Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

We present analytically the exact solutions of the Schrödinger equation in the N-dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU(1,1). Some expectation values for 〈r ^?2〉, 〈r ²〉, 〈T〉, 〈V〉, 〈H〉, 〈p ²〉 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann–Feynman theorems. Each solution obtained is dimensions and parameters dependent.     

Polarization catastrophe in the polaronic Wigner crystal

We consider a three dimensional Wigner crystal of electrons lying in a host ionic dielectric. Owing to their interaction with the lattice polarization, each localized electron forms a polaron. We study the collective excitations of such a polaronic Wigner crystal at zero temperature, taking into account the quantum fluctuations of the polarization within the Feynman harmonic approximation. We show that, contrary to the ordinary electron crystal, the system undergoes a polarization catastrophe when the density is increased. An optical signature of this instability is derived, whose trend agrees with the experiments carried out in Nd-based cuprates. Received 4 July 2002 Published online 17 September 2002     

Scaling behaviour of the Hellmann potential with different strength parameters

We are reporting the scaling behaviour of the bound state energies associated with the Hellmann potential, with different strength parameters, using the Laguerre basis. We show the existence of a crossover phenomenon for the energy spectrum; the scaling laws for bound states as we approach the continuum are calculated. Close to the bound–resonance phase transition region, state energies and wavefunctions for the Hellmann potential, with different strength parameters, have been studied.     

A power counting theorem for Feynman integrals on the lattice

A convergence theorem is proved, which states sufficient conditions for the existence of the continuum limit for a wide class of Feynman integrals on a space-time lattice. A new kind of a UV-divergence degree is introcduced, which allows the formulation of the theorem in terms of power counting conditions.     

Effect of Chemical Potential Shift on Thermodynamical Properties of the Mixed Valence Compounds

Starting from the SU(N_d) Anderson lattice model in the slave boson formalism, we study the effect of the chemical potential shift on the thermodynamic properties of the mixed valence lattice system by using the Green's function technique. In the mean field approximation, the self-consistent equations of the mean field parameters and the chemical potential are obtained. The average number off electrons, the magnetic susceptibility and the specific heat are calculated. The numerical studies show that the shift of the chemical potential has a strong effect on the thermodynamic properties.     

Thermally averaged orbital diamagnetism of a localized wigner oscillator

Summary Electron crystallization due to sufficiently strong Coulomb repulsions leads to a model of electrons oscillating about lattice sites in harmonic potentials. We have studied the orbital diamagnetism of such a localized Wigner oscillator in an applied magnetic field of arbitrary strength. The two contributions from orbital angular momentum and from Langevin-Pauli behaviour are separately calculated using Feynman's theorem. Possible relevance to the melting curve of the Wigner crystals in a magnetic field is pointed out.

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Riassunto La localizzazione di elettroni per effetto di repulsioni coulombiane sufficientemente forti porta ad un modello di elettroni che oscillano attorno a siti reticolari in potenziali armonici. Si studia il diamagnetismo orbitale di un siffatto oscillatore localizzato di Wigner in campo magnetico d'intensità arbitraria. Il contributo dovuto al momento angolare orbitale e quello di Langevin-Pauli sono calcolati separatamente mediante il teorema di Feynman. Si discute la possibile connessione dei risultati con il problema della curva di fusione del cristallo di Wigner in campo magnetico.

     

Excitonic metal–insulator phase transition of the Mott type in compressed calcium

It has been experimentally found that, under the static compression of a calcium crystal at room temperature, it undergoes a series of structural phase transitions: face-centered cubic lattice → body-centered cubic lattice → simple cubic lattice. It has been decided to investigate precisely the simple cubic lattice (because it is an alternative lattice) with the aim of elucidating the possibility of the existence of other (nonstructural) phase transitions in it by using for this purpose the Hubbard model for electrons with half-filled ns-bands and preliminarily transforming the initial electronic system into an electron–hole system by means of the known Shiba operators (applicable only to alternative lattices). This transformation leads to the fact that, in the new system of fermions, instead of the former repulsion, there is an attraction between electrons and holes. Elementary excitations of this new system are bound boson pairs—excitons. This system of fermions has been quantitatively analyzed by jointly using the equation-of-motion method and the direct algebraic method. The numerical integration of the analytically exact transcendental equations derived from the first principles for alternative (one-, two-, and three-dimensional) lattices has demonstrated that, in systems of two-species (electrons + hole) fermions, temperature-induced metal–insulator phase transitions of the Mott type are actually possible. Moreover, all these crystals are in fact excitonic insulators. This conclusion is in complete agreement with the analytically exact calculations of the ground state of a one-dimensional crystal (with half-filled bands), which were performed by Lieb and Wu with the aim to find out the Mott insulator–metal transition of another type.     

铝、铜、镍三元合金系中τ相的晶体结构变迁

A thorough investigation by means of X-rays has been carried out with the purpose to determine the nature of the ternary phase τ in Al-Cu-Ni alloys. In contrast with the conventional concept of alloy phase which is characterized by a definite type of crystal structure, systematic structure changes are found in the single phase field of τ which occupies quite an extensive area in the isothermal section of the phase diagram at room temperature. There are eight types of structures altogether, all derived from a basic rhombohedron with corners occupied by Al atoms and centres either occupied by the heavy atoms or remaining vacant. The basic rhombohedron is the building stone in the crystal architecture. By transforming the basic rhombohedron into a hexagonal prism in the usual way, all structures may be considered to be built up by stacking together a number of these hexagonal prisms along the triad. The transformation of one structure into another is quite systematic in the way that the number of the stacking stories in the unit cell increases according to the order 10, 11, 12, 13, 14, 15, 16, 17. The atomic arrangements in the different structures are closely related too, in the respect that they are all superstructures due to the presence of ordered vacancies in the rhombohedral centres.The principal factor controlling the formation of these structures has been fully considered. In view of the fact that the change of structure types follows closely with the content of Ni or Cu for alloys of constant Al content, the atomic size factor appears to be unimportant in the formation of these alloys. It has been shown that for alloy phases of the defect lattice type as the r-phase, the most fundamental factor is the average number of valency electrons per structural unit which is the basic rhombohedron in the present case. By assuming Hume-Rothery's valencies, the average number of valency electrons remains remarkably constant throughout the entire phase field, while the electron concentration varies with compositions. It has also been pointed out that for alloy phases where there is no unit cell change, the average number of electrons per structural unit is equivalent to the number of electrons per unit cell, and for alloy phase where there is no defect, this is in effect equivalent to the electron concentration.     

Current saturation in CdS

An iteration procedure for calculating the high electric fields found in piezoelectric semi-conductors beyond the onset of current saturation is described. The procedure uses a wave equation derived from the well known formula for electron mobility of Feynman, Hellwarth, Iddings and Platzman in which the lattice coordinates have been removed. The zero order state in the procedure is that of electrons pursuing a constant velocity path, (infinite effective mass approximation), the velocity being taken at a phase velocity of acoustic shear modes. To the next order electrons are bound by and oscillate in a quasi-potential, which itself travels at the shear wave velocity. Electrons in a single well act coherently in producing a potential strong enough to bind them despite their Coulomb repulsion. We estimate the number of electrons bunched into a single droplet, as well as the electric field to sustain this motion, i.e. the field in the high field domain.     

Na||Sb-Pb-Sn液态金属电池电极的价电子结构与热-电性能计算

应用固体与分子经验电子理论系统地研究液态金属池Na||Sb-Pb-Sn电极的价电子结构与热、电性能.研究结果表明:电极合金的价电子结构与其性能密切关联.阴极合金Na_1–xIA_x (IA=K, Rb, Cs)的晶格电子随着掺杂量的增加而减少,诱发合金的熔点、结合能随掺杂量的增加而降低. Na离子输运到阳极,与阳极Sb-Sn-Pb形成产物NaSb_3, NaSn, Na₁₅Sn_4, NaPb.其理论熔点与实验相符. NaSb_3的平均晶格电子数最少,开路电压最高.研究表明:对于Na||Sb-Pb-Sn液态金属电池体系而言,晶格电子扮演重要的角色,可以调控电极的热、电性能.     

双模随机同向晶场对spin-1和spin-1/2混合自旋纳米管中Blume-Capel模型平均磁化强度的影响

利用有效场理论研究了纳米管上双模随机同向晶场中混合自旋Blume-Capel模型格点的平均磁化强度,得到了系统格点的平均磁化强度与双模随机晶场的取值概率、外磁场、晶场参数和晶场强度比值的关系。结果表明：取值概率、外磁场、交换相互作用、晶场强度比值和晶场强度等诸多因素相互竞争,使系统表现出比恒定晶场作用的Blume-Capel模型更为丰富的磁化现象;双模随机同向晶场会抑制系统的平均磁化强度,使其基态饱和值小于5/6;外磁场导致系统的二级相变消失;一定条件下系统发生一级相变;系统的平均磁化强度呈现部分缺失和负值现象。     

GaN及其Ga空位的电子结构

用团簇埋入自洽计算法对宽禁带半导体GaN的电子结构进行了自旋极化的、全电子、全势场的从头计算,得到了与实验值符合的GaN晶体禁带宽度以及价带中N2p带、N2s带和Ga3d带之间的相对位置.在此基础上Ga空位计算(无晶格畸变)显示,Ga空位周围的费米面显著高于正常GaN晶格的费米面.因此Ga空位周围N原子的处于费米面上的2p电子很易被激发成正常晶格处的传导电子 关键词： GaN 电子结构 团簇埋入自洽计算     

Time dependence of the average charge and current in a dissipative mesoscopic circuit

Taking into consideration the interactions between electrons and phonons,we have studied the temporal evolution of the average charge and current in a dissipative mesoscopic RLC circuit.Our results show that a mesoscopic RLC circuit can be treated as an interactive system between an electromagnetic harmonic oscillator and many lattice harmonic oscillators;this is called the bathing of the harmonic oscillators.The results also show that the quantum equation of motion of the linear mesoscopic RLC circuit is identical in form to its classical equation of motion,the only difference between them being their respective meanings.In order to thoroughly study the quantum properties of a dissipative mesoscopic circuit,we have to consider not only the electromagnetic energy of the circuit,but also the crystal lattice vibration energy and the interactive energy between electrons and phonons.     

Ab initio calculation of vibrational spectra of orthorhombic IV–VI layered crystals

Phonon modes of IV–VI semiconductor crystals with the orthorhombic structure of the crystal lattice have been calculated from first principles using the linear response method. The calculations are compared with the results of theoretical calculations available in the literature for some of the crystals and with the experimental data obtained by IR and Raman spectroscopies. Equilibrium lattice parameters and phonon spectra are calculated for all the crystals.     

Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method

A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the “refinement” of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31000 K. The minimum point weakly depends on plasma density. Owing to quantum effects, the electron component is “heated” well before electrons are completely bound in the field of protons.     

A theorem on the particle number and density of states in the Kondo problem

A theorem is derived for the Kondo model describing the interaction of conduction electrons with a localized magnetic impurity. The theorem states that the model preserves exact particle-hole symmetry. This implies that for fixed chemical potential the average particle number is unchanged as compared to the noninteracting case independent of temperature and applied magnetic field. The consequences of the symmetry property for the one particle density of states are also investigated. Finally the theorem proves to be a useful tool to check current approximate theories of the Kondo effect on their validity.     

Characteristic losses of electrons and the electron structure of thallium chloride

The complete set of fundamental optical functions of a thallium chloride crystal is calculated on the basis of the familiar experimental spectrum of volume characteristic losses of electrons using the Kramers-Kronig relations in a range of 0–25 eV. The loss and permittivity spectra are decomposed into elementary components and their main parameters are determined. Basic features of integrated and decomposed spectra are established.