Non-local correlation effects and metal-insulator transition in the s-d exchange model

The metal-insulator transition within the s-d exchange model is studied by the Dynamical Mean Field Theory and Dual Fermion approaches. The latter takes into account nonlocal correlation effects which are shown to be essential. In particular, the critical values of the s-d exchange coupling constant for these two methods turn out to be different by a factor of more than 2 (for the case of square lattice and spin 1/2 localized electrons). The calculations were performed using a Continuous-Time Quantum Monte Carlo method. The difference of the quantum spin-1/2 case and the classical-spin case is discussed. For the quantum case the sign of s-d exchange coupling constant is relevant which demonstrates the importance of the Kondo effect.     

On the exchange term of the interacting Boson-Fermion Hamiltonian

The exchange term of the Interacting Boson Fermion Model is investigated by using I. Talmi's method based on the shell model. A quadrupole operator of a three-proton system is formed; the protons are quadrupole-coupled to the neutron-bosons. Seniority conserving and seniority non conserving terms are considered. The particle number dependence of the parameters is investigated for the single-j shell. The relation between exchange and direct, seniority non conserving terms is examined. Approximate formulas are given for the multi-j shell.     

A simple state-dependent exchange functional for calculating Hartree-Fock bandstructures in semiconductors and insulators

A functional which takes the nonlocal character of the exchange selfenergy fully into account is derived within the nearly-free electron model for a spherical Fermi surface. This exchange functional when combined with the Hartree bandstructure gives approximate Hartree-Fock (HF) bands which agree surprisingly well with ab-initio HF-bands for covalent semiconductors and rare gas solids.     

Fermion condensation and non Fermi liquid behavior in a model with long range forces

The phenomenon of the so called Fermion condensation, a phase transition analogous to Bose condensation but for Fermions, postulated in the past to occur in systems with strong momentum dependent forces, is reanalyzed in a model with infinite range interactions. The strongly non Fermi Liquid behavior of this system is demonstrated analytically at T = 0 and at T ≠ 0 in the superconducting and normal phases. The validity of the quasiparticle picture is investigated and seen to hold true for temperatures less than the characteristic temperature T _f of the Fermion condensation.     

The exchange and correlation energy at a metal surface

The change in exchange and correlation energy at a metal surface is calculated in the RPA for the infinite barrier model of a surface. At the electron density of Al, this is + 1350 erg/cm², much less than the values given by approximate solutions of the RPA equations. About half the change in correlation energy comes from the change in plasmon zero-point energy.     

The quantum theory of nucleon correlation in finite nuclei. II. Higher order correlation effects and additive pair approximation

In the first part of this article it was shown that the variational solution of the Schroedinger equation of a finite Fermion system can be written as a finite sum of A terms (for A particles) the first of which is the Hartree-Fock energy, while the rest represent the correlation effects. In the first part explicit formulas for the 2-particle correlation energy were given. In this paper explicit formulas are given for the higher order correlation energies. It is shown that two different models can be developed depending on the orthogonality condition used. Beginning with the 4th order effects the “linked” and “unlinked” correlation terms are separated. An exact formula is given for the case in which only the 2-particle effects, linked and unlinked are taken into account. The “additive pair approximation” in which the correlation energy is given as the sum of 2-particle energies is investigated and it is shown to be related to the exact formula by a clearly defined set of approximations. Various possible applications of the model are discussed.     

Nuclear magnetic resonance study of the heavy-fermion system URu2Si2

Nuclear magnetic resonance (NMR) and relaxation studies on ²⁹Si have been carried out on the heavy Fermion system URu₂Si₂. Above the Kondo temperature of about 60 K, the nuclear relaxation time T₁ is nearly temperature independent, which is consistent with the occurrence of fluctuations of localized U moments. Below about 60 K T₁ is inversely proportional to temperature suggesting that the system behaves like a Fermi liquid. A sharp increase in T₁ occurs below 17 K which is probably associated with the opening of an energy gap at the Fermi surface due to the formation of a spin density wave state. Below about 10 K, T₁ reacquires the inverse temperature dependence observed in the 17 K ∼ 60 K temperature range.     

Pairing in 4-component fermion systems: The bulk limit of SU(4)-symmetric Hamiltonians

Fermion systems with more than two components can exhibit pairing condensates of a much more complex structure than the well-known single BCS condensate of spin-up and spin-down fermions. In the framework of the exactly solvable SO(8) Richardson-Gaudin (RG) model with SU(4)-symmetric Hamiltonians, we show that the BCS approximation remains valid in the thermodynamic limit of large systems for describing the ground-state energy and the canonical and quasiparticle excitation gaps. Correlations beyond BCS pairing give rise to a spectrum of collective excitations, but these do not affect the bulk energy and quasiparticle gaps.     

Operator method for calculating the spectrum of states in the framework of the extended dicke model

A system of N two-level atoms interacting with a resonant single-mode quantum field (the Dicke model) is described using the operator method for solving the Schrödinger equation. The spectrum of states is calculated without recourse to the rotating-wave approximation and the assumption regarding smallness of the linear sizes of the system as compared to the radiation wavelength. Analytical approximate expressions are obtained for the energy spectrum. These expressions approximate the energy spectrum over the entire range of Hamiltonian parameters in the normal and collective states of the system and make it possible to calculate the thermodynamic characteristics.     

Energy transfer as a random walk with long-range steps

We consider the incoherent energy transport in molecular crystals, where the transfer rates stem from Coulombic and exchange interactions. For substitutionally disordered lattices we present in a first passage model the excitation decay due to trapping by randomly distributed traps; the decay is related to the distribution of the number of distinct sites visited during the timet and is expressible through the cumulants of this distribution. The validity domains of approximate decay laws based on the first few cumulants are also discussed. We exemplify the findings for dipolar transfer rates between randomly distributed molecules on a square lattice, by comparing the random walk on the random system to its CTRW (continuous time random walk) counterpart.     

Bulk properties of rotating nuclei and the validity of the liquid drop model at finite angular momenta

Out of self-consistent semi-classical calculations performed within the so-called Extended Thomas-Fermi approach for 212 nuclei at all even angular momentum values I ranging between 0 and 80 ħ and using the Skyrme SkM¹ effective force, the I-dependence of associated liquid drop model parameters has been studied. The latter have been obtained trough separate fits of the calculated values of the strong interaction as well as direct and exchange Coulomb energies. The theoretical data basis so obtained, has allowed to make a rough quantative assessment of the variation with I of the usual volume and surface energy parameters up to spin of ∼ 30–40ħ. As a result of the combined variation of the surface and Coulomb energies, it has been shown that this I-dependence results in a significant enhancement of the fission stability of very heavy nuclei, balancing thus partially the well-known instability due to centrifugal forces.     

The quantumstatistical aspects of the independent-particle model for the nucleus

We present a new justification of the independent particle model for the nucleus. It is based on a statistical theory of the short-range correlations in large Fermion systems. The statistical operator of many-body Fermion systems — if averaged over a suitable ensemble — can be written as a product of statistical operators for a one-body system. The statistical operator for the one-body system obeys a Hartree-Fock equation. Physical interpretation and conclusions are discussed.     

Generalization of the Independent Pair Model to degenerate nuclear states

The equations of the Independent Pair Model for finite nuclei are generalized to nuclear states non describable by a single shell model configuration. As an application of these generalized equations to excited states, the energy of the excitedT=0,J ^π=0⁺ -state of⁴He has been calculated by an approximate solution. Using a spin-averaged square well potential with hard core and Serber exchange character, with all parameters beeing determined from two-nucleon data, the calculation yields an excitation energy of 21.58 MeV compared to the experimental value of about 20.1 MeV.     

Study of Platinum Isotopes: A Comparison of the Fermion Dynamical Symmetry Model and the Interacting Boson Model

The systematics of the even platinum isotopes are described within the framework of the Fermion Dynamical Symmetry Model. By using a pairing—plus—quadrupole type interactions, we show that the transitional behavior of these isotopes can be effectively accounted for. Good agreement is obtained between theory and data for energy levels, B(E₂) values, electric quadrupole moments, gyromagnetic factors, and the isomer shifts and isotope shifts for ^190—196Pt. The Calculations are also compared with various results obtained from the Interacting Boson Model. Consequently, our numerical calculation show that a very accurate effective SO(6) dynamical sysmmetry exists around ¹⁹⁶Pt, even though the proton-neutron coupled system (SO^π(8)×SP^ν(6)) does not formally contain such a dynamical symmetry in the fermion dynamical symmetry model. Implications of this effective dynamical symmetry are discussed.     

FERMION COHERENT STATE AND QUARK CONFINEMENT

Two characteristics of the Fermion coherent state are given in this paper. One is the duality of the Fermion coherent state. The other is the indefiniteness of their eigenvalues. The SLAC bag model is also discussed by using the Fermion coherent state methodology. Our zesults agree with the SLAC bounded state iolutions, so that quark confinement can be phenomenally, illustrated.In addition, rje have found a gluon-ball solution and a non-bounded state solution, which are absent from the SLAC theory. Hence,the method of the Fermion coherent state is effective.     

Collective effects in atoms via a schematic model

Linear response theory is used to investigate the collective excitation spectra of the outer shells of heavy atoms. A model, based on the approximate separability of particle-hole interaction matrix elements, is solved in closed form and found to be in semi-quantitative agreement with experiment for the vibrations of the 4d shell in Xenon. The separability of these matrix elements in the relevant energy region is shown to be due to a general property of wave functions of atomic potentials. A comparison is also made with full random phase approximation calculations for Xe. It is shown that the schematic model contains all the relevant features to describe the enhanced photo-absorption of this system in the far ultraviolet. The role of anf-wave resonance in the average atomic field is stressed in connection with this enhancement. Detailed agreement between the schematic model and experiment is less good than that obtained from the full random phase calculation, the differences arising due to an approximate treatment of exchange in the former calculation. The total dipole strength in the photo-electric region is approximately the same for both calculations however and in reasonable accord with experiment.     

Analysis of the evaporation-corrected mass and charge distributions in the Ar+Mo reactions

Partly and strongly damped fragments from the reactions³⁶Ar+⁹²Mo and⁴⁰Ar+¹⁰⁰Mo are measured atE _Lab=270 MeV. The extracted mass and charge distributions are carefully corrected forγ, n, p andα particle evaporation. The resulting primary distributions are analysed with theoretical models which assume statistical neutron and proton exchange on the potential energy surface of the projectile-target system. Dynamical-deformation effects in the framework of the surface friction model are included.     

Radiation of electric arc burning in argon

Using real experimentally obtained integral values, the paper deals with modelling of electric arc stabilised by flowing gas. Attention is focused namely on approximate estimation of radiation coefficient of argon. A designed model of electric arc burning in argon of atmospheric pressure inside arc heater’s anode channel is described. The model makes it possible to compute axial and/or radial dependencies of some quantities of interest (temperature, velocity, electric field intensity, arc radius, etc.), and subsequently to judge energy exchange between the arc and its surroundings. Sets of model’s input data, including arc voltage, arc current, argon flow-rate, and flow-rates and temperatures of water cooling individual parts of the arc heater, have been measured during numerous experiments. In a studied case with relatively high argon flow-rate, radiation has been found to be prevailing mechanism of energy transfer from arc to anode channel walls. Based on this finding, techniques have been designed for simple approximate estimation of radiation coefficient of argon in a limited extent of temperatures. As an example, they have been tested on a particular set of measured and computed data. Argon radiation coefficient estimated in this way has been compared with the results of theoretical computations carried out by other authors. Considering simplifications used and differences between a real situation and an ideal theoretical model, agreement of the results is within satisfactory limits.