Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the d-orbital, the charge-transfer energy between the d- and p-orbitals and the hopping integrals between p-d, d-d and p-p orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method. Received 5 October 2000 and Received in final form 8 December 2000     

Effects of a k⃗-dependent Hybridisation on the Fermi surface of an extended d–p Hubbard model

ABSTRACT

The topology of the Fermi surface of an extended d–p Hubbard model is investigated using Green's function technique in a n-pole approximation. The effects of the d–p hybridisation on the Fermi surface are the main focus in the present work. Nevertheless, the effects of doping, Coulomb interaction and hopping to second-nearest-neighbours on the Fermi surface, are also studied. Particularly, it is shown that the crossover from hole-like to electron-like Fermi surface (Lifshitz transition) is deeply affected by the d–p hybridisation. Moreover, the pseudogap present in the low doping regime is also affected by the hybridisation. The results show that both the doping and the hybridisation act in the sense of suppresses the pseudogap. Therefore, the systematic investigation of the Fermi surface topology, shows that not only the doping but also the hybridisation can be considered as a control parameter for both the pseudogap and the Lifshitz transition. Assuming that the hybridisation is sensitive to external pressure, the present results agree qualitatively with recent experimental data for the cuprate Nd-LSCO.     

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t₁/t₀ (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V₁, and the on-site interaction (with the amplitude V₀) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V₀/V₁. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.     

Random sequential adsorption of polydisperse spherical particles: An integral-equation theory

Our previously developed integral-equation theories were applied to incorporate the effect of polydispersity in the study of the random sequential addition of spherical particles. By using the simplest uniform size distribution, we found that results from theories were in consistence with the Monte Carlo simulation results. Some deviations were seen, which resulted from the exclusion effects of polydisperse particles. It was found in the simulations that with increasing densities, small particles adsorbed preferentially and the size distribution skewed towards the smaller particles. Therefore, to accurately predict the correct radial distribution functions, the more appropriate size distributions are needed. For all size ranges, which were 0.40d–1.60d, 0.75d–1.25d, and 0.90d–1.10d, the radial distribution functions from theory at number densities of 0.2, 0.4 and 0.65 were in good agreements with those from the simulations.     

Emission of light nuclei (<Emphasis Type="Italic">p,d, t</Emphasis>, α) in the process of annihilation of slow antiprotons in nuclear emulsion

The annihilation of slow (∼7 MeV) antiprotons in nuclear emulsion has been studied. The yields and energy spectra of p, d, t, and α particles in the evaporation region have been measured. The shape of the spectra of p, d, and t is in agreement with the Maxwell distribution and the excitation energy of a nucleus is consistent with a theoretical estimate for evaporation from the equilibrium state. The probability of the absorption of antiprotons inside the nucleus estimated from the multiplicity of h particles is ɛ = (2.0 ± 0.6) × 10⁻². The relative d/p yield coincides with a similar ratio appearing in the capture of slow π⁻ mesons by nuclei in the nuclear emulsion. The yields of t and α particles in the process of the annihilation of antiprotons are much higher than those in a similar process for pions. To identify g particles (0.29 < β < 0.70), energy losses dE/dx on ionization and multiple scattering have been measured. In this velocity region, the yields of p, d, t, and pions have been observed. The ratios (n _d /n _p ) _g , (n _d /n _p ) _b , and n _d /n _p measured in the capture of π⁻ mesons are almost the same. In this velocity range (g particles), α particles have not been observed.     

Negative magnetoresistance in the regime of hopping conduction through <Emphasis Type="Italic">p</Emphasis> states at quantum dots

The magnetoresistance in the system of quantum dots with hopping conduction and filling factor 2 < ν < 3 in the limit of small quantum dots has been considered. In this case, hopping conduction is determined by p states. It has been shown that the system exhibits negative magnetoresistance associated with a change in the wavefunctions of p states in a magnetic field. This mechanism of magnetoresistance is linear in magnetic field in a certain range of fields and can compete with the known interference mechanism of magnetoresistance. The magnitude of this magnetoresistance is independent of the temperature at fairly low temperatures and increases with a decrease in the size of a quantum dot.     

Lifetime measurements and calculations in La I

Radiative lifetime measurements have been performed, with a time-resolved laser-induced fluorescence technique, for 20 odd-parity levels of La I belonging to the configurations 5d ²6p, 5d6s6p and 4f5d6s. The new results are compared with the few experimental data available in the literature and with theoretical calculations including configuration interaction effects. The agreement theory-experiment is generally satisfying but discrepancies are observed for some levels emphasizing the difficulty to get a reliable theoretical model in such a heavy and complex neutral element.Received: 26 January 2004, Published online: 22 June 2004PACS: 32.70.Cs Oscillator strengths, lifetimes, transition moments - 42.62.Fi Laser spectroscopy     

Fine-structure energy levels, oscillator strengths and lifetimes in Co XV

Excitation energies from ground state for 97 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s ²2s ²2p ⁶)3s ²3p, 3s ³ p ², 3s ²3d, 3p ³, 3s3p3d, 3p ²3d, 3s3d ², 3s ²4s, 3s ²4p, 3s ²4d, 3s ²4f, and 3s3p4s configurations of Co XV are calculated, using extensive configuration-interaction (CI) wave functions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. Our calculated excitation energies, including their ordering, are in excellent agreement with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology (NIST) wherever available. The mixing among several fine-structure levels is found to be very strong, with most of the strongly mixed levels belonging to the (1s ²2s ²2p ⁶)3p ²3d and 3s3d ² configurations. The strong mixing among several fine-structure levels makes it very difficult to identify them uniquely. Perhaps, that may be the reason for the lack of both experimental and theoretical results for these levels. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. In this calculation we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.     

Methane-assisted combustion synthesis of nanocomposite tin dioxide materials

Combustion synthesis of tin dioxide (SnO₂) was studied using a new synthesis approach where the combustion environment was augmented to control the temperature and flow conditions using methane as a supplemental fuel. The experiments were carried out at atmospheric pressure using a multi-element diffusion flame burner with a gas-phase precursor for SnO₂ and solid-phase precursor for metal additives. In the methane-assisted (MA) system, the inert carrier gas was replaced with methane as the transport gas for the SnO₂ and metal additive precursors. Two additive precursors were investigated: gold acetate and aluminum acetate. Particle morphology, primary particle size, crystallinity, phase, molecular and elemental composition were studied using transmission electron microscopy, X-ray diffraction, and energy-dispersive spectroscopy. Particle imaging velocimetry and thermocouple measurements provided velocity and temperature data for the synthesis environment experienced by particles. The MA system provided conditions for rapid sintering of particles into large faceted single crystals of SnO₂ (d_p = 46 nm) compared to methane unassisted system (d_p = 19 nm), thus offering a degree of control over grain size. Additionally, large aspect ratio (2.6 ± 0.9) single crystal SnO₂ particles were produced using the MA system. Gold-doped SnO₂ produced using the MA system yielded gold particles encapsulated in a layer of SnO₂. The characteristic reaction-, coagulation- and sintering-times were investigated for nanoparticle formation in the two systems using simplified models. The analysis provided qualitative justification for the trends observed in particle morphology. The modification of characteristic times in this study demonstrates a route for controlling size and morphology of single or multicomponent systems.     

Nucleation and hysteresis in Ising model: classical theory versus computer simulation

We have studied the nucleation in the nearest neighbour ferromagnetic Ising model, in different (d) dimensions, by extensive Monte-Carlo simulation using the heat-bath dynamics. The nucleation time () has been studied as a function of the magnetic field (h) for various system sizes in different dimensions (d=2,3,4). The logarithm of the nucleation time is found to be proportional to the power (-(d-1)) of the magnetic field (h) in d dimensions. The size dependent crossover from coalescence to nucleation regime is observed in all dimensions. The distribution of metastable lifetimes are studied in both regions. The numerical results are compared and found to be consistent with the classical theoretical predictions. In two dimensions, we have also studied the dynamical response to a sinusoidally oscillating magnetic field. The reversal time is studied as a function of the inverse of the coercive field. The applicability of the classical nucleation theory to study the hysteresis and coercivity has been discussed. Received: 21 January 1998 / Accepted: 17 March 1998     

Long time tails in stationary random media. I. Theory

Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay like t^–(d/2+1), while the time correlation function associated with the super-Burnett coefficient decays liket ^–d/2 for long times. The theory is applicable to a wide variety of dynamical and stochastic systems including the Lorentz gas and hopping models. We find new, general expressions for the coefficients of the long time tails which agree with previous results for exactly solvable hopping models and with the low-density results obtained for the Lorentz gas. Finally we mention that if the moving particles are charged, then the long time tails imply that there is an ^d/2 contribution to the low-frequency part of the frequency-dependent electrical conductivity.     

Bethe Ansatz Solution of Discrete Time Stochastic Processes with Fully Parallel Update

We present the Bethe ansatz solution for the discrete time zero range and asymmetric exclusion processes with fully parallel dynamics. The model depends on two parameters: p, the probability of single particle hopping, and q, the deformation parameter, which in the general case, |q| < 1, is responsible for long range interaction between particles. The particular case q = 0 corresponds to the Nagel-Schreckenberg traffic model with v _max = 1. As a result, we obtain the largest eigenvalue of the equation for the generating function of the distance travelled by particles. For the case q = 0 the result is obtained for arbitrary size of the lattice and number of particles. In the general case we study the model in the scaling limit and obtain the universal form specific for the Kardar-Parisi-Zhang universality class. We describe the phase transition occurring in the limit p→ 1 when q < 0.     

小世界网络上的扩散限制的聚集-湮没反应动力学

通过Monte-Carlo模拟,研究了基于NW网络的两种类集团不可逆聚集-湮没过程的动力学行为.在系统中,两个同种类集团相遇,将不可逆地聚集成一个更大的集团;不同种类的两个集团相遇,则发生部分湮没反应.模拟结果表明,1)当捷径量化参数p相对较大或较小时,系统经较长时间演化后,集团密度c(t)和粒子密度g(t)呈现幂律形式,c(t)∝t^－α和g(t)∝t^－β,其中幂指数α和β满足α=2β的关系;2)当p为其他值时,集团密度和粒子密度随时间按非严格的幂 关键词： 聚集-湮没过程 小世界网络 反应动力学 Monte-Carlo模拟')" href="#">Monte-Carlo模拟     

Network Forming Fluids: Yukawa Square-Well <Emphasis Type="Italic">m</Emphasis>-Point Model

Thermal and connectivity properties of the Yukawa square-well m-point (YSWmP) model of the network forming fluid are studied using solution of the multidensity Ornstein-Zernike and connectedness Ornstein-Zernike equations supplemented by the associative mean spherical approximation (AMSA). The model is represented by the multicomponent mixture of Yukawa hard spheres with m_s^am_{s}^{a} square-well sites, located on the surface of each hard sphere. To validate the accuracy of the theory, computer simulation is used to calculate the structure, thermodynamic and connectivity properties of the one-component YSW4P version of the model which is compared against corresponding theoretical data. In addition, connectivity properties of the model were studied using Flory-Stockmayer (FS) theory. Predictions of the AMSA for the thermal properties of the model (radial distribution functions (RDF), internal energy, pressure, fractions of the particles in different bonding states) are in good agreement with computer simulation predictions. Similarly, good agreement was found for the connectedness RDF (CRDF), except for the statepoints located close to the percolation threshold, where the theory fails to reproduce the long-range behavior of the CRDF. Results of both theories (AMSA and FS) for the mean cluster size are reasonably accurate only at low degrees of association. Predictions of the FS theory for the percolation lines are in a good agreement with computer simulation predictions. AMSA predictions of percolation are much less accurate, where corresponding percolation lines are located at a temperatures approximately 25% lower then those calculated using computer simulation.     

Theoretical study of the MgAr molecule and its ion Mg<Superscript>+</Superscript>Ar: potential energy curves and spectroscopic constants

The adiabatic potential energy curves of the low-lying electronic states of the MgAr molecule dissociating into Mg (3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p)+Ar have been investigated. The electronic structure of the Mg-Ar molecule is calculated using [Mg²⁺] and [Ar] core pseudopotentials complemented by the core polarization operators for both atoms, considering the molecule to be a two-electron system. The derived spectroscopic constants of the ground state and lower excited states are in good agreement with available experimental and theoretical work. In addition, for the purpose of checking the pseudopotential accuracy on a simpler related system, low lying potential energy curves of the single active electron Mg⁺Ar ion are also reported and the corresponding molecular constants are compared with those in the existing literature.     

Statistical properties of Lyapunov exponents and of quantum conductance of random systems in the regime of hopping transport

The statistics of the zero-temperature conductance and the Lyapunov exponents of one-, two- and three-dimensional disordered systems in the regime of strong localization is studied numerically. In one dimension, the origin of the universality of the moments of the conductance is explained. The relation between the most probable value of the conductance and its configurational average is discussed. The relative fluctuations of the conductance (and of the resistance) are shown to grow exponentially with the system length. In higher dimensions the conductance is almost entirely determined by the smallest of the Lyapunov exponents. The statistics of the conductance is therefore the same as in the one dimensional case. A model is proposed for the treatment of the fluctuations in hopping transport at finite temperatures. An exponential dependence of the relative fluctuations of the conductance/resistance on the temperature is predicted, log (δg/g) ∞ T^?a with α = 1/(d+1). It is concluded that the presently available experimental data on the temperature dependence of the conductance fluctuations in the hopping regime can be understood by replacing the system size in the zerotemperature result for the fluctuations of the conductance by the hopping length.     

Calculation of Oscillator Strength in the Sc I-Spectrum

The oscillator strengths of the main transition from the 3d 4s 4p-states to the groundstate 3d 4s² of Sc I are calculated on using wave functions derived by diagnolization of the interaction matrix elements of the 3d 4s 4p-, 3d² 4p- and 4s² 4p-configurations. The relevant dipole matrix elements are reduced by application of tensor algebra to the unknown one-electron matrix elements 〈4s‖r‖4p> and <3d‖r‖4p〉. These radial integrals are calculated from experimental lifetimes and oscillator strengths as well as from theoretical models. The resulting absolute oscillator strengths show a fairly good agreement with the experimental data, the uncertainties being smaller than 10 percent for the strongest transitions.     

Relativistic transition wavelenghts and probabilities for spectral lines of Ne II

Transition wavelengths and probabilities for several 2p ⁴ 3p-2p ⁴ 3s and 2p ⁴ 3d-2p ⁴ 3p lines in fluorine-like neon ion (NeII) have been calculated within the multiconfiguration Dirac-Fock (MCDF) method with quantum electrodynamics (QED) corrections. The results are compared with all existing experimental and theoretical data.     

Energy levels, oscillator strengths and lifetimes in Ar V

We have calculated the excitation energies, oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions among the 46 LS levels belonging to the configurations 3s ²3p ², 3s3p ³, 3s ²3p3d, 3p ⁴, 3s ²3p4s, 3s ²3p4p, 3s3p ²(² S)4s, 3s3p ²(² P)4s, 3s3p ²(⁴ P)4s, 3s3p ²(² D)4s, 3s ²3p4d and 3s ²3p4f of Si-like Argon. These states are represented by extensive Configuration-Interaction (CI) wavefunctions obtained using the CIV3 computer code of Hibbert. From our transition probabilities we have also calculated the radiative lifetimes of singlet and triplet states of Ar V. Our results are compared with other available theoretical calculations and experimental data. To assess the importance of relativistic effects on our calculated values, we have also carried out calculations in the intermediate-coupling scheme using the Breit-Pauli Hamiltonian. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made so that the energy splittings are as close as possible to the experimentally compiled energy values of the National Institute for standards and Technology (NIST). The energy splitting of 85 fine-structure levels, the oscillator strengths and transition probabilities for electric-dipole-allowed and intercombination transitions and the lifetimes of some fine-structure levels are presented and compared with available experimental and other theoretical values. In this calculation, we also predict new data for several fine-structure levels where no other theoretical and experimental results are available.     

Schloegl’s Second Model for Autocatalysis on a Cubic Lattice: Mean-Field-Type Discrete Reaction-Diffusion Equation Analysis

Schloegl’s second model for autocatalysis on a hypercubic lattice of dimension d≥2 involves: (i) spontaneous annihilation of particles at lattice sites with rate p; and (ii) autocatalytic creation of particles at vacant sites at a rate proportional to the number of diagonal pairs of particles on neighboring sites. Kinetic Monte Carlo simulations for a d=3 cubic lattice reveal a discontinuous transition from a populated state to a vacuum state as p increases above p=p _e . However, stationary points, p=p _eq (≤p _e ), for planar interfaces separating these states depend on interface orientation. Our focus is on analysis of interface dynamics via discrete reaction-diffusion equations (dRDE’s) obtained from mean-field type approximations to the exact master equations for spatially inhomogeneous states. These dRDE can display propagation failure absent due to fluctuations in the stochastic model. However, accounting for this anomaly, dRDE analysis elucidates exact behavior with quantitative accuracy for higher-level approximations.