Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Magnetic circular dichroism in the absorption of theF A centre in KCl doped with Li and Na

Summary The spin-orbit structure ofF _A centres in KCl:Li and KCl:Na have been studied by means of the magnetic circular dichroism. Due to theirC _4V symmetry theF _A centres have two different spin-orbit parameters, Δ^‖ and Δ^⊥, which only in the KCl:Li case follow the relation: Δ^‖ < Δ_F < Δ^⊥ as expected from the theory. For a close comparison we have also reported our measurement of the spin-orbit coupling ofF centre in KCl. The spin-orbit parameters of theF andF _A centres have been determined using the method of moment.     

d-Symmetry superconductivity as a consequence of valence-bond type correlations

It is shown that d _x ²−y ² symmetry of superconducting order due to valence bond (VB) type correlations is possible. The VB correlations are compatible with antiferromagnetic (AF) spin order. For the two-dimensional Hubbard model with arbitrary doping, the variational method of local unitary transformations is used to construct explicitly a uniform state with VB structure. The d-channel attraction of holes is a consequence of the modulation of hops by the populations of centers accompanying VB formation, and the parameters of the modulation are determined variationally. The increase in the density of states at the Fermi level accompanying AF splitting of the band, which is absent in the paramagnetic state, is important for the gap width. The gap width and its ratio to T _c are of the order of 2Δ≃0.1t and 2Δ/kT _c≃4–4.5 with U/t≃8. The agreement between the phase diagram found and experiment is discussed. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 350–355 (10 March 1998)     

Renormalization group functions of the φ<Superscript>4</Superscript> theory from high-temperature expansions

It has been previously shown that calculation of the renormalization group (RG) functions of scalar ϕ⁴ theory reduces to analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG functions of the four-dimensional theory can be calculated for arbitrary coupling constant g with an accuracy of 10⁻⁴ for the Gell-Mann-Low function β(g) and with an accuracy of 10⁻³–10⁻² for anomalous dimensions. The expansions of the renormalization group functions up to the 13th order in g ^−1/2 have been obtained.     

Strong decay Δ<Superscript>++</Superscript>→<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">π</Emphasis> with light-cone QCD sum rules

We calculate the strong coupling constant g _{ΔN π} and study the strong decay Δ⁺⁺→p π with light-cone QCD sum rules. The numerical value of the strong coupling constant g _{ΔN π} is consistent with the experimental data. The small discrepancy may be due to the failure to take into account perturbative corrections.     

Fine structure of the dipole excitations of the even-even 160Gd nucleus in the spectroscopic region

In this study, the result of calculations using rotational, translational and Galilean invariant quasiparticle random-phase approximation is presented for the low-lying dipole excitations in the even-even ¹⁶⁰Gd nucleus. Calculations are carried out for both ΔK=1 and ΔK=0 branches. The analysis shows that the main part of spin-1 states, observed at energy 2.4–4 MeV in ¹⁶⁰Gd, have M1 character and are interpreted as main fragments of the scissors mode. The calculations indicate the presence of a few prominent negativeparity dipole ΔK=1 states in the investigated energy region, in agreement with experiment.      

Effects of minimal supersymmetry standard model in neutral <Emphasis Type="Italic">K</Emphasis><Superscript>0</Superscript> meson mixing

Mixing of neutral K ⁰ mesons is studied in the framework of the minimal supersymmetric model (MSSM) with a Yukawa type II sector and explicit violation of CP invariance in the Higgs potential. Mixing parameters Δm _LS and ɛ are calculated in the limit of the four-fermion approximation with charged Higgs boson exchange. This work specifies the data presented in [1] more precisely and, taking into account the influence of new contributions on the above observables, proves the small degree of supersymmetric effects for a system of K ⁰ mesons.     

Investigation of Δ(3,3) resonance effects on the properties of neutron-rich double magic spherical finite nucleus, <Superscript>132</Superscript>Sn,in the ground state and under compression

Within the framework of the radially constrained spherical Hartree–Fock (CSHF) approximation, the resonance effects of delta on the properties of neutron-rich double magic spherical nucleus ¹³²Sn were studied. It was found that most of the increase in the nuclear energy generated under compression was used to create massive Δ particles. For ¹³²Sn nucleus under compression at 3.19 times density of the normal nuclear density, the excited nucleons to Δs were increased sharply up to 16% of the total number of constituents. This result is consistent with the values extracted from relativistic heavy-ion collisions. The single particle energy levels were calculated and their behaviours under compression were examined. A meaningful agreement was obtained between the results with effective Hamiltonian and that with the phenomenological shell model for the low-lying single-particle spectra. The results suggest considerable reduction in compressibility for the nucleus, and softening of the equation of state with the inclusion of Δs in the nuclear dynamics.     

Adsorption of a semiflexible wormlike chain

Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a self-similar monomer concentration profile c(x) ∼ x ^-4/3 near the surface (when the distance to the surface x is much smaller than the chain persistence length l /2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2-dimensional) trains of wormlike short loops (flat blobs) and coil-like (3-dimensional) loops forming a triple-layer structure: contact layer (x < Δ) of adsorbed fragments virtually laid on the surface, proximal layer (Δ < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Δ defines the range of monomer/surface attraction, Δ ≪ l. The adsorption transition is continuous. However, its relative width is small (T ^* is the adsorption temperature, ΔT is the relevant temperature interval): ∼ , i.e. a discontinuous transition in the limit Δ/l↦ 0. Received 10 October 2002 and Received in final form 22 November 2002 RID="a" ID="a"Permanent address: Physics Department, Moscow State University, Moscow 119992, Russia. e-mail: semenov@polly.phys.msu.ru     

A Generalization of the Stillinger–Lovett Sum Rules for the Two-Dimensional Jellium

In the equilibrium statistical mechanics of classical Coulomb fluids, the long-range tail of the Coulomb potential gives rise to the Stillinger–Lovett sum rules for the charge correlation functions. For the jellium model of mobile particles of charge q immersed in a neutralizing background, the Stillinger–Lovett sum rules give the charge and second moment of the screening cloud around a particle of the jellium. In this paper, we generalize these sum rules to the screening cloud induced around a pointlike guest charge Zq immersed in the bulk interior of the 2D jellium with the coupling constant Γ=β q ² (β is the inverse temperature), in the whole region of the thermodynamic stability of the guest charge amplitude Z>−2/Γ. The derivation is based on a mapping technique of the 2D jellium at the coupling Γ = (even positive integer) onto a discrete 1D anticommuting-field theory; we assume that the final results remain valid for all real values of Γ corresponding to the fluid regime. The generalized sum rules reproduce for arbitrary coupling Γ the standard Z=1 and the trivial Z=0 results. They are also checked in the Debye–Hückel limit Γ→0 and at the free-fermion point Γ=2. The generalized second-moment sum rule provides some exact information about possible sign oscillations of the induced charge density in space.     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

Large N 2D Yang-Mills Theory and Topological String Theory

We describe a topological string theory which reproduces many aspects of the 1/N expansion of SU(N) Yang-Mills theory in two spacetime dimensions in the zero coupling (A= 0) limit. The string theory is a modified version of topological gravity coupled to a topological sigma model with spacetime as target. The derivation of the string theory relies on a new interpretation of Gross and Taylor's “Ω^-1 points ”. We describe how inclusion of the area, coupling of chiral sectors, and Wilson loop expectation values can be incorporated in the topological string approach. Received: 3 March 1994 / Accepted: 2 February 1995     

New Variational Perturbation Theory Based on q−Deformed Oscillator

A new variational perturbation theory is developed based on the q−deformed oscillator. It is shown that the new variational perturbation method provides 200 and 10 times better accuracy for the ground state energy of anharmonic oscillator than the Gaussian and the post Gaussian approximation, respectively, for weak coupling.     

The investigation of 0<Superscript>+</Superscript> ↔ 0<Superscript>−</Superscript><Emphasis Type="Italic">β</Emphasis> decay in some spherical nuclei

The 0⁺ ↔ 0⁻ first-forbidden β decay transitions have been investigated for some spherical nuclei. The theoretical framework is based on a proton-neutron quasiparticle random phase approximation (pnQRPA). The Woods-Saxon potential basis has been used in our calculations. The transition probabilities have been calculated within the ξ approximation. The relativistic β moment matrix element has been calculated both directly without any assumption and assuming that it is proportional to the non-relativistic one.     

On certain correspondences among various coupled-cluster theories for closed-shell systems

In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T−T ⁺) is exactly sameorder by order inT with the size-consistent energy functional 〈ψ|H|ψ〉/〈ψ|ψ〉 recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T−T ⁺), both non-variational and variational approaches lead to identical equations upto any given order inT andT ⁺ inT∼T ₂ approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, inT∼T ₂ approximation, for a total of quadratic powers inT andT ⁺, same as Cizek’s linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound.     

Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces

When estimating solutions of dissipative partial differential equations in L^p-related spaces, we often need lower bounds for an integral involving the dissipative term. If the dissipative term is given by the usual Laplacian −Δ, lower bounds can be derived through integration by parts and embedding inequalities. However, when the Laplacian is replaced by the fractional Laplacian (−Δ)^α, the approach of integration by parts no longer applies. In this paper, we obtain lower bounds for the integral involving (−Δ)^α by combining pointwise inequalities for (−Δ)^α with Bernstein's inequalities for fractional derivatives. As an application of these lower bounds, we establish the existence and uniqueness of solutions to the generalized Navier-Stokes equations in Besov spaces. The generalized Navier-Stokes equations are the equations resulting from replacing −Δ in the Navier-Stokes equations by (−Δ)^α.     

Dielectric relaxation study of sulfolane in carbon tetrachloride solution from microwave absorption data

The dielectric constant (ɛ′) and dielectric loss (ɛ″) for dilute solutions of sulfolane in carbon tetrachloride solution have been measured at 9.885 GHz at different temperatures viz. 25°C, 30°C, 35°C and 40°C by using standard microwave techniques. Following the single frequency concentration variational method, the dielectric relaxation time (τ) and dipole moment (μ) have been calculated. It is found that dielectric relaxation process can be treated as the rate process, just like the viscous flow. Based on the above studies, monomer structure of sulfolane in carbon tetrachloride has been inferred. Energy parameters (ΔH _g , ΔF _g , ΔS _g ) for dielectric relaxation process of sulfolane in carbon tetrachloride at 25°C, 30°C, 35°C and 40°C have been calculated and compared with the corresponding energy parameters (ΔH _η , ΔF _η , ΔS _η ) for the viscous flow.     

Analysis of Δ<Superscript>0</Superscript>(1232) production in collisions of protons with carbon nuclei at 4.2 GeV/c

The production of Δ⁰(1232)-resonances in p+¹²C collisions at 4.2 GeV/c was analyzed with 4π acceptance. The mass distribution of Δ⁰(1232) was reconstructed using an angular criterion. The fraction of charged π ⁻-mesons coming from Δ⁰(1232) decay was estimated and compared to those obtained in earlier works. The momentum, transverse momentum, kinetic energy, and rapidity distributions as well as invariant cross sections of Δ⁰(1232)-resonances were reconstructed in the laboratory frame. The mean kinematical characteristics of the reconstructed Δ⁰(1232) were compared to those of participant protons in experiment and within some of the models. The freeze-out temperature of Δ⁰(1232) estimated in the present analysis was compared with those obtained using different methods for Δ(1232) produced with other sets of colliding nuclei at various incident energies. The relative number of nucleons excited to Δ⁰ (1232) at freeze-out conditions in p+¹²C collisions was estimated.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.