Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility χ(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of χ(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic–antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen. Supported in part by NSF Grant No. PHY 01-00.     

Photophoresis of coarse aerosol particles with nonuniform thermal conductivity

The photophoresis of a coarse solid spherical aerosol particle in a one-component gas of nonuniform temperature is examined with consideration of the inertial effects in the hydrodynamic equations and the temperature jump in the Knudsen layer. The problem is solved in the spherical coordinates r, Θ, and ϕ. The photophoresis of a homogeneous particle is considered first. Then the results are generalized to an inhomogeneous particle. A particle whose thermal conductivity χ _i varies as a function of r is chosen as a model which describes a broad class of natural and artificially produced aerosol particles. It is shown that the error can be significant if the variable internal thermal conductivity χ _i =χ _i (r) of the particle is ignored and only the value of the thermal conductivity on its surface χ _i (a) is considered, on the assumption that the particle is homogeneous. It is also shown that a particle with a variable internal thermal conductivity χ _i =χ _i (r) and a density of heat sources within it q _i (r,Θ) can be regarded as a homogeneous particle with a thermal conductivity γχ _i (a) and a heat-source density m(r)q _i (r,Θ). Recurrence formulas for gand m(r) in the general case are presented. Analytical expressions for γ and m(r) are found for a model particle with pronounced inhomogeneity. Zh. Tekh. Fiz. 68, 1–6 (April 1998)     

Charmless nonleptonic <Emphasis Type="Italic">B</Emphasis> decays into scalar and pseudoscalar mesons

The charmless nonleptonic decay modes B → f ₀ K(π) involving a scalar and a pseudoscalar meson in the final state are studied. The scalar meson f ₀ is considered as a q̄q state, as favored by some recent studies. Using the generalized factorization approach, the branching ratios and CP violation parameters are computed for these modes. The form factors are calculated using the results from relativistic light front quark model and the ISGW2 model. It is found that the direct CP violation parameters in these modes are small. However, the obtained branching ratios are not in agreement with the experimental data. Therefore, these modes may be considered as possible probes for new physics.      

Dual properties of orthogonal polynomials of discrete variables associated with the quantum algebra <Emphasis Type="Italic">U</Emphasis><Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(<Emphasis Type="Italic">su</Emphasis>(2))

We show that for every set of discrete polynomials y _n (x(s)) on the lattice x(s), defined on a finite interval (a, b), it is possible to construct two sets of dual polynomials z _k (ξ(t)) of degrees k = s-a and k = b-s-1. Here we do this for the classical and alternative Hahn and Racah polynomials as well as for their q-analogs. Also we establish the connection between classical and alternative families. This allows us to obtain new expressions for the Clerbsch-Gordan and Racah coefficients of the quantum algebra U _q (su(2)) in terms of various Hahn and Racah q-polynomials. Dedicated to the memory of our teacher and friend Arnold F. Nikiforov (18.11.1930–27.12.2005).     

Fitting Cosmological Data to the Function <Emphasis Type="Italic">q</Emphasis>(<Emphasis Type="Italic">z</Emphasis>) from GR Theory: Modified Chaplygin Gas

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: ΛCDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ ². We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q ₀ = − 0.65 ±0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q ₀ = − 0.67 ±0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: Ω _X0 = 0.81 ±0.03 for the Union2 dataset and Ω _X0 = 0.83 ±0.03 using the Constitution dataset.     

The exclusive reaction of pion quasi-elastic knockout from nucleon <Emphasis Type="Italic">p(e,e′ π)B</Emphasis> to various states of the final baryon-spectator <Emphasis Type="Italic">B</Emphasis> and the quark models for the pion cloud of nucleon

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N _1/2-(1535), N _1/2+(1440) are calculated in two models, the microscopic model of ³ P ₀ scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N _1/2-(1535) but are rather different for the Roper resonance N _1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).     

Covariant tensor formalism for partial-wave analyses of ψ decays into γB¯, γγV and ψ(2s)↦γχ<Subscript>c0,1,2</Subscript> with χ<Subscript>c0,1,2</Subscript>↦K¯πand 2π<Superscript>+</Superscript>2π<Superscript>-</Superscript>

With accumulation of high statistics data at BES and CLEO-c, many new interesting channels can get enough statistics for partial-wave analysis (PWA). Among them, ψ↦γpˉ,γΛˉ,γΣˉ,γΞˉ channels provide a good place for studying baryon-antibaryon interactions; the double radiative decays ψ↦γγV with V ≡ ρ,ω,φ have a potential to provide information on the flavor content of any meson resonances (R) with positive charge parity (C = +) and mass above 1 GeV through ψ↦γR↦γγV; ψ(2s)↦γχ_c0,1,2 with χ_c0,1,2↦Kˉπ⁺π^- and 2π⁺2π^- decays are good processes to study χ_cJ charmonium decays. Using the covariant tensor formalism, here we provide theoretical PWA formulae for these channels.     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Improved (1s)<Superscript>2</Superscript> variational model for helium

The ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e ^−γ(rA/a _o)ⁿe^−γ(rB/a _o)ⁿ. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 E _h (E _h =1 hartree) in comparison with the traditional (n=1) result of −2.84766 E _h . This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 E _h ) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 E _h , the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).     

Magnetization of an electron plasma by microwave pulses: Faraday induction

It has been argued theoretically that the recently proposed vacuum fieldB ⁽³⁾ is not accompanied by a real electric fieldE ⁽³⁾ . Experimental evidence for this interence is available in the data reported by Deschampset al. [10], using microwave magnetization of an electron plasma set up in helium gas. Faraday induction due toB ⁽³⁾ does not occur in the inert gas and is not observed experimentally in the absence of free electrons. WheneverB ⁽³⁾ interacts with free electrons, however, Faraday induction occurs through a pulse of induced magnetization (i.e., induced orbital electronic angular momentum).     

Search for theχ′ c charmonium states as solution to the CDFψ′ puzzle

The efforts of Roy-Sridhar-Close-Cho-Wise-Trivedi to resolve the CDFψ′ anomaly with cascades from above-thresholdχ′ _c states require well defined signatures [a small total width and a large branching fraction forχ′ _cJ →γ+ψ′] for the solution to be viable. Here we estimate the production of such states from BR(B→χ′ _cJ +X)BR(χ′ _cJ →γψ′) andγγ production ofχ′ _c2 at CLEO II, and comment on the feasibility of testing the hypothesis in terms of current experimental capabilities.     

Magnetic and thermal properties of CuFeS<Subscript>2</Subscript> at low temperatures

The magnetic moment M, the magnetic susceptibility χ, and the thermal conductivity of chalcopyrite CuFeS₂, which is a zero-gap semiconductor with antiferromagnetic ordering, have been measured in the temperature range 10–310 K. It has been revealed that the quantities χ(T) and M(T) increase anomalously strongly at temperatures below ∼100 K. The temperature dependence M(T) is affected by the magnetic prehistory of the sample. An analysis has demonstrated that the magnetic anomalies are associated with the presence of a system of noninteracting magnetic clusters in the CuFeS₂ sample under investigation. The formation of the clusters is most likely caused by the disturbance of the ordered arrangement of Fe and Cu atoms in the metal sublattice of the chalcopyrite, which is also responsible for the phase inhomogeneity of the crystal lattice. The inhomogeneity brings about strong phonon scattering, and, as a result, the temperature dependence of the thermal conductivity coefficient exhibits a behavior characteristic of partially disordered crystals.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

O(n) tricriticality in two dimensions

We present exact results for several universal parameters of the tricritical O(n) model in two dimensions. The results apply to the range −2⩽n⩽3/2, and include the central charge and three scaling dimensions, associated with temperature, magnetic field and the introduction of an interface. Since these results are based on an extrapolation of known relations between the O(n) and the Potts model, they cannot be considered as rigorous. For this reason, we perform an accurate numerical analysis of the central charge and the critical exponents. This analysis, which is based on transfer-matrix calculations on the honeycomb lattice, is in a full and precise agreement with the theoretical predictions.      

The connection between photon mass andB (3) : The poincaré group

The longitudinal vacuum fieldB ⁽³⁾ is an experimental observable which produces by magnetization a well-defined square-root beam power density dependence. Its longitudinal polarization implies that the helicities of the photon are +1, 0, and –1, and that the little group of the Poincaré group is the rotation group 0(3) of a massive boson. The mass of the photon (m) is therefore related directly toB ⁽³⁾ through the Proca equation, and it is concluded that experimental evidence forB ⁽³⁾ is also evidence for finitem.     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.     

Magnetic susceptibility of multilayered carbon nanotubes

A theoretical study of the magnetic susceptibility of multilayered carbon nanotubes in fields both parallel, H _∥, and perpendicular, H _⊥, to the tube axis has been carried out disregarding electron-electron interaction. The temperature dependences of the magnetic susceptibility obtained exhibit a nontrivial form for H _∥, which is related to the quasi-one-dimensionality of such a system as the nanotube. The dependences of the magnetic susceptibility on chemical potential χ(μ) have also been derived. At low temperatures, χ(μ) has sharp peaks in fields H _∥, which is connected with the presence of singularities in the density of states of nanotubes. The effect of interlayer coupling on magnetic susceptibility of small-radius tubes has been investigated numerically. Fiz. Tverd. Tela (St. Petersburg) 40, 1950–1954 (October 1998)     

Density excitations of a harmonically trapped ideal gas

The dynamic structure factor S(q, ω) of a harmonically trapped Bose gas has been calculated well above the Bose-Einstein condensation temperature by treating the gas cloud as a canonical ensemble of non-interacting classical particles. The static structure factor is found to vanish s8 q ² in the long-wavelength limit. We also incorporate a relaxation mechanism phenomenologically by including a stochastic friction force to study S(q, ω). A significant temperature dependence of the density fluctuation spectra is found. The Debye-Waller factor has been calculated for the trapped thermal cloud as a function of q and the number N of atoms. A substantial difference is found for small- and large-N clouds.     

Out-of-equilibrium quantum field dynamics in external fields

The quantum dynamics of the symmetry-broken λ(Φ ²)² scalar-field theory in the presence of an homogeneous external field is investigated in the large-N limit. We consider an initial thermal state of temperature T for a constant external field J. A subsequent sign flip of the external field, J→ - J, gives rise to an out-of-equilibrium nonperturbative quantum field dynamics. We review here the dynamics for the symmetry-broken λ(Φ ²)² scalar N component field theory in the large-N limit, with particular stress in the comparison between the results when the initial temperature is zero and when it is finite. The presence of a finite temperature modifies the dynamical effective potential for the expectation value, and also makes that the transition between the two regimes of the early dynamics occurs for lower values of the external field. The two regimes are characterized by the presence or absence of a temporal trapping close to the metastable equilibrium position of the potential. In the cases when the trapping occurs it is shorter for larger initial temperatures.