Theories of electrons in one-dimensional disordered systems

A critical survey of the literature on the theory of electronic states in, and electron transmission through, models of one-dimensional disordered solids and liquids is given in the first part. Reference to work on three-dimensional systems is included, especially where exact results have been obtained. The relationship between this subject and the problem of elastic vibrations in disordered solids is pointed out. A complete exposition of the authors' work on one-dimensional conductivity is then presented. It provides a rigorous solution of the problem of average resistance, and of the variance (fluctuations) of resistance, for important classes of disorder which are carefully and precisely defined. Conclusions regarding the role of disorder with respect to the transmission properties are presented and discussed. It is also pointed out that, with appropriate modifications, the results apply generally to wave propagation in inhomogeneous media.     

在相干态表象中精确求解无旋波近似的Jaynes-Cummings模型

在相干态表象中精确求解了无旋波近似的Jaynes-Cummings模型，并导出了相应的限制性条件．所求得的解析解与用微扰论求得的近似解比较，当微扰级数取无穷时所得结果一致．本文的方法能方便地推广到三能级系统的讨论． 关键词：     

3-D numerical modeling and simulation of nanoscale FinFET for the application in ULSI circuits

A complete three-dimensional numerical modeling of nanoscale FinFET including quantum-mechanical effects for the application in future ULSI circuits has been developed. The exact potential profile in the channel has been computed by obtaining a self-consistent solution of 3D Poisson–Schrödinger equation using Leibmann's iteration method. The threshold voltage shift, drain and transfer characteristics have been estimated and the results were compared with the device simulator and experimental results. The model is purely a physics based one and overcomes the major limitations of the existing 2D/3D analytical models by providing a more accurate result and this model is validated by comparing with the existing results as well as the experimental results.     

Diffraction radiation from a finite-conductivity screen

An exact solution has been found for the problem of diffraction radiation appearing when a charged particle moves perpendicularly to a thin finite screen having arbitrary conductivity and frequency dispersion. Expressions describing the diffraction and Cherenkov emission mechanisms have been obtained for the spectralangular forward and backward radiation densities.     

Compositional effect on thermo-mechanical,thermal and tensile properties of cis-polyisoprene and chloroprene rubber blends

Blends of cis-polyisoprene (CPI) and chloroprene rubber (CR) have been prepared in different blend compositions by solution casting. Structural characterization of these blends has been done using X-ray diffraction and scanning electron microscopy. The experimental values of thermo-mechanical properties, mechanical properties and thermal conductivity of so-prepared blends determined using dynamic mechanical analyzer and thermal constant analyzer have been presented. Crosslink density has been determined using different models. Experimental results from thermo-mechanical properties show that all the blends are immiscible. Tensile strength, toughness, Young's modulus and thermal conductivity of these blends were found to be higher than that of pure CPI and pure CR. However, mechanical properties of 25/75(V/V) of CPI/CR blend and thermal conductivity of 75/25(V/V) of CPI/CR blend have been found to be highest.     

The 2-site Hubbard and $\mathsf{t}$-$\mathsf{J}$ models

The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Greens function formalism. The exact solution of the t-J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response properties have been studied as functions of the external parameters and compared between the two models and with some numerical and exact results. It has been shown that the 2-site Hubbard model already contains the most relevant energy scales of the Hubbard model: the local Coulomb interaction U and the spin-exchange one . As a consequence of this, for some relevant properties (kinetic energy, double occupancy, energy, specific heat and entropy) and as regards the metal-insulator transition issue, it has resulted possible to almost exactly mime the behavior of larger systems, sometimes using a higher temperature to get a comparable level spacing. The 2-site models have been also used as toy models to test the efficiency of the Greens function formalism for composite operators. The capability to reproduce the exact solutions, obtained by the exact diagonalization technique, gives a firm ground to the approximate treatments based on this formalism.Received: 16 July 2003, Published online: 30 January 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.)     

Effective medium theory of A.C. Hopping conductivity for random-bond lattice models

We apply standard effective medium techniques to calculate the A.C. hopping conductivity of a system where the sites are located on a regular lattice but the intersite hop-rate is a random variable. The method is a generalization of Kirkpatrick's treatment of the D.C. conductivity of such a system. The results are compared with exact solution of the one-dimensional bond percolation problem and good agreement is found.     

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre–matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.     

Influence of surface roughness on the electrical conductivity of semiconducting thin films

The Green function solution of the Boltzmann transport equation has been applied in case of no magnetic field by ignoring any volume impurities. Gaussian, exponential and power law models for the surface roughness correlation function have been studied and the results have been compared with the ones obtained by other methods. It has been found that the electrical conductivity σ$\sigma$ increases with increasing correlation length l$l$ for the first two models, while for the third model σ$\sigma$ value is of the same order as the first two models. Therefore we show that the shape of the surface roughness can strongly influence the electrical properties.     

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.     

Spherically Symmetric Solutions of Light Galileon

We have been studied the model of light Galileon with translational shift symmetry ? → ? + c. The matter Lagrangian is presented in the form \(\mathcal {L}_{\phi }= -\eta (\partial \phi )^{2}+\beta G^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi \). We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of \(f(R,R^{\mu \nu }T_{\mu \nu }^{m})\). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon’s field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ? = t, which it is remembered by us dilaton field.     

Travelling Wave Solution of Korteweg-de Vries-Burger's Equation

An attempt has been made to obtain exact analytical travelling wave solution of Korteweg-de Vries-Burger's (KdVB) equation by the so-called tanh-method. This equation can be derived for dust ion acoustic shocks by using reduction perturbation method. It is found that an exact solution of the KdVB equation is obtained by tanh-method, provided the parameters involved satisfy a constraint relation. However a special exact analytical solution can be obtained where no such restriction is necessary. This solution has the structure of a shock wave. Numerical solution is also obtained for travelling wave with or without the assumption of the constraint relation. We have also found a singular solution in terms of cosech and coth functions.     

Growth index with the exact analytic solution of sub-horizon scale linear perturbation for dark energy models with constant equation of state

Three decades ago Heath found the integral form of the exact analytic growing mode solution of the linear density perturbation δ on sub-horizon scales including the cosmological constant or the curvature term. Recently, we obtained the exact analytic form of this solution in our previous work [1]. Interestingly, we are able to extend this solution for general dark energy models with the constant equation of state ωde${\omega }_{\mathit{de}}$ in a flat universe. This analytic solution provides the accurate and efficient tools for probing the properties of dark energy models such as the behavior of the growth factor and the growth index. We investigate the growth index and its parameter at any epoch with this exact solution for different dark energy models and find that the growth index is quite model dependent in the redshift space, 0.25?z?1.5$0.25?z?1.5$, so observations of the structure growth around this epoch would be very interesting. Also one may be able to rule out some dark energy models by using the analysis from this exact solution. Thus, the analytic solution for the growth factor provides the very useful tools for future observations to constrain the exact values of observational quantities at any epoch related to the growth factor in the dark energy models.     

Transport Coefficients in Some Stochastic Models of the Revised Enskog Equation

A stochastic model of the revised Enskog equation is considered. A choice of the smearing function suggested by the work of Leegwater is used to apply the model to the repulsive part of the Lennard-Jones potential and the inverse-power soft-sphere potential. The virial coefficients obtained from the equilibrium properties of the models are in excellent agreement with the known exact coefficients for these models. The transport coefficients for the repulsive Lennard-Jones (RLP) model are also computed and appear to be of comparable accuracy to the Enskog-theory coefficients applied directly to a hard-sphere system, although exact results for the RLP with which to make an extensive comparison are not yet available. The pressure and the transport coefficients obtained from the model (shear viscosity, thermal conductivity, and self-diffusion) are compared with the pressure and the corresponding transport coefficients predicted by the Enskog and square-well kinetic theories.     

THE CRITICAL DYNAMICS OF THE KINETIC ISING MODELS ON THE SYSTEMS WITH Rmin> 2

We perform the exact TDRG transformations on the kinetic Ising model of the braced ladder whose R_min is 5. Within our knowledge, this is the only example that the exact TDRG transformations have been performed on a system with R_min >2. We show that under Achiam's linear response theory there must be important excitations of the multi-spin operators in the kinetic Ising models of the systems with R_min > 2, the dynamic critical behaviours of the systems are greatly affected by these excitations. Moreover, we get the conclusion that for the kinetic Ising models of the systems with R_min=∞ exact TDRG calculationa are impossible. The complete new and interesting results are given.     

Exact and model operators for magnon-phonon interactions in antiferromagnets

A theoretical study is given of magnon-phonon interactions in antiferromagnetic materials. The roles of magnons and phonons as heat carriers and as sources of thermal resistance have been taken into consideration. The exact collision operator which represents the magnon-phonon interactions involved in the transport Boltzmann equations has been replaced by a model operator which possesses the same important properties. The effect of other scattering processes that either phonons or magnons are involved has also been investigated. A new expression for the thermal conductivity has been derived. It includes terms which represent both Normal and Umklapp magnon-phonon processes. The results obtained by using the new expression agree quantitatively with the experimental measurements on Fe Cl₂     

Tunneling conductivity in lithiated transition metal oxide cathode Li<Subscript>0.9</Subscript>[Ni<Subscript>1/3</Subscript>Mn<Subscript>1/3</Subscript>Co<Subscript>1/3</Subscript>]O<Subscript>1.95</Subscript>

Electrical complex ac conductivity of the compound Li_0.9[Ni_1/3Mn_1/3Co_1/3]O_1.95 has been studied in the frequency range 10 Hz–2 MHz and in the temperature range 93–373 K. It has been observed that the frequency dependence of the ac conductivity obeys a power law and the temperature dependence of the ac conductivity is quite weak. The experimental data have been analyzed in the framework of several theoretical models based on quantum mechanical tunneling and classical hopping over barriers. It has been observed that the electron tunneling is dominant in the temperature range from 93 K to 193 K. A crossover of relaxation mechanism from electron tunneling to polaron tunneling is observed at 193 K. Out of the several models discussed, the electron tunneling and the polaron tunneling models are quite consistent with the experimental data for the complex ac conductivity. The various parameters obtained from the fits of the experimental results for the real and imaginary parts of the conductivity to the predictions of these models are quite reasonable.     

Validity of Scalar Approaches to Radiation Modes of the GaAs-Based 1.3-μm Diode Lasers Designed for the Optical–Fibre Communication

The work presents a comparison between results of optical simulations based on the scalar and vectorial models applied to both stripe – geometry Fabry-Perot (FPL) as well as vertical-cavity surface-emitting (VCSEL) diode lasers designed for the 1.3-μm optical–fibre communication. As compared to vectorial optical approaches, scalar ones are known to be less exact but simultaneously they need as many as approximately 100 times shorter computation time, which favours those models in many applications. Therefore, vectorial models should be applied only in cases of confirmed faulty performance of scalar ones. While the Effective Index Method and the Effective Frequency Method have been chosen as scalar approaches to FPLs and VCSELs, respectively, simulations, the Method of Lines has been used in both cases as a vectorial one. Scalar models have been found to be quite exact in the case of a determination of the effective refractive index and wavelength of emitted radiation, whereas their exactness in the lasing threshold analysis is much worse, especially in the case of higher-order modes. Our analysis is concluded with the determination of the regions where both models give satisfactorily close results.     

Structure–conductivity relations of simulated highly porous nanoparticle aggregate films

Electrical conductivity of porous films composed of nanoparticle aggregates is theoretically evaluated with respect to aggregate structure and film packing density. The aggregates are fractals composed of 5–30 primary particles with diameter of 10 nm. The film properties are derived from simulated boxes in the range of 0.5–1 μm. The electrical conductivity across the films of packing densities ranging from 0.01 to 0.15 was studied. All films prepared by an aerosol deposition technique, which uses nanoparticle aggregates, exhibited percolation behavior between planes parallel to the moving direction of the aggregates. They also followed the classical percolation relation for electrical conductivity while the critical percolation packing density depends on the aggregate size and structure used to build the films. Films using larger aggregates as building blocks have higher electrical conductance than smaller aggregates close to the percolation limit. For validation and supplementary information, two independent models are developed: one model follows the percolation theory to get detailed physical insights and another one computes the exact conductivities but at the cost of some details. This analysis gives new insights into the conduction backbone structures of these films with regard to neck contacts within an aggregate and grain boundary contacts between aggregates. The results shown are important for solar application of these films and especially for gas sensors where high sensitivity is often counteracted by low conductivity.