Chiral condensate beyond the one-loop approximation

A two-dimensional model involving a fermion field and a self-interacting scalar field with Yukawa interaction is studied beyond the one-loop approximation. It is shown that, in this model, the chiral condensate vanishes at two values of the Yukawa coupling constant. In one case, the respective symmetry is restored, while, in the other case, it is not restored.     

Pseudo-Goldstone boson masses in a one-loop approximation

A one-loop calculation of pseudo-Goldstone boson masses in a spontaneously broken gauge model indicates that they are either identically zero or too large (of the order of several GeV) to be identified with the pion masses. The former possibility, which suggests that the pion mass may have its origin in even higher order weak and electromagnetic corrections, is investigated.     

On the gauge-dependence of the one-loop effective potential in self-consistent dimensional reduction

By allowing the gauge-parameter used to impose the harmonic gauge in M⁴ × S¹ Kaluza-Klein theory with a non-vanishing bare cosmological constant to vary, we show that the physical predictions, such as the effective gauge coupling constant and the radius of the internal dimension, stemming from consideration of the one-loop effective potential, are gauge-dependent.     

Octet-decuplet baryon mass splittings from self-consistent one-loop perturbation theory

The bag model of confined relativistic quarks in chiral-invariant interaction with scalar, pseudoscalar, vector, and pseudovector mesons, as well as gluons, is used to calculate the masses and wave functions of the spin-1/2 baryon octet and spin-3/2 decuplet, using selfconsistent Brillouin-Wigner bound state perturbation theory. Chiral symmetry breaking is invoked with the sigma model. SU (6) and SU (3) symmetries are broken by the experimental meson spectrum, and a strange quark mass. Mass corrections are calculated to one loop order, limited to the baryons of the octet and decuplet and the lowest lying mesons. Encouraging results are obtained, especially for theΔ — N and theΣ — Λ splittings. Convergence and stability have not been demonstrated, but are evidently improved by the self-consistency requirement. An initial parameter tuning gives a fit to all the octet and decuplet masses within ≦0.02 GeV, at the price of choosing the bag radius, the non-strange baryon input bag mass, and the strange quark mass. Even these small discrepancies can be dramatically reduced by fine-tuning the vector meson coupling and including an instanton contribution peculiar to theΛ.     

Theoretical study of the effect of the Coulomb blockade and Kondo resonance in the density of states using self-consistent field approximation

In a recent paper, we theoretically investigated the density of states of the composite channel–contact system in the Coulomb and Kondo regimes using the self-consistent field approximation. There are the main experimental observations of vibration features in the Coulomb blockade [H. Park et al., Nature (London) 407, 57 (2000)] and Kondo [L. H. Yu et al., Phys. Rev. Lett. 93, 266802 (2004)] regimes. In the Kondo regime, our results show that one peak at $E=\mu$ can be observed in the density of states at low temperatures (0.0026 eV ≤ k_BT ≤ 0.0000026 eV). Also, the real part of ∑₃ has one minimum peak at $E=-\mu$ and the real par of ∑₂ has one maximum peak at $E=-\mu$ for 0.01 ≤ μ ≤ 0.07 in the Kondo regime at low temperatures.     

Nuclear level densities in self-consistent field approximation

The effect of two-body nature of the nuclear shell model potential on the recent numerical calculations of the nucleai level density has been examined. For the two most widely used single particle energy level schemes based on harmonic oscillator and Woods-Saxon potential, this effect is shown to significantly modify the excitation energy dependence of the level densisties.     

Weak self-consistent approximation scheme in many-body systems

In this paper we show a possibility of restricting the usual self-consistency conditions in approximations to many-body systems. Instead of requiring thermodynamic consistency for even non-physical one-particle quantities, we impose it for the physically relevant quantities only. As a consequence of this less severe requirement, one does not lose any physically relevant information, but one can construct new types of approximations. As an example a parametric approximation scheme is given.     

Octet and decuplet magnetic and axial couplings from one-loop self-consistent perturbation theory

Octet and decuplet wave functions, obtained in a recent precision fit to the spectrum using one-loop self-consistent perturbation theory of mesons and gluons interacting with bagged relativistic quarks, are used to evaluate axial couplings and magnetic moments. Results are fully competitive with other models and provide further support to one-loop self-consistent perturbation theory as a useful model of baryon structure.     

Ordering of ternary alloys in the self-consistent field approximation

In the self-consistent field approximation, without allowance for correlation, a static theory of the ordering of ternary alloys is constructed which makes it possible to take into account the long-range nature of the interatomic interaction forces in substitutional and interstitial alloys. The theory enables one to take into account the possible existence in the alloy of two subsets of points differing by the species of atoms that occupy them. The stability of the disordered state in such alloys is analyzed and an expression obtained for the temperature at which the disordered state loses stability.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 61–64, November, 1980.     

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     

Exact crossover Green function in the two-channel and two-impurity Kondo models

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our numerical renormalization group calculations, the single exact function applies for an arbitrary mixture of the relevant perturbations in each model. This rich behavior resulting from finite channel asymmetry, interlead charge transfer, and/or magnetic field should be observable in quantum dot or tunneling experiments.     

Quasiharmonic approximation for a crystal in the self-consistent field method

An equation of state is derived for fcc crystals on the basis of earlier studies, and the stability of the crystalline phase and polymorphic transitions are discussed.Translated from lzvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol.12, No. 1, pp. 18–23, January, 1969.     

The bound one-dimensional “relativistic” polaron in a one-loop approximation

A quasirelativistic model of the narrow-gap semiconductor is considered. The interaction of the Dirac electron field with the non-dispersive phonon field in the short-range external potential (impurity) is taken into account. The classical solutions corresponding to the discrete spectrum are found. The fermion vacuum polarization effect is studied within the one-loop approximation.     

Model boson fluid with disorder in the self-consistent field approximation

We study the ground-state properties of a model neutral boson fluid in the presence of disorder effects. The effective interaction between the bosons is obtained through the self-consistent field method which renormalizes the bare interaction consisting of a hard-core repulsive potential with an attractive tail at zero temperature. We introduce disorder effects within a number-conserving approximation by modifying the density–density response function. Our results for the static structure factor and the collective mode dispersion reflect the effect of disorder in qualitative agreement with other calculational approaches.     

Scanning tunneling spectroscopic evidence of crossover transition in the two-impurity Kondo problem

To explore the crossover transition in the two-impurity Kondo problem, we calculate the differential conductance (dI / dV) corresponding to scanning tunneling spectroscopy (STS) measurements of a magnetic dimer adsorbed on a metal surface covered by a decoupling layer. With the aid of the numerical renormalization group (NRG) technique, we find that the peak structure of the dI / dV spectra near the Fermi level changes gradually as a function of the adatom separation and the coupling between the adatom localized spins and the metal surface conduction band. When the coupling becomes small, the peak disappears and, instead, a dip structure appears near the Fermi level. This dip structure is the manifestation of the strong antiferromagnetic correlation between the localized spins. We conclude that the gradual change of the dI / dV structure from a peak structure to a dip structure is an evidence of the crossover transition in the two-impurity Kondo problem.     

The self-consistent diagram approximation for lattice systems

We apply the self-consistent diagram approximation to calculate equilibrium properties of lattice systems. The free energy of the system is represented by a diagram expansion in Mayer-like functions with averaging over states of a reference system. The latter is defined by one-particle mean potentials, which are calculated using the variational condition formulated. As an example, numerical computations for a two-dimensional lattice gas on a square lattice with attractive interaction between nearest neighbours were carried out. The critical temperature, the phase coexistence curve, the chemical potential and particle and vacancy distribution functions coincide within a few per cent with exact or with Monte Carlo data. Received 18 March 1999 and Received in final form 8 November 1999     

A self-consistent Ornstein-Zernike approximation for the site-diluted Ising model

We propose a theory for the site-diluted Ising model which is an extension to disordered systems of the self-consistent Ornstein-Zernike approximation of Hoye and Stell. By using the replica method in the context of liquid-state theory, we treat the concentration of impurities as an ordinary thermodynamic variable. This approach is not limited to the weak-disorder regime or to the vicinity of the percolation point. A preliminary analysis using series expansion shows that it can predict accurately the dependence of the critical temperature on dilution and can reproduce the nonuniversal behavior of the effective exponents. The theory also gives a reasonable estimate of the percolation threshold.     

The self-consistent mean spherical approximation for the one-component plasma

The consequences of choosing the adjustable hard-core diameter in the mean spherical approximation for the one-component plasma so as to achieve thermodynamic consistency between the energy and compressibility equations are investigated. Such a choice is found to be possible only for >8.5 and, although the resulting correlation functions are discontinuous, the height of the main peak in the static structure factor is remarkably accurate. Two especially noteworthy aspects of the thermodynamic results are that the compressibility equation is much more accurate than in any previous approximation free of input from computer simulations and that the nonstatic part of the internal energy has a ^1/4 dependence in the strong coupling limit in agreement with Monte Carlo data.     

Kondo coupling and Curie temperature of in the coherent potential approximation

The ferromagnetism of Ga_1-xMn_xAs is studied in the coherent potential approximation (CPA). In this work, we used the exact Hilbert transformation of the face-centered cubic (fcc) density of states (DOS), which is different from the usual semi-circle DOS employed in previous works. Using Weiss molecular theory, we obtained a nonlinear relation of Curie temperature with respect to Kondo coupling. Our calculated T_C agrees very well with measured values.