Critical temperature of infinitely long chains from Wertheim's perturbation theory

Wertheim's theory is used to determine the critical properties of chains formed by m tangent spheres interacting through the pair potential u(r). It is shown that within Wertheim's theory the critical temperature and compressibility factor reach a finite non-zero value for infinitely long chains, whereas the critical density and pressure vanish as m ^-1.5. Analysing the zero density limit of Wertheim's equation or state for chains it is found that the critical temperature of the infinitely long chain can be obtained by solving a simple equation which involves the second virial coefficient of the reference monomer fluid and the second virial coefficient between a monomer and a dimer. According to Wertheim's theory, the critical temperature of an infinitely long chain (i.e. the Θ temperature) corresponds to the temperature where the second virial coefficient of the monomer is equal to 2/3 of the second virial coefficient between a monomer and dimer. This is a simple and useful result. By computing the second virial coefficient of the monomer and that between a monomer and a dimer, we have determined the Θ temperature that follows from Wertheim's theory for several kinds of chains. In particular, we have evaluated Θ for chains made up of monomer units interacting through the Lennard-Jones potential, the square well potential and the Yukawa potential. For the square well potential, the Θ temperature that follows from Wertheim's theory is given by a simple analytical expression. It is found that the ratio of Θ to the Boyle and critical temperatures of the monomer decreases with the range of the potential.     

Anharmonic Oscillator and Double-Well Potential: Approximating Eigenfunctions

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by V=m ² x ²+g x ⁴ at arbitrary g ≥ 0 for m ²>0 and m ²<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory Mathematics Subject Classifications(2000) 34L40, 34B08, 41A99     

Contributions to the Gaussian Line Broadening of the Proxyl Spin Probe EPR Spectrum Due to Magnetic-Field Modulation and Unresolved Proton Hyperfine Structure

A simple expression is derived to compute the total Gaussian linewidth of a Voigt line that is broadened by sinusoidal magnetic-field modulation as follows: ΔH^G_pp(H_m)²= ΔH^G_pp(0)²+ κ²H²_m, where ΔH^G_pp(H_m) is the Gaussian linewidth observed with an modulation amplitudeH_m/2 and ΔH^G_pp(0) is the Gaussian linewidth in the limit of zero modulation. The field modulation contributes an additional Gaussian broadening of κH_m, where κ is a constant, which adds in quadrature to ΔH^G_pp(0) to give the total Gaussian linewidth. Denoting the overall linewidth of the Voigt line in the absence of modulation broadening by ΔH⁰_pp(0), it is shown, both by analytical means and by spectral simulation, that the constant κ is equal to 1/2 in the limit ofH_m ΔH⁰_pp(0); however, using values ofH_mas large as ΔH⁰_pp(0) leads to only minor departures from κ = 1/2. The formulation is valid both for Lorentzian and Voigt lines and is tested for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (3-carboxy proxyl) in CCl₄and in aqueous buffer. This spin probe was studied because the proxyl group is the only major spin-probe moiety whose Gaussian linewidth had not been characterized in the literature. For 3-carboxy proxyl, it is found that ΔH^G_pp(0) = 1.04 ± 0.01 G independent of solvent polarity. Precision values of the¹⁴N hyperfine coupling constant for 3-carboxy proxyl at 9.5°C are as follows: 14.128 ± 0.001 G in CCl₄and 16.230 ± 0.002 G in aqueous buffer. The temperature dependence of ΔH^G_pp(0) and the¹⁴N hyperfine coupling constant are reported as empirical equations. Results of the present work taken together with previously published data permits accurate correction for the effects of inhomogeneous broadening due to unresolved hyperfine structure and modulation broadening for the majority of spin probes in common use.     

The Quantum Excess Free Energy for Two Component Plasma

The aim of this paper is to calculate the quantum excess free energy until the third virial coefficient for the two component plasma (TCP). We consider only the thermal equilibrium plasma in the case of nλ³_ab ≪ 1 where λ²_ab = (ħ²/(m_abKT)) is the thermal De Broglie wave‐length. The second and third virial coefficients are represented in forms of a convergent series expansion in terms of the interaction Parameter ξ²_ab = ((e_ae_b)/(λ_abKT)). We obtained the excess free energy until the third virial coefficient to the order ξ⁶_ab. The effects of symmetry are taken into account, also the exchange effects were taken in account. We compared our results with others. Upon comparison with Ebeling et al. one observes that the considerable contribution of the third virial coefficient in the region of high temperatures (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Parameter Planes of λz<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript> exp(z) for <Emphasis Type="Italic">m</Emphasis> ≥ 2*

We consider the families of entire transcendental maps given by F _λ,m (z) = λz ^m exp(z), where m ≥ 2. All functions F _λ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A ^*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A ^*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of which serve as a model for F _λ,m , in the sense that they are related by means of quasiconformal surgery to F _λ,m . Both authors were supported by MTM2005-02139/Consolider (including a FEDER contribution) and CIRIT 2005 SGR01028. The first author was also supported by MTM2006-05849/Consolider (including a FEDER contribution).     

Electronic structure of TiO<Subscript>2</Subscript> rutile with oxygen vacancies: Ab initio simulations and comparison with the experiment

The electronic structure of TiO₂ rutile with oxygen vacancies, which is a promising insulator, has been analyzed. The ab initio density functional calculations, as well as the comparative analysis of the results obtained in the σ-GGA spin-polarized generalized approximation and those obtained by the σ-GGA + U method with allowance for Coulomb correlations of d electrons titanium atoms in the Hartree-Fock approximation for the Hubbard model, have been performed. It has been found that the effective electron mass in rutile is anisotropic and there are both light (m _e ^* = (0.6–0.8)m ₀, where m ₀ is the free-electron mass) and heavy (m _e ^* > 1m ₀) electrons, whereas holes in rutile are only heavy (m _e ^* ⩾ 2m ₀). It has been shown that the σ-GGA + U method gives a deep occupied level in the band gap and that an oxygen vacancy in rutile is an electron and hole trap.     

Fermion masses

In this paper, we show that 2m _e m /(m _e ² +m ² = (g _V/g _A) _e ² . From this expression, the Weinberg mixing parameter is shown to be 0·2254 or 0·2746. Assuming that the electron and muon neutrino masses are degenerate, we find thatm _v = (g _V/g _A) _e ² . (m _e m )/M _WL, where M_WL is the mass of the standard W^± boson. The neutrino mass turns out to be 6·5 eV. The -neutrino mass is found to be about 81 MeV. The masses of c, t, s and b quarks are found to be respectively 1·7 GeV, 21·2 GeV, 0·57 GeV and 2·18 GeV by assumingm _d=m _u= 0·3 GeV. All these masses agree with other estimates except the b quark which has about half of its expected value.     

“Regge-like” relations for stable (non-evaporating) black holes

Within a purely classical formulation of “strong gravity,” we associated hadron constituents (and even hadrons themselves) with suitable stationary, axisymmetric solutions of certain new Einsteintype equations supposed to describe the strong field inside hadrons. Such equations are nothing but Einstein equations—with cosmological term—suitably scaled down. As a consequence, the cosmological constant Λ and the massesM result in our theory to be scaled up, and transformed into a “hadronic constant” and into “strong masses,” respectively. Due to the unusual range of Λ andM values considered, we met a series of solutions of the Kerr-Newman-de Sitter (KNdS) type with rather interesting properties: aim of the present work is putting forth such results, while “translating” them into the more popular language of ordinary gravity. The requirement that those solutions be stable, i.e., that their temperature (or surface gravity) bevanishingly small, implies the coincidence of at least two of their (in general, three) horizons. Imposing the stability condition of a certain horizon does yield (once chosen the values ofJ, q and Λ) mass and radius of the associated black hole. In the case of ordinary Einstein equations and for stable blackholes of the KNdS type, we get in particular Regge-like relations among massM, angular momentumJ, chargeq and cosmological constant Λ; which did not receive enough attention in the previous literature. For instance, with the standard definitionsQ ² = Gq²/(4πε ₀ c ⁴), a ≡ J/(Mc), m ≡GM/c ², in the case Λ=0 in whichm ²=a²+Q² and ifq is negligible, we findm ²=J. When considering, for simplicity, Λ>0 andJ=0 (andq still negligible), then we obtainm ² = 1/(9Λ). In the most general case, the condition, for instance, of “triple coincidence” among the three horizons yields for |Λa ²|<< 1 the couple of independent relationsm ² = 2/(9Λ) andm ² = 8(a ² + Q². Another interesting point is that—with few exceptions—all such relations (amongM, J, q, Λ) lead to solutions that can be regarded as (stable) cosmological models. Work partially supported by INFN, MURST, and CNR and by CNPq, FAPESP, and CAPES.     

Proper-Time Relativistic Dynamics on Hyperboloid

The dynamics of a point-like relativistic particle with respect of the proper time is formulated on the hyperboloid p ² ₀–p ²=M ² c ². The Hamilton-Jacobi equations on the hyperboloid are derived for the particles with mass (M ²=m ², m>0), for the particles with zero-mass (M=0, m>0), and for the neutrino. It is shown, in a certain factorization of the momentum, the model can be identified with Nambu's three-dimensional phase space formalism. A first quantized version of the model is formulated according to a canonical scheme of quantization (Schrödinger quantization scheme).     

Static finite energy solutions of a classical field theory with positive mass-square

Static finite energy solutions of the field theory described by are obtained. Some of the interesting features of this model are (1) the mass-square here is positive unlike in the λφ⁴ Higg's model, (2) the potential has three global minimas, (3) the spectrum is bounded from below unlike in the λφ⁴ theory with λ<0, (4) there are two kink and two antikink solutions, (5) unlike sine-Gordon and λφ⁴ models here there are two particles with masses m and 2m. Nontopological finite energy solutions have also been obtained for gφ ⁶ field theory with g < 3λ ² / 16m ².     

Mean square number fluctuation for a fermion source and its dependence on neutrino mass for the universal cosmic neutrino background

Using the general formulation for obtaining chemical potentialμ of an ideal Fermi gas of particles at temperature T, with particle rest mass m₀ and average density 〈N〉/V, the dependence of the mean square number fluctuation 〈ΔN ²〉/V on the particle mass m₀ has been calculated explicitly. The numerical calculations are exact in all cases whether rest mass energym ₀c² is very large (non-relativistic case), very small (ultra-relativistic case) or of the same order as the thermal energy k_BT. Application of our results to the detection of the universal very low energy cosmic neutrino background (CNB), from any of the three species of neutrinos, shows that it is possible to estimate the neutrino mass of these species if from approximate experimental measurements of their momentum distribution one can extract, someday, not only the density 〈N _v〉/V but also the mean square fluctuation 〈Δ _v ² 〉/V. If at the present epoch, the universe is expanding much faster than thermalization rate for CNB, it is shown that our analysis leads to a scaled neutrino massm _v instead of the actual massm _0v .     

Absence of long-range order with long-range potentials

A particular form of Mermin's inequality is analyzed for repulsive inverse power potentials [V(r)=e ² r ^–m/m] in ad-dimensional space. For long-range potentials (m d) the system is put into a stabilizing background. Long-range order is shown to be excluded ford (m + 2)/2 whenm d, while for short-range potentials (m > d) we recover Mermin's result (d 2). For Coulomb systems (m=d – 2) and the experimentally studied electron surface layer (d = 2,m=1), long-range order cannot be excluded by the present argument.     

Free-to-bound radiative recombination in highly conducting InN epitaxial layers

We present a theoretical simulation of near-band-edge emission spectra of highly conducting n-InN assuming the model of ‘free-to-bound’ radiative recombination (FBRR) of degenerate electrons from the conduction band with nonequilibrium holes located in the valence band tails. We also study experimental photoluminescence (PL) spectra of highly conducting InN epitaxial layers grown by MBE and MOVPE with electron concentrations in the range (7.7×10¹⁷–6×10¹⁸) cm⁻³ and find that the energy positions and shape of the spectra depend on the impurity concentration. By modeling the experimental PL spectra of the InN layers we show that spectra can be nicely interpreted in the framework of the FBRR model with specific peculiarities for different doping levels. Analyzing simultaneously the shape and energy position of the InN emission spectra we determine the fundamental bandgap energy of InN to vary between E_g=692 meV for effective mass m_n0=0.042m₀ and E_g=710 meV for m_n0=0.1m₀.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Emission of quasi-thermal ions from a solid bombarded by cluster ions

Comparative studies of the emission of quasi-thermal atomic and cluster ions from V, Nb, Ta, Au, and In targets bombarded by cluster ions Au _m ⁻(m = 1–9), as well as from Si and Bi targets bombarded by cluster ions Au _m ⁻(m = 1–9) and Bi _m ⁻(m = 1–5), with energy E ₀ ranging from 6 to 21 keV are carried out. In the case of bombardment by heavy cluster ions, the fraction of the quasi-thermal component in the energy spectra of sputtered atomic ions reaches 50 (for V, In, and Au), 70 (Nb), or more than 90% (Ta). In addition, quasi-thermal ions play a considerable part in the emission of small cluster ions Au₂⁺, In₂⁺, In₃⁺, and Bi _n ⁺(n = 2–7). The results of the generalizing investigation favor the presence of thermal spike conditions at cluster bombardment and their appreciable contribution to the emission of atomic and small cluster ions.     

Electrooptical Kerr constant and third-order susceptibility measurements in nematic liquid crystals and their mixtures

We report for the first time the determination of the real part of the third order nonlinear susceptibilities ⁽³⁾ (–, , 0, 0) in the isotropic phase of two nematic liquid crystalsp-(ethoxybenzylidine)-p-butylaniline (EBBA) andp-(methoxybenzylidene)-p-butylaniline (MBBA) from electrooptic Kerr effect experiments. The highest value of ⁽³⁾ observed near nematic-to-isotropic transition temperature, at 632.8 nm is found to be 1.067×10^–20 m²V^–2 for EBBA and 6.602×10^–20 m²V^–2 for MBBA.     

Classical in-plane negative magnetoresistance and quantum positive magnetoresistance in undoped InSb thin films on GaAs (1 0 0) substrates

Magnetoresistance (MR) effects have been investigated in perpendicular and parallel magnetic fields at 300, 80 K and liquid He temperatures for undoped InSb thin films 0.1–2.3 μm thick grown on GaAs(1 0 0) substrates by MBE. At high temperatures, the intrinsic carriers show the parabolic negative MR observable only in magnetic fields parallel to the film. The skipping-orbit effect due to surface boundary scattering in the classical orbits in the plane vertical to the film has been argued to be responsible for the negative MR. At low temperatures (T=80 K), the transport is dominated by the two-dimensional (2D) electrons in the accumulation layers at the InSb/GaAs(1 0 0) hetero interface; MR is positive and shows a logarithmic increase with anisotropy between parallel and perpendicular field orientation, arising from the 2D weak anti-localization (WAL) that reflects the interplay between the spin-Zeeman effect and strong spin–orbit interaction caused by the asymmetric potential at the interface (Rashba term). The zero-field spin splitting energy of Δ₀13 meV, the electron effective mass of m^*0.10m₀ seven times of the band edge mass in bulk InSb and the effective g-factor of |g^*|15 in the accumulation layer have been inferred from fits of MR for the 0.1 μm thick film to the 2D WL theory.     

Exactly solvable XY model of the spin Peierls transition

The exact solution of the problem of the ground state of theXY-spin system on a deformed chain is found. At finite magnetizationm it is characterized by the double periodic structure and has a finite-band spectrum of spin excitations. Atm 0 the phase transition from the incommensurate into the dimerized state is accompanied by the soliton lattice formation.     

On Meson Masses

It is shown that in the framework of an analytical confinement, when quark and gluon propagators are induced by a vacuum self-dual gluon field with constant strength, the masses of mesons with quantum numbers Q = (J ^P ,n), where n is the radial quantum number, and quark constituents m ₁, m ₂ are described with reasonable accuracy by the formula The positive parameter A _Q is unique for all mesons with a fixed quantum number Q. Sets of mesons J ^P = 1⁻, 0⁺, 1⁺, 2⁺, 3⁻ for n = 0 and 1⁻ , 2⁺ for n > 0 and different flavor constituent quarks (u = d, s, c, b) are considered.