Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.     

The ′T Hooft-Polyakov monopole near the Prasad-Sommerfield limit

A perturbative classical monopole solution for the SO(3) gauge theory is constructed in the limit of small but non-vanishing Higgs potential. This corresponds to the limit $\text{μ}{}^2\text{2M}{}_{\mathrm{W}}{}^2\text{=}\text{λ}\text{? 1}$, where μ equals the mass of the scalar particle and M_W equals the mass of the intermediate vector particles. The monopole solution and mass are found to involve non-analytic functions of λ: $\text{γ}$ and λ ln λ. The monopole mass M_m is calculated to order $\text{μ}{}^2\text{M}{}_{\mathrm{W}}$ as

$\text{M}{}_{\mathrm{m}}\text{=}\text{4π}\text{e}{}^2\text{M}{}_{\mathrm{w}}\text{1+}\text{1}\text{2}\text{μ}\text{M}{}_{\mathrm{w}}\text{+}\text{1}\text{2}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}\text{ln}\text{μ}\text{M}{}_{\mathrm{w}}\text{+0.7071}\text{μ}{}^2\text{M}{}^2{}_{\mathrm{w}}$

.     

Phenomenological predictions of the SO(10) supersymmetric grand unified model

The phenomenological predictions of the SO(10) supersymmetric grand unified model (SO(10) SGUM) for the mass scales M₁, M₂, weak angle ifsin²θ_w, quark-leptons mass ratios $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, $\text{m}{}_{\mathrm{t}}\text{m}{}_{\mathrm{<mtext>b</mtext>}}$, $\text{m}{}_{\mathrm{\tau }}\text{m}{}_{\mathrm{\nu }}{}_{\mathrm{\tau }}$ and proton lifetime τ_p are estimated by using renormalization group analysis at one-loop level. In contrast with SU(5) SGUM, we find that the SO(10) SGUM still has problems with τ_p but not with sin²θ_w and $\text{m}{}_{\mathrm{<mtext>b</mtext>}}\text{m}{}_{\mathrm{\tau }}$, which may suggest that supersymmetry would be bro at a mass scale $\text{?10}{}^7\text{GeV}$.     

Deep inelastic structure functions of the photon

Three independent structure functions of a real photon can be measured in photon-photon collisions in e^±e^? storage rings. These are M₁ and M_L (related to the usual structure functions W₁andνW₂, as defined for any target) and a third function M₃, which arises from the strong plane polarisation of the colliding photons. We show, using a dispersion relation in the photon mass, that M₃ and the longitudinal structure function M_L both scale and are independent of the vector-dominant hadronic structure of the real photon. Therefore in a parton model, or in the quark light-cone algebra, they are given by the bare quark box diagrams which also dominate when both photons have large q²; this uniquely predicts the behaviour , $\text{M}{}_3\text{= [(}\text{1}\text{2}\text{π)Σ e}{}_{\mathrm{i}}{}^4\text{](?x}{}^2\text{)}$ for the real photon structure functions in the Bjorken limit (q₂² → ?∞, q₁²=0, x=?q₂²/2q₁·q₂=constant).     

Parity violation in atoms in SO(3) gauge models

We have evaluated the parity-violation contribution in atoms in the framework of SO(3) gauge theory. Various hadronic models have been used: first, for simplicity, the unrealistic five-quark one, next, others involving three ordinary SU(3) triplets for which all unwanted strangeness-changing processes are suppressed, up to order $\text{Gα}\text{or}\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$. In the free quark approximation, we obtain quite similar parity-violation effects which are proportional to $\text{GαΔM}{}^2\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}^2$ (ΔM² is the difference of squared masses of leptons (M_X0² ? M_ν² = M_X0²), or of quarks (ΔM_q²)). Namely, in large atoms (Z ? 1) the electronic contribution which is proportional to

gives the largest effect ($\text{σ}{}_{\mathrm{?}}\text{,}\text{p}{}_{\mathrm{?}}\text{and}\text{m}{}_{\mathrm{?}}$are the spin, momentum operators and mass of the lepton). Parity-violating effects in SO(3) gauge models are ?10^?4 smaller than those evaluated in the Weinberg theory with a neutral parity-violating current and will remain undetectable in the near future.     

Concepts of convergence for a quantum law of large numbers

We introduce the notion of uniform convergence of an operator sequence relative to a state operator, and we compare it with the notion of almost everywhere convergence, introduced by Gudder. We show that a sequence (M_n) of mean-value operators

$\text{M}{}_{\mathrm{n}}\text{=}\text{1}\text{n}\text{∑n}\text{i=1}\text{1?…?A}{}_{\mathrm{i}}\text{?1?…,}$

defined on the infinite tensor product $\text{?}\text{i}\text{H}{}_{\mathrm{i}}$, converges relative uniformly to $\text{x}\text{1}$ if and only if it converges almost everywhere to $\text{x}\text{1}$.     

Anomalous mass dependence of glueball exclusive decay rates

Exclusive decays such as G → ππ are studied in the framework ofperturbative QCD. We discuss the possibility of the constituent gluons' virtualness scaling as the glueball mass M_G, which is a picture equivalent to a glueball containing a few slow-moving, heavy gluons. In this case, the decay rate exhibits a pinch singularity which enhances it by a factor of order (M_G²/m_q²)² over the dimensional scaling expectation. This singularity is partially suppressed by Sudakov effects which reduce the enhancement factor to $\text{(M}{}_{\mathrm{<mtext>G</mtext>}}{}^2\text{/m}{}_{\mathrm{<mtext>q</mtext>}}{}^2\text{)}{}^{\mathrm{2n}}\text{,}\text{where}\text{n ? 0.4}$.     

Fermion-fermion condensates and CP violation

We discuss some theoretical difficulties of the standard Kobayashi-Maskawa scheme for CP violation and present an alternative scenario where CP violation arises through non-vanishing phases in fermion-fermion condensates. We illustrate our ideas in the context of a left-right symmetric model with a hierarchy of mass scales (M_WR?M_WL). We show that the mass scale hierarchy leads naturally to a negligible θ-parameter at tree level, , with this result being preserved in higher order. The resulting theory of CP violation in the kaon sector is of the superweak type and the electric dipole moment of the neutron is essentially determined by θ. There is no direct connection in the model between the phases responsible for the univers's baryon asymmetry and those responsible for CP violation in the kaon system — a result we claim is a general feature of gauge theory models of unified interactions.     

Dipole moment function and vibration-rotation matrix elements of HCl35 and DCl35

The infrared intensity measurements and molecular beam electric resonance dipole moment measurements for HCl and DCl have been reviewed. A method not previously exploited is used to determine infrared matrix elements from the electric resonance dipole moment measurements. A ‘best’ set of matrix element values was selected for HCl and from these the M_i-coefficients of a polynomial dipole moment approximation were determined; M₀ = 1.0935±0.0007 D, $\text{M}{}_1\text{= 0.947±0.023 D/}\text{A}\text{?}$, $\text{M}{}_2\text{= 0.015±0.041 D/}\text{A}\text{?}{}^2$, $\text{M}{}_3\text{= -0.814± 0.116 D/}\text{A}\text{?}{}^3$. Calculations using this dipole moment function for both HCl and DCl are shown to give good agreement with available band strength and vibration-rotation interaction factor measurements. RKR potentials are also calculated for both molecules.     

Multiplicities in lepton-hadron processes

The average multiplicity in deep inelastic electro- and neutrinoproduction at large ω(ω～s/Q² + 1) is related in Feynman's version of the parton model to the average multiplicities in high-energy electron-positron annihilation and hadron-hadron scattering. The relation is: , where C_e⁺e^? and C_h are, respectively, the coefficients of ln(s/M_1⊥²) in the multiplicities from e⁺-e^? and P-P in to hadrons, and M_1⊥ is an average transverse mass.     

Some aspects of the quark parton model

A modified Kuti-Weisskopf model which satisfies the Feynman threshold constraints is considered further. Detailed predictions for the sum of neutrino and anti-neutrino differential cross sections on nucleon (which can be readily compared with forthcoming NAL data), the shapes of the structure functions $\text{?}{}_2{}^{\mathrm{\nu p,\nu n}}$ and the ratio $\text{?}{}_2{}^{\mathrm{\nu p}}\text{/?}{}_2{}^{\mathrm{\nu n}}$, and spin-dependence of inelastic electron-nucleon scattering versus scaling variable x are delineated. We also compare in some detail the general features of our model with the “model independent” approach of Feynman for quark parton theory.     

The uniform and the strong topology on realizations of the algebra of polynomials

It is shown that under quite general assumptions on the operators A₁,…,A_n (unbounded, symmetric) and on the domain $\text{D}$ on the realization $\text{P}\text{(A}{}_1\text{,…,A}{}_{\mathrm{n}}\text{)}$ of the algebra of polynomials $\text{P}\text{(x}{}_1\text{,…,x}{}_{\mathrm{n}}\text{)}$, the strongest locally convex topology τ_st coincides with the uniform topology τ_$\text{D}$ as well as with the strong operator topology τ_s. In the case n = 2 some conditions are given, under which these general assumptions are fulfilled.     

A small parameter in the 1Nc expansion and narrowness of hadronic resonances

The dynamical basis for the validity of the $\text{1}\text{N}{}_{\mathrm{c}}$ expansion is investigated in the context of QCD in 1 + 1 dimensions. This is carried out by studying the first non-leading corrections in $\text{1}\text{N}{}_{\mathrm{c}}$ to the mass operator in the space of physical states. The correction to the real part of the mass operator has a direct implication for the convergence of the $\text{1}\text{N}{}_{\mathrm{c}}$ expansion, since a small effective parameter is identified, where its smallness depends on the dynamical circumstances in a known way. The generated imaginary part of the mass operator provides us with an insight concerning the question of the narrowness of hadronic resonances. In order to have a more realistic contact with our world, we include also effects due to the flavor symmetry group SU(N_f). This allows us to understand better the validity and usefulness of the notions of resonance dominance and (smooth) Regge behavior. We also discuss the expansion with $\text{N}{}_{\mathrm{f}}\text{N}{}_{\mathrm{c}}$ fixed and compare the results with those obtained from Dual Resonance Model. It is remarked that a nonuniformity exists between the limits N_c → ∞, N_f = fixed and N_c → ∞, $\text{N}{}_{\mathrm{f}}\text{N}{}_{\mathrm{c}}\text{=}\text{fixed}$, which may affect physical quantities.     

A thermodynamic study of nonstoichiometric cerium dioxide

Thermogravimetric measurements were performed on nonstoichiometric CeO_2?x in the temperature range 750–1500°C and from oxygen pressures of 10^?2 to 10^?26 atm. From this data the deviation from stoichiometry x = x(T, P_o2) was determined. The thermodynamic quantities Δ$\text{H}$_o2 and Δ$\text{S}$_o2 were calculated in the region 0.001? x ? 0.3 and found to be independent of temperature.In the composition region 0.001< x < 0.006, the variation of Δ$\text{S}$_o2 with x is consistent with a defect model involving randomly distributed doubly ionized oxygen vacancies. The experimental dependence of x and σ (electrical conductivity) is shown to be consistent with this model as Δ$\text{H}$_o2 (≈ -10 eV) exhibits a slight dependence on x. It is postulated that the variation in Δ$\text{H}$_o2 may result from lattice parameter increases with x, while the defects remain essentially randomly distributed.In the composition region 0.006 < x < 0.1, x ∝ with 1 < n < 5, and in the region 0.1 < x < 0.3, x ∝ with n increasing rapidly with x to n? 30. This behavior is believed to result from increasing defect interaction with increasing departures from stoichiometry. It is interesting to note that the ordered phase observed by Bevan and Kordis between CeO_1·72 and CeO_1·70 was not observed in this study at temperatures between 1300° and 1500°C.     

Calculation of baryon masses in quantum chromodynamics

The polarization operator of quark currents with baryon quantum numbers is considered in quantum chromodynamics. The non-zero mean vacuum values of the field operator products are taken into account. The sum rules are obtained assuming that in the virtuality region ～1 GeV, among the mean vacuum values violating the chiral invariance, the most important is $\text{〈0|}\text{ψ}\text{ψ|0〉}$. Saturating these sum rules by the lowest baryonic states one is able to calculate the masses of the isobar Δ and nucleon N, M_Δ = 1.4 GeV, M_N = 1 GeV, up to 15% through the known value $\text{〈0|}\text{ψ}\text{ψ|0〉}$. The mass splitting in the baryonic decuplet $\text{M}{}_{\mathrm{\Sigma 1}}\text{?M}{}_{\mathrm{\Delta }}\text{= 125}\text{MeV}$ is calculated in first order in the current strange quark mass m_s = 150 MeV. Certain results for other baryonic resonances have also been obtained.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Fission and decay of excited nuclei

The statistical theory of the decay of excited nuclei including the competition between particle emission and fission is considered. Fission barriers are given by a phenomenological formula which is an analog of the known Cameron formula and approximates well experimental data on nuclei up to transuranic elements. The contribution of shell corrections and odd-even effects is discussed. The calculated ratios of evaporation and fission widths Γ_n/Γ_f agree with experiment even in the region of nuclei with Z > 90. The $\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}$ values depend weakly on excitation energy for nuclei with Z ≈ 90, While in other regions this dependence proves rather strong. The last conclusion does not contradict known experimental data since in experiments one usually measures some effective value $\text{〈}\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}\text{〉}$, which is only indirectly related to the real $\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}$, values. It is shown that the calculated values of $\text{〈}\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}\text{〉}$ depend on excitation energy either. The effects of angular momentum and uncertainty in the choice of level density parameter are discussed.     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

Studies of interface phonons

The vibrational modes localized at the interface between two distinct crystals have been studied for a simple crystal model obeying all of the invariance conditions required for models used in studies of dynamical properties of crystal surfaces, and giving rise to Rayleigh surface waves. The two crystals are assumed to be semi-infinite simple cubic and to have the same lattice parameter a. They differ by their mass (M and M_A) and the central force interactions between first (K and K_a) and second nearest neighbors $\text{1}\text{2}\text{K}$ and $\text{1}\text{2}\text{K}{}_{\mathrm{A}}$. The interface is obtained by coupling the (001) free surfaces of these distinct crystals by central force intractions (K^'). We find that the variation of the interaction conditions (K^') at the interface and of the $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{A}}\text{M}{}_{\mathrm{A}}\text{)}$ parameter has the following qualitative effects on the properties of surface and bulk phonons. When (K^') increases from zero to a finite value, the frequencies of the surface phonons increase and are splitted in the case of two identical crystals. One can say that the surface phonons are transformed into interface modes. For some values of $\text{K}{}^{\mathrm{\text{'}}}\text{K}$ and $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{<mtext>A</mtext>}}\text{M}{}_{\mathrm{<mtext>A</mtext>}}\text{)}$ parameters these interface phonons may be admixed with bulk phonons and thus become virtual interface states.