Random-phase approximation and its extension for the O(2) anharmonic oscillator

We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations arround the static solution in the time-dependent Hartree-Bogoliubov equation. We draw the parallel between the two approaches.Received: 8 July 2003, Published online: 5 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 24.10.Cn Many-body theory     

Renormalization of relativistic self-consistent Hartree-Fock approximation

The renormalization of the relativistic self-consistent Hartree-Fock approximation is restudied. It is shown that the renormalization procedure suggested by Bielajew and Serot can be greatly simplified and the renormalization achieved in a way no more complicated than that of the relativistic self-consistent Fock approximation, if the parameters in the counterterms are allowed to be density-dependent and the renormalization of the tadpole self-energy is treated appropriately. A transformation relation between the four- and three-dimensional representation of the baryon self-energy is presented and a self-consistent Hartree-Fock scheme different from that considered by Bielajew and Serot studied. The renormalized integral equations for the baryon self-energy which includes effects from the Dirac sea are reformulated in a three-dimensional form. Explicit expressions are derived. Received: 29 August 1997 / Revised version: 30 April 1998     

Temperature Dependent Relativistic Microscopic Optical Potential and Mean Free Paths of Nucleons

The microscopic optical potential,mean free paths and Schrodinger equivalent potential of nucleons at finite temperature in nuclear matter are studied based on Walecka's model and thermo field dynamics.We let only the Hartree-Fock self-energy of nucleon represent to be the real part of the microscopic optical potential and the fourth order of meson exchange diagrams,i.e. the core polarization represent the imaginary part of microscopic optical potential in nuclear matter.The microscopic optical potential of finite nuclei is obtained with the local density approximation.     

Density dependent exchange contribution to partial differential mu/ partial differential n and compressibility in graphene

We calculate partial differentialmu/ partial differentialn (where mu=chemical potential and n=electron density), which is associated with the compressibility, in graphene as a function of n, within the Hartree-Fock approximation. The exchange-driven Dirac-point logarithmic singularity in the quasiparticle velocity of intrinsic graphene disappears in the extrinsic case. The calculated renormalized partial differentialmu/ partial differentialn in extrinsic graphene on SiO2 has the same n;{-(1/2)} density dependence but is 20% larger than the inverse bare density of states, a relatively weak effect compared to the corresponding parabolic-band case. We predict that the renormalization effect can be enhanced to about 50% by changing the graphene substrate.     

重整化平均场理论及其在铜氧化物高温超导材料中的应用

对铜氧化物高温超导体的研究是凝聚态物理中最重要的问题之一.理论研究上的困难在于铜氧化物高温超导材料中单占据条件所导致的强关联效应.铜氧化物高温超导材料可以用t-J模型进行描述,而上述的单占据条件则体现于t-J模型中的Gutzwiller投影算符.重整化平均场理论(RMFT)是一种处理这类由Gutzwiller投影算符所导致的强关联效应比较有效的方法.本文首先对铜氧化物高温超导材料进行简单的介绍.然后我们将重点介绍Gutzwiller近似.最后我们会介绍重整化平均场理论,以及其在铜氧化物高温超导材料和其他一些强关联材料中的应用.     

Realistic one-particle density matrix and single-particle description of nuclei

Starting from the experimental data on elastic electron scattering, realistic one-particle density matrices for ¹⁶O and ⁴⁰Ca are obtained, both with fractional occupation numbers and full occupation of the first A natural orbitals. A phenomenological single-nucleon Hamiltonian is then constructed and diagonalized. The deduced single-particle energies are compared with those obtained in the Hartree-Fock approximation. The consistency of all experimental data concerning the ground state is checked with the aid of a sum rule for the total binding energy involving only the one-particle density matrix and the hole energies.     

On the theory of chemisorption

A solution of the Anderson model for chemisorption including correlation effects is presented. The solution becomes exact in three limiting cases (largeU, smallU i.e. Hartree-Fock and the so-called symmetric strong coupling limit) of the intra atomic Coulomb repulsionU and the hopping termV. Excellent agreement of our approximation with Schrieffer's exact numerical results for the binding energy of a small model system is found. Our results for the binding energy and the charge of the adsorbate show a significant improvement over the Hartree-Fock approximation. The single particle spectral density of the H-F approximation turns out to be even qualitatively wrong in the largeU strong coupling limit.     

Correlated squeezed-state approach for the ground state of strongly correlated electrons coupled to local Holstein phonons

Summary In the present work we have applied the correlated squeezed-state approach to investigate the ground state of the extended Hubbard model which is coupled to local Holstein phonons. Our study begins with decoupling the electron and phonon subsystems approximately by introducing a variational correlated squeezed-state ansatz for the phonons. Then assuming the renormalized intersite electron correlation of the effective electronic Hamiltonian to be attractive and the renormalized on-site correlation repulsive, we have applied the generalized Hartree-Fock approximation to obtain the ground state of the system, which is a superconducting state with intersite pairing. With optimal values of the variational parameters the correlated squeezed-state approach will by construction yield a ground-state energy lower than those obtained in previous studies. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is noticeably weakened. This weakening of the reduction effect should, in turn, significantly affect other physical properties of the system.     

WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS

The weak coupling approximate Schwinger-Dyson equation of the straton's pro-pagator in 4-dimensional QCD theory and the problem of the straton's confinement are discussed. It is proved that, when we choose Landaugauge, the obtained Sch-winger-Dyson integral equation of the straton's propagator can be transformed into a very simple form. Then we change it into a first order non-linear differential equation. It has two solutions: a confining solution and a solution that has no con-finement for the stratons. The effective potential in QCD is derived by functional method, and the ground-state energy difference between these two solutions is discussed. In our approximation, we calculate the vacuum graph to the 2-loop diagrams, We may conclude that stratons are not confined in our approximation.     

The Solution of Dynamical Equation of Motion of IBM-Ⅱ in Continuous Variable Representation

In this article the solution of dynamical equation of motion of IBM-Ⅱ in continuous variable representation is discussed.With appropriate transformation and approximation,the on-phase part of system manifests the vibration-rotation mode and the off-phase part the 'scissor mode',ect.In the last section the energy spectrum of ¹⁵⁶Gd is calculated.The result can well reproduce the algebraic result of IBM-Ⅱ.     

Angular momentum projected Hartree-Fock-Theory

The Euler Lagrange equations corresponding to the Hartree-Fock variational problem after angular momentum projection (PHF) are derived. The exact equations are simplified employing the Gaussian overlap approximation. The solution of the PHF equations in this approximation is seen to be not much more complicated than the solution of the normal HF problem.     

A PRIMARY RESEARCH OF THE PHONON RENORMALIZATION OF NUCLEAR FIELD THEORY

By taking proper self-energy subdiagrams of phonon as Fig. 1(1), the Dyson'sequation and the corresponding eigenequations of the renormalized phonon are obtained.The sum rule and the energy weighted sum rule of phonons are given.     

Relativistic Hartree-Fock schemes and effect of self-consistency

A new effect of self-consistency in the relativistic Hartree-Fock (HF) approximation is studied by a simple model and a renormalized calculation. A comparison is made between two different HF schemes: one requiring self-consistency in the HF potential (scheme P) and the other in the baryon propagator (scheme BP). Our results show that scheme P is a good aproximation to scheme BP for the calculation of the baryon propagator and the self-consistency requirements make the results obtained by the two schemes closer to each other, because the self-consistency in scheme BP diminishes the continuum part of the spectral representation for the baryon propagator, while the self-consistency in scheme P yields a baryon propagator which approximates closely to the HF result contributed by the converged single particle part of the above spectral representation alone. Received: 12 March 1999 / Revised version: 6 September 1999     

Hybridization effect on the Falicov-Kimball model

The extended Falicov-Kimball model which includes the hybridization effect between the localized electron state and the conduction band is treated within the Hartree-Fock approximation at T=0 K. The occupation number n_e of the conduction band is calculated as a function of the localized level. The both discontinuous and continuous changes of n_e appear in a certain region of parameters. This result may correspond to the experimental facts of samarium-monochalcogenides under pressure.     

Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are two different cases that are studied in detail: (i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. For the case of quasiparticles, the exact occupation number asymptotically tends to a statistical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes whereas in the stable particle case, the distribution of particles does not thermalize with the bath. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian, and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.     

Hybridization effect on phase transitions in the Falicov-Kimball model

The Falicov-Kimball model extended by the hybridization between the localized electron states and the conduction band states is studied in Hartree-Fock approximation. Taking into account the periodicity of the system, the occupation number of the localized levels always varies continuously with the level energy for non-vanishing hybridization. This result is in contradiction with earlier mean-field calculations which are not self- consistent for the periodic model. Since first order phase transitions in intermediate valence compounds such as SmS have been observed experimentally, it follows that their explanation needs a more general theoretical frame than the model considered here.     

Susceptibility and specific heat of intermediate valence compounds studied in mean-field theory of a periodic anderson model

The periodic Anderson model for a lattice of magnetic ions is investigated in Hartree-Fock approximation. Attention is paid to different solutions of the self-consistency equations corresponding to ferromagnetic or antiferromagnetic ordering of the local magnetic moments. The effect of hybridization leading to reduced magnetic moments strongly depends on the position of the localizedf levels relative to the conduction band. For paramagnetic solutions with a non-integer value for thef level occupation number comparison is made with properties of intermediate valence rare earth compounds. The mean-field results for the susceptibility and specific heat agree with essential features found for these substances.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

BERRY'S PHASE FACTORS IN MOVING FRAMES OF REFERENCE AND THEIR OBSERVABLE EFFECTS

Under non-relativistic conditions,the properties of adiabatic solutions of the Schrodinger equation in moving frame of reference and the behaviours of the corresponding Berry's Phase are analysed.Two cases of translation and rotation are discussed in detail,which show that the existence of Berry's phase depends on the choice of frame of reference.While Bitter and Dubbers's experiment is explained by the first-order approximation in our discussion,the nonadiabatic effects in this experiment are predicted by the second-order approximation when the adiabatic condition is broken.     

高频波激发低频磁场和离子声波的重整化强湍动理论

本文给出了高温等离子体中高频波激发低频磁场和离子声波强湍动过程的重整化理论,以便改善通常的弱非线性处理方法,从Vlasov-Maxwell方程组出发,在Fourier表象中得到了包含“最发散”和“次发散”效应互相耦合的高频和低频传播于重整化方程组,从而获得了高、低频振荡粒子重整化分布函数和场的耦合关系。在“最发散”重整化近似下,我们求解了高低频传播子方程组,得到了展开到v₄(高频湍动场能密度与等离子体热能密度之比)一次方的近似解和重整化介电函数等表达式。然后,在Fourier逆变换下导得了我们所要的时空表用中重整化强湍动方程组。最后,作为一个说明重整化作用的例子,在一维稳态下求解了孤立子的形式。 关键词：