Showing papers in "Progress of Theoretical Physics in 1971"

Relativistic quantum mechanics of one-dimensional mechanical continuum and subsidiary condition of dual resonance model

Abstract: Relativistic quantum mechanics of a finite one-dimensional continuum is studied in the framework of Dirac's generalized Hamiltonian dynamics. It is shown that the wave equation and subsidiary conditions found by Virasoro in the dual resonance model are equivalent to relativistic quantum mechanics in our system. Interaction with external fields is also studied briefly.

A Reformulation of the Coherent Potential Approximation and Its Applications

Abstract: In order to give a formalism to calculate from the first principle the electronic structure of substitutionally disordered alloys in the coherent potential approximation (CPA), we re­ formulate the CPA based on the t-matrix of the muffin-tin potential and extend the KKR method of the energy band calculation to concentrated alloys by introducing the concept of the coherent t-matrix. In close connection with this, a formulation is given to calculate, with the use of the locator and coherent locator, the local and total densities of states of al­ loys based on the tight-binding model. In this model the transfer integral as well as the atomic level depends on the atomic species on sites, and the transfer integral between A and

A Theory of Phonons in Amorphous Solids and Its Implications to Collective Motion in Simple Liquids

Abstract: 331 A theoretical study is made of phonons in amorphous solids using a self-consistent phonon scheme. In treating the structural disorder inherent in the problem, a theory is for­ mulated from the viewpoint of multiple scattering theory and designed to give phonon eigen­ frequencies which are expressed in terms of many-body correlation functions of atoms as well as of interatomic potentials in the solids. For this purpose, a conditional averaging procedure is applied to equations for phonon Green's functions, obtainable using the renormalized har­ monic approximation. A set of hierarchy equations is thereby obtained, for which various decoupling approximations are employed. As an application of the results obtained here, numerical calculations of the eigenfrequencies of longitudinal and transverse phonons in liquid argon are made using the "quasi-crystalline approximation" and the Lennard-Janes model potential. Fairly good agreement with experiment is obtained. A systematic and approximate self-consistent method for treating the hierarchy equations, which may be of some use in studying the general properties of the energy spectra of elementary excitations in disordered systems, is also obtained.

One-Dimensional Electron Gas with Delta-Function Interaction at Finite Temperature

Abstract: In recent papers Gaudin) and Yang) gave the ground state energy of a onedimensional electron gas with a delta-function interaction)-S) as a solution of a set of coupled integral equations. We try to treat the thermodynamic properties of this system as a one-dimensional Bose gas and a one-dimensional Heisenberg model.> For this purpose it is necessary to obtain all of the energy eigenvalues of the Hamiltonian. In § 2 we review the work of Gaudin and Yang on the wave function. There appear two kinds of parameters k and A. In § 3 we make conjectures on the distributions of k's and A's in the complex plane. In § 4 the energy spectrum of the Hamiltonian for repulsive interaction is obtained and the integral equations which describe the thermodynamic properties are derived. In § 5 these integral equations are solved for some special cases. In §§ 6 and 7 we treat the electron gas with an attractive delta-function interaction.

Symmetry Breaking of the Chiral U(3)⊗U(3) and the Quark Model

Abstract: Through the recent analyses it has become apparent that strong interactions obey an approximate symmetry, chiral SU(3) Q9SU(3), which is realized by pseudoscalar Goldstone bosons in the symmetry limit. Nonvanishing masses of the actual pseudoscalar mesons are attributed to breaking of the symmetry. The main feature of the symmetry breaking can be well understood by assuming that the symmetry breaking part of the Hamiltonian density belongs to a single (3, 3*) EB (3*, 3) representation of SU(3) @SU(3) .) There still remain, however, some problems concerning r; and X mesons. When we consider the above-mentioned facts from the viewpoint of the quark model, Nambu's argumene) provides a very satisfactory explanation: In the symmetry limit, the quark has a vanishing bare mass, and its physical mass arises as a self-energy accompanied with the appearence of massless pseudoscalar mesons which are the bound-states of the quark-antiquark system. A simple explanation of the symmetry breaking term will be made by introducing a small quark mass. In this approach, however, it may be meaningful to make an investigation of transformation properties, including the chiral phase transformation q-? exp (icpJ..or5/2) q, i.e. extending the basic transformation group to U(3)@U(3). We will call the transformation property under chiral phase transformation, \"chirality\". For example, if a Hamiltonian has interactions of, at most, four-fermion type, SU(3) Q9SU(3) invariance means invariance under U(3) ® U(3). In this case, if we introduce the symmetry breaking term u 0 cu8 which has the same chirality as the quark mass term, we have

A Calculation of the Electronic Structure of an Impurity Atom of Non-Transition Element in Nickel

Abstract: (Received April 6, 1971) The basic mechanism in the rapid decrease of the saturation magnetization of Ni-base dilute alloys with increasing concentration of non-transition elements is elucidated by carrying out an ab initio calculation with the use of the pseudo-Greenian method which was developed previously for the general use in the calculation of electronic structure of metals and alloys. It is the essential point of the mechanism that the number of s and p symmetry states be­ low the Fermi level does not change very much even in the presence of a deep impurity potential because of the interference between the d band and the OPW state of host Ni. A useful expression of the Greenian of pure Ni which is needed in the calculation is derived also by use of the pseudo-Greenian method.

Theory of Phase Transitions in Solid Methanes. VII : The Intermolecular Potential and the Crystalline Field

Abstract: The interaction between methane molecules in the solid state is discussed under the assumption of the pairwise interatomic interaction. A formal expression for the intermolecular interaction is derived in a form reflecting both molecular orientations and molecular symmetry. The isotropic part of this expression is compared with the potentials obtained from the second virial coefficients. The anisotropic parts dependent on the orientations of both molecules are worked out and compared with the James-Keenan model. Furthermore, the crystalline fields are obtained which a methane molecule feels in rare gas matrices as well as in solid methane.·

Gross Theory of First Forbidden β-Decay

Abstract: The gross theory of nuclear /3-decay developed by Yamada, Takahashi and Koyama for allowed transitions is extended to include the first forbidden transitions. The effect of the giant-resonance is taken into consideration by using sum rules. The /3-strength functions of both allowed and first forbidden transitions and the /3-decay half-lives are calculated. It is shown that the theory can explain the gross properties of the first ·forbidden transitions as well as the allowed ones. In particular, the theoretical /3-strength functions of neutron­ deficient heavy nuclei are compatible with experimental data recently obtained by Hansen et al. It is also shown that the first forbidden transitions often predominate over the allowed transitions in heavy nuclei.

Theory of the Unrestricted Hartree-Fock Equation and Its Solutions. I

Abstract: Classification and characterization of the solutions of UHF equation are discussed on the. basis of a group theoretical consideration on their behavior for spin rotation and time reversal. It is shown that UHF solutions can be classified into eight classes with distinct behavior for spin rotation an:d time reversal. The properties of density matrix to characterize the eight classes are derived. From the properties, standard forms. of orbital for the eight classes are derived.

Resistive Anomalies at Magnetic Critical Points

Abstract: The electrical resistivity associated with spin scattering near magnetic critical points is calculated in the model where conduction electrons interact with another electron system such as d electrons through the spin exchange interaction using the temperature Green's functions and diagram technique. It is shown that the origin of the resistive anomaly near the ferromagnetic critical point is different from that near other critical points such as the antiferromagnetic transition point. In the ferromagnetic case the resistive anomaly arises from scattering associated with the short-range spin fluctuations and consequently the tem­ perature derivative of the resistivity dp/ dT should vary like the magnetic specific heat, as was suggested by Fisher and Langer. On the other hand, in other magnetic cases with periodic magnetic structures such as rare earth metals, resistive anomalies originate from critical scattering due to long-range spin fluctuations around the magnetic lattice vector. In such cases dpjdT shows the anomaly proportional to -sign(t) ltl-

Localization of Normal Modes and Energy Transport in the Disordered Harmonic Chain

Abstract: A generalization of the formula for heat current that was given by Matsuda and Ishii is derived which is valid for a wider variety of systems than was the original one. The limits of its applicability are discussed. The expression is evaluated numerically for disor­ dered chains of lengths up to 1000 atoms, with results that substantially support the IF­ assumption of Matsuda and Ishii.

On Origin and Physical Meaning of Ward-Like Identity in Dual-Resonance Model

Abstract: It is shown for the string model that the Ward-like identities in the dual-resonance model proposed by Fubini, Veneziano and Virasoro follow directly from the requirement that the theory must be covariant under an arbitrary transformation of the Lagrange coordinate labeling each constituent part of the string. Thus at least for the string model, these identities are a necessary consequence of a general principle to be satisfied by any consistent physical theory. Our discussion is restricted to the case a (0) = 1, i.e., intercept one.

Flux-Line Lattices of Pure Type II Superconductors with Anisotropic Fermi Surface

Abstract: The free energy appropriate for a pure single crystal type II superconductor with an anisotropic Fermi surface is calculated near the upper critical field H 0 , at low tempera· tures. It is shown that various flux-line lattices can occur depending on the magnitude of the anisotropy and the direction of the applied magnetic field relative to the crystal axis. § I. Introduction In a previous paper1> devoted to the analysis near T 0 , we have shown qualitatively that in a superconductor with an anisotropic Fermi surface of cubic symmetry, an equilateral triangular flux-line lattice is stable just below the transi­ tion temperature, but other lattice structures occur depending on the magnitude of the anisotropy and the direction of the applied magnetic field relative to the crystal axis at low temperatures. Furthermore, the anisotropy removes the degeneracy for the direction of the array of the flux-line. In fact, experiments2> show many structures of the flux-line lattice (FLL) and a certain correlation between its array and the crystal axes. The FLL ar­ rangement of PbTl, for example, is qualitatively consistent with the results of I. That is, a square FLL exists in the magnetic field parallel to the four-fold crystal symmetry axis ( [1.0.0] direction), while the FLL remains to be an equilateral triangular when the field is parallel to the three-fold crystal symmetry axis ( [1.1.1] direction). In this paper we investigate FLL near the upper critical field at low tem­ peratures extending the work of I because the anisotropy has a large effect on the properties of a superconductor at those temperature region. In the following we use the unit system h=kB=c=l.