Showing papers in "Progress of Theoretical Physics in 1975"

Relationships among Inverse Method, Bäcklund Transformation and an Infinite Number of Conservation Laws

Abstract: It is shown that inverse method, Backlund transformation and an infinite number of conservation laws are closely related. The derivation of Backlund transformation from the fundamental equations of inverse method is explicitly shown. Also it is shown that conser· vation la~ is obtained in a simple way from the. Riccati form of inverse method and the derivation of conservation law from Backlund transformation is possible.

Perturbation Expansion for the Anderson Hamiltonian. III

Abstract: Thermodynamical quantities are expanded in perturbation series with respect to the Coulomb repulsion U for the Anderson Hamiltonian with electron-hole symmetry and 'their general terms of perturbation are investigated. By these processes the mutual. relations among these quantities are discussed. It is confirmed that the thermodynamical quantities such as the specific heat. and the scattering t-matrix are expressed in terms of two quantities; the even and odd parts of the susceptibility as far as low-lying excitations are concerned. These results are entirely consistent with the Nozieres phenomenological Fermi liquid theory based on the s-d exchange model. . §I. Introduction In the :first paper1h*> of' this series, we presented a perturbation theoretical approach to the Anderson Hamiltonian2> with electron-hole symmetry and showed that each term of the perturbation expansion for the thermodynamical quantities, in particular for the free energy, can be expressed by an imaginary time integral of the product of two antisymmetric determinants constructed by unperturbed local d-electron temperature Green's functions. In the second paper by Yam ada, B) each term in the perturbation expansions for the specific heat, the susceptibility, the resistivity and the density-of~state s for the localized d-state has been calculated up to fourth order. In the course of calculation it . has been found that some general relations hold between thermodynamical quantities, in particular, the T-linear specific heat· is proportional to the even part of the susceptibility. This finding immediately leads us to the result that the ratio of the susceptibility to the coefficient of the T-linear specific heat becomes twice as large in the s-d limit as the value in the case of no correlation. This paper deals with further development along this line: Here, discussion is mainly concentrated on the. general properties of the perturbation series for thermodynamical quantities in the Anderson model. The basic Hamiltonian in this paper is the Anderson Hamiltonian with electron-hole symmetry (Ed= -tU), which is divided into two parts, the unperturbed part H 0 and the perturbation H' as follows:

The Korringa Relation for the Impurity Nuclear Spin-Lattice Relaxation in Dilute Kondo Alloys

Abstract: We present a proof of the Korringa· relation for the impurity nuclear spin-lattice relaxation of transition-metal impurities in simple metals. Two important mechanisms are considered; the relaxation due to the d-spin fluctuations and the d-orbital fluctuations. By using the 5-fold degenerate Anderson model it is shown that the Korringa relation is valid at low temperatures T

Finding Eigenvalue Problems for Solving Nonlinear Evolution Equations

Abstract: The problem of determining what nonlinear evolution equations are exactly solvable by inverse scatte;ing techniques is simplified by considering a linear limit. By linearizing a given eigenvalue problem and. the associated time evolution operator, it .. is possible to determine the class of linearized dispersion relation (s) of the exactly solvable nonlinear evolution equations. Examples are given to illustrate the method.·

A Possible Model for New Resonances Exotics and Hidden Charm

Abstract: We assign ψ(3695) to an exotic meson cc(pp+nn) and ψ(3105) to a vector meson cc, respectively. Then we can explain naturally two facts: 1) ψ(3695) decays strongly to ψ(3105) + 2π and 2) there is very little ψ(3695) production compared with ψ(3105) production in pN scattering at Brookhaven. In this model we expect two broad resonances at 3.7 ∼4.1 GeV and at ∼4.1 GeV. We also predict another resonance at ∼6.2 GeV, which will be a sharp resonance if the mass is smaller than twice the mass of the lowest mass state of cc.

α-α Scattering at Intermediate Energies Applicability of Orthogonality Condition Model and Upper Limit of Isoscalar Meson-Nucleon Coupling Constants Inferred from Potential Tail

Abstract: Intermediate energy a-a scattering is studied by the resonating group method with the Coulomb exchange kernel, in order to resolve the discrepancy between the potential tail for the S, D and G waves and that for higher partial waves which was reported in a previous phenomenological analysis_ but hardly understandable from a microscopic point of view. It is shown that this discrepancy can be removed if we employ the new solution of the pha;;e shift analysis. Validity of the orthogonality condition model in the inelastic region is shown if a suitable imaginary potential ·is added to the direct potential. The real phase shifts of the !-wave dominated by the direct potential tail restrict the coupling constants of isoscalar mesons with nucleon as g62/4n=3.5~6 and g.'/4n=8~11.

Application of Mode-Coupling Theory to Nonlinear Stress Tensor in Fluids

Abstract: In a steady state of fluid the nonlinear dependence of stress tensor on a thermal driving force is investigated by a direct extension of the mode-coupling theory to far-from-equilibrium situation. The steady state is generated from a local equilibrium state having the same average values of gross variables as in the steady state. In the lowest approximation for the mode-coupling term ·the explicit expression of the stress tensor is obtained and evaluated. The effects of the higher mode-coupling approximations on the stress tensor are also briefly examined.

Structure and Stability of Accretion-Disk around a Black-Hole

Abstract: Structure and stability of a stationary thin-disk formed around a black-hole are studied using the conventional formula for the viscous stress. The disk is classified into an optically thick case, an optically thin case and an intermediat.e case in which the comptonization plays an important role. Thermal and ·secular stabilities are examined in each of the above three cases. High temperatures . in excess of 10°'K are expected in the optically thin case and in the comptonization dominant case. However, it is shown that in these case_s the disk is unstable for the thermal perturbation. § I. Introduction It has been known that some of Xcray sources consist close binary systems. Among these X-ray sources, especially Cyg X-1 is of great interest since it is believed as a black-hole candidate. Boltonn anaiysed spectroscopic and photometric data of HD 226868, which was highly believed to be associated with Cyg X-1, and found that the mass of the invisible component was greater than 7.4 M®. Even if the lower limit of the above mass is assumed for Cyg X-1, it is far massive than the upper limit of a stable neutron star ( r-.../2M®). Moreover, recently Roths­ child et a1. 2' and Oda et al. 3' presented evidence for millisecond pulses from Cyg X-1. It seems that these short time variations also indicate the existence of a black-hole. In a close binary system the material overflowing from the primary star. has a considerable amount of angular momentum against the secondary star, probably a black-hole for Cyg X-1. As a result the centrifugal force prevents the infall of the material toward the secondary star when it balances with the gravitational force; The material rotates in a circular orbit. If there exists an effective outward trans­ porting mechanism for angular momentum, the material keeping nearly Keplerian motion falls gradually toward the secondary star. A gaseous disk is formed around the secondary star and X-ray emission is expected since gravitational energy is released by the infalling material. Pringle and Rees,4' Shakura and Sunyaev5' and Novikov and Thorne 6' studied the structure of such a disk, and discussed the X-ray spectrum emitted from the surface of the disk. As for the transporting mechanisms for angular momentum Shakura et al. assumed turbulent and magnetic viscous forces. Tn terms· of them the tan­ gential viscous stress Pr6 is expressed as

Polarized Electroproduction in Asymptotically Free Gauge Theories

Abstract: Deep inelastic polarized electron-nucleon scattering is analyzed in asymptotically free gauge theories of the strong interactions. Anomalous dimensions of the relevant operators are calculated to second order in perturbation theory. The asymptotic form. for the moments of g, ( = M'11G,) is derived. It is shown that both the Bjorken and the Burkhardt-Cottingham sum rules hold in the limit, but that the approach to the limit valueis logarithmic for the former sum rule and is like ·inverse powers of Q' for the latter. The ratio of g, for two different values of Q' near threshold is calculated. Finally it is shown that the asymptotic limit of the transverse asymmetry near threshold can be determined only by the informations on g, and F, at some fixed large Q'.

Zero-Point Spin Reduction of an Antiferromagnet

Abstract: Zero-point spin reduction in the low-dimensional antiferromagnet is discussed by the spin wave theory taking into accOtmt kinematical interaction due to finite magnitude of spin. This method is applied to KCuF, and the result is in good agreement with the ob­ served one. Furthermore the values of zero-point spin reduction of several other chain· structure antiferromagnets are predicted. §.1. Introduction A large zero-point spin reduction in the antiferromagnet of the low dimen~ sionality has recently been observed. In the layer-structure antiferromagnet K 2MnF 4, the observed values of zero-point spin reduction agree with those of a simple two-dimensional spin-wave theory.D It has been found that the zero-point spin reduction in the one-dimensional antiferromagnet' KCuF 8 is nearly 45%. 2) However, the kinematical interaction d,ue .to the restriction on the number of spin deviations possible at any given site cannot always be neglected i.n the antiferro- · magnet of the low dimensionality even at absolute zero. Especially the zero-point spin reduction of the ideal spin-wave theory diverges in the one0dimensional Heisen­ berg antiferromagnet. As the zero-point spin reduction should not. be over the spin magnitude S, the divergence means that the spin-wave theory which does not take· account of the kinematical interaction cannot be trusted. The effect of the kinematical interaction for zero-point spin reduction was first estimated by Herbert 8J for the Heisenberg antiferromagnet with each spin 8=1/2,, but he did not give any attention to the low-dimensional antiferromagnet. In the present paper his method is extended to the case of general S, and the effe'ct of the ki~ematical interaction is taken into account in the calculation of the zero-point spin reduction, and several antiferromagnetic chain-structure compounds are dis­ cussed.

The Unrestricted Hartree-Fock Theory of Chemical Reactions. V The Reaction of Three Hydrogens in Isosceles Triangular Conformations

Abstract: A UHF theoretical analysis is carried out for the reaction of three hydrogens in iso­ sceles triangular conformations. It is shown that the UHF ground state of the H 8 system consists of· three different "electronic phases"; an RHF configuration in a region of acute triangles, an ASDW configuration in a region of flat triangles and a TSDW configuration iri a region near equilateral triangles. The potentials of the UHF states are calculated and their interconnection relation is studied. A configurational analysis in terms of the RHF orbitals is carried out for the UHF states at equilateral triangles. It is shown that the TSDW state is a good approximation to ·the full CI ground state. The reason for the missing of the Jahn-Teller cusp in the UHF ground state potential is discussed. Importance of spin flipping instabilities in mechanistic characterization of radical reactions is pointed out. In previous papers,n-5> we have carried out unrestricted Hartree-Fock (UHF) theoretical analyses of the chemical reactions in singlet ground state. We consider, in this paper, the three hydrogen system with isosceles triangular conformations as one of the simplest model system for insertion reactions of free radicals. We show from an analysis of the H 3 system that instability of a ground state configu­ ration and appearance of a new ground state of broken symmetry character are phenomena which may occur not only in the reacting systems with a singlet ground state but also in the systems with a doublet ground state, i.e., in free radical reactions. The UHF ground state of the H 3 system undergoes "electronic phase transitions" between a restricted Hartree-Fock (RHF), an axial spin density wave (ASDW) and a torsional spin density wave (TSDW) configurations, indicating the presence of a hierarchy of doublet radicals with electronic structures of increas­ ing complexities as in singlet radicals discussed previously.5> A configurational analysis is carried out for the ASDW and the TSDW states at equilateral triangles in order to clarify the nature of the electronic correlation effects incorporated into the UHF states. The reason for the missing of the Jahn-Teller cusp6> in the UHF ground state

Possible Phases and Some Properties of the One-Dimensional Metal with the Half-Filled Band

Abstract: A one-dimensional metal with a half-filled band is studied by the model of Dzyaloshinskii and Larkin. The .next-order renormalization group theory is applied. The invariant charges become smooth functions over all temperature. The possible phases-the singlet and the triplet Cooper pairing states, and SDW and CDW ·states at T ~0 are discussed. The criterion for these phases depends on th~ bare coupling constants via their signs and relative magni­ tudes. The phase diagram differs from that of the first-order theory. The Green's function, the vertex function, and 2pF and uniform response functions are found in the asymptotic power form. The exponents are- univ~rsal except for the case of the repulsive couplings. The results are compared with the exact theorems abo~t the Hubbard and Tomonaga models.