-Panahi, et al. [Nat. Phys. 7, 434 (2011)]. In square optical lattice, the emergence of peaks at \(\left( { \pm \frac{\pi }{a}, \pm \frac{\pi }{a}} \right)\) in the time-of-flight absorption pictures, which is believed to be a sort of evidence of the existence of a supersolid phase, is clearly seen when the system enters the compressible phase from charge-density-wave phase.     

基于有限元法的光子并矢格林函数重整化及其在自发辐射率和能级移动研究中的应用

任意微纳结构中量子点的自发辐射率和能级移动均可用并矢格林函数表达.当源点和场点在同一位置时,格林函数的实部是发散的.为解决这一发散问题,可采用重整化格林函数方法.本文提出一种计算重整化格林函数和散射格林函数的方法.该方法利用有限元,计算点电偶极子的辐射场,将其在量子点体积内做平均得到重整化的并矢格林函数,减去均匀空间中解析的重整化格林函数,得到重整化的散射格林函数.在均匀空间情况下,本方法所得数值结果与解析解一致.将该方法应用到银纳米球系统,以解析的散射格林函数作为参考,结果表明该方法能准确处理散射格林函数的重整化问题.将该方法应用到表面等离激元纳米腔中,发现有极大的自发辐射增强和能级移动,且该结果不依赖于量子点的体积.这些研究在光与物质相互作用领域具有积极的意义.     

Molecular dynamics study of phonon-mediated thermal transport in a Ni50Al50 melt: case analysis of the influence of the process on the kinetics of solidification

The phonon-mediated contribution to the thermal transport properties of liquid NiAl alloy is investigated in detail over a wide temperature range. The calculations are performed in the framework of equilibrium molecular dynamics making use of the Green–Kubo formalism and one of the most reliable embedded-atom method potentials for the intermetallic alloy. The phonon-mediated contribution to the thermal conductivity of the liquid alloy is calculated at equilibrium as well as for the steady state. The relative magnitude of the thermal conductivity decrease induced by the transition to the steady state is estimated to be less than 2% below 2000 K and less than 1% at 3000 and 4000 K. It is also found that the phonon-mediated contribution to the thermal conductivity of the liquid alloy can be accurately estimated (well within 1%) on the basis of an approximation which invokes the straightforwardly accessible microscopic expression for the total heat flux without demanding calculations of the partial enthalpies needed for the precise evolution of the reduced heat flux (pure heat conduction). On the basis of these calculations, the correspondence between the experimentally observed and modelled kinetics of solidification due to a difference in thermal conductivity is discussed.     

Effect of boundary treatments on quantum transport current in the Green’s function and Wigner distribution methods for a nano-scale DG-MOSFET

In this paper, we conduct a study of quantum transport models for a two-dimensional nano-size double gate (DG) MOSFET using two approaches: non-equilibrium Green’s function (NEGF) and Wigner distribution. Both methods are implemented in the framework of the mode space methodology where the electron confinements below the gates are pre-calculated to produce subbands along the vertical direction of the device while the transport along the horizontal channel direction is described by either approach. Each approach handles the open quantum system along the transport direction in a different manner. The NEGF treats the open boundaries with boundary self-energy defined by a Dirichlet to Neumann mapping, which ensures non-reflection at the device boundaries for electron waves leaving the quantum device active region. On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region. In both cases the space-charge effect is accounted for by a self-consistent coupling with a Poisson equation. Our goals are to study how the device boundaries are treated in both transport models affects the current calculations, and to investigate the performance of both approaches in modeling the DG-MOSFET. Numerical results show mostly consistent quantum transport characteristics of the DG-MOSFET using both methods, though with higher transport current for the Wigner equation method, and also provide the current–voltage (I–V) curve dependence on various physical parameters such as the gate voltage and the oxide thickness.     

Turbulent scalar flux transport in head-on quenching of turbulent premixed flames: a direct numerical simulations approach to assess models for Reynolds averaged Navier Stokes simulations

The statistical behaviour and the modelling of turbulent scalar flux transport have been analysed using a direct numerical simulation (DNS) database of head-on quenching of statistically planar turbulent premixed flames by an isothermal wall. A range of different values of Damköhler, Karlovitz numbers and Lewis numbers has been considered for this analysis. The magnitudes of the turbulent transport and mean velocity gradient terms in the turbulent scalar flux transport equation remain small in comparison to the pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation when the flame is away from the wall but the magnitudes of all these terms diminish and assume comparable values during flame quenching before vanishing altogether. It has been found that the existing models for the turbulent transport, pressure gradient, molecular dissipation and reaction-velocity fluctuation correlation terms in the turbulent scalar flux transport equation do not adequately address the respective behaviours extracted from DNS data in the near-wall region during flame quenching. Existing models for transport equation-based closures of turbulent scalar flux have been modified in such a manner that these models provide satisfactory prediction both near to and away from the wall.     

Numerical resolution of the modified Langevin equation using a differential expression: Application to the Jiles magnetostriction law of approach

The Langevin equation is classically used to model the anhysteretic magnetization curve. A modified version of this equation has been introduced by Jiles to take into account the effects of magnetostriction on the anhysteretic magnetization behavior when a ferromagnetic material undergoes mechanical stresses. The numerical resolution of the modified Langevin equation is usually performed with a root-finding algorithm. In this paper, a differential form of the modified Langevin equation is proposed, allowing a faster numerical resolution.     

The influence of the dynamics of ionic multiplets onto electronic transport properties of heavy-fermion systems: a semi-phenomenological approach

We present calculations of the electronic transport properties of heavy-fermion systems within a semi-phenomenological approach to the dynamical mean field theory. In this approach the dynamics of the Hund's rules 4f (5f )-ionic multiplet split in a crystalline environment is taken into account. Within the scope of this calculation we use the linear response theory to reproduce qualitative features of the temperature-dependent resistivity and hall conductivity, the magneto-resistivity and the thermoelectric power typical for heavy-fermion systems. The model calculations are directly compared with experimental results on CeCu ₂ Si ₂. Received 30 June 2000 and Received in final form 15 December 2000     

Role of the d-f Coulomb interaction in intermediate valence and Kondo systems: a numerical renormalization group study

Using the numerical renormalization group method, the dependences on temperature of the magnetic susceptibility χ(T) and specific heat C(T) are obtained for the single-impurity Anderson model with inclusion of d-f the Coulomb interaction. It is shown that the exciton effects caused by this effect (charge fluctuations) can significantly change the behaviour of C(T) in comparison with the standard Anderson model at moderately low temperatures, whereas the behaviour of χ(T) remains nearly universal. The ground-state and temperature-dependent renormalizations of the effective hybridization parameter and f-level position caused by the d-f interaction are calculated, and satisfactory agreement with the Hartree-Fock approximation is derived.     

Exciton dynamics in nanostar dendritic systems using a quantum master equation approach: core monomer effects and possibility of energy transport control

The directional energy transport, i.e. exciton migration, in nanostar dendritic systems composed of two-state monomer units is studied using a quantum master equation approach. We examine the effects of the variation in the excitation energy of the monomer in the core region (core monomer) on the multistep exciton migration from the periphery to the core based on the relaxation factors among exciton states originating in weak exciton-phonon coupling. It turns out that when the core monomer possesses both an excitation energy slightly lower than that of the first generation and a partial exciton overlap with the first generation, more efficient and rapid exciton migration to the core is expected as compared with other core monomer cases with the energy level closer to or much lower than that of the first generation.