Leading-order actions of Goldstino fields

This paper starts with a self-contained discussion of the so-called Akulov–Volkov action S_AV\mathcal{S}_{\mathrm{AV}}, which is traditionally taken to be the leading-order action of the Goldstino field. Explicit expressions for S_AV\mathcal{S}_{\mathrm{AV}} and its chiral version S_AV^ch\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} are presented. We then turn to the issue on how these actions are related to the leading-order action S_NL\mathcal{S}_{\mathrm{NL}} proposed in the newly proposed constrained superfield formalism. We show that S_NL\mathcal{S}_{\mathrm{NL}} may yield S_AV/S_AV^ch\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} or a totally different action S_KS\mathcal{S}_{\mathrm{KS}}, depending on how the auxiliary field in the former is integrated out. However, S_KS\mathcal{S}_{\mathrm{KS}} and S_AV/S_AV^ch\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory.     

A Level 1 Large-Deviation Principle for the Autocovariances of Uniquely Ergodic Transformations with Additive Noise

A large-deviation principle (LDP) at level 1 for random means of the type $$M_n \equiv \frac{1}{n}\sum\limits_{j = 0}^{n - 1} {Z_j Z_{j + 1} ,{\text{ }}n = 1,2,...}$$ is established. The random process {Z _n} _n≥0 is given by Z _n = Φ(X _n) + ξ _n , n = 0, 1, 2,..., where {X _n} _n≥0 and {ξ _n} _n≥0 are independent random sequences: the former is a stationary process defined by X _n = T ⁿ(X ₀), X ₀ is uniformly distributed on the circle S ¹, T: S ¹ → S ¹ is a continuous, uniquely ergodic transformation preserving the Lebesgue measure on S ¹, and {ξ_n} _n≥0 is a random sequence of independent and identically distributed random variables on S ¹; Φ is a continuous real function. The LDP at level 1 for the means M _n is obtained by using the level 2 LDP for the Markov process {V _n = (X _n, ξ _n , ξ _n+1)} _n≥0 and the contraction principle. For establishing this level 2 LDP, one can consider a more general setting: T: [0, 1) → [0, 1) is a measure-preserving Lebesgue measure, $\Phi :\left[ {0,\left. 1 \right)} \right. \to \mathbb{R}$ is a real measurable function, and ξ _n are independent and identically distributed random variables on $\mathbb{R}$ (for instance, they could have a Gaussian distribution with mean zero and variance σ²). The analogous result for the case of autocovariance of order k is also true.     

Thermoelectric power of the vitreous electrolyte (AgI)0.79(Ag2O.B2O3)0.21

We have determined the thermoelectric power ? of the high ionic conductivity glass (AgI)_0.79(Ag₂O.B₂O₃)_0.21; ? is negative throughout the investigated T range, 320–500 K. The heat of transport of the mobile Ag⁺, Q_Ag, taken as the slope of the straight line fitting ? versus 1/T, is quite lower than the activation energy obtained from conductivity data, viz. Q_Ag = 2.81 kcal/mole^-1 < E_act = 4.34 kcalmole^-1. To circumvent this discrepancy, the analysis of the experimental data is carried out as follows: (i) it is supposed that Q_Ag = E_act in agreement with the free ion theory for solid electrolytes; (ii) the vibrational part of the silver ion entropy, S(Ag⁺, vib), is assumed to be equal to the entropy of silver, S(Ag); (iii) on the ground of a structural model for this kind of glasses, the ideal configurational entropy of the mobile Ag⁺, S(Ag⁺, conf)_id, is evaluated through a statistical approach. The ideal ionic entropy is defined as S(Ag⁺)_id = {S(Ag⁺, vib) + S(Ag⁺, conf)_id}; (iv) the difference {S(Ag⁺)_exp - S(Ag⁺)_id} is viewed as an excess entropy and is described according to the classical model of the regular solutions.     

Transparent potentials at fixed energy in dimension two. Fixed-energy dispersion relations for the fast decaying potentials

For the two-dimensional Schrödinger equation $$[ - \Delta + v(x)]\psi = E\psi , x \in \mathbb{R}^2 , E = E_{fixed} > 0 (*)$$ at a fixed positive energy with a fast decaying at infinity potentialv(x) dispersion relations on the scattering data are given. Under “small norm” assumption using these dispersion relations we give (without a complete proof of sufficiency) a characterization of scattering data for the potentials from the Schwartz classS=C _∞ ^(∞) (?²). For the potentials with zero scattering amplitude at a fixed energyE _fixed (transparent potentials) we give a complete proof of this characterization. As a consequence we construct a family (parametrized by a function of one variable) of two-dimensional spherically-symmetric real potentials from the Schwartz classS transparent at a given energy. For the two-dimensional case (without assumption that the potential is small) we show that there are no nonzero real exponentially decreasing, at infinity, potentials transparent at a fixed energy. For any dimension greater or equal to 1 we prove that there are no nonzero real potentials with zero forward scattering amplitude at an energy interval. We show that KdV-type equations in dimension 2+1 related with the scattering problem (*) (the Novikov-Veselov equations) do not preserve, in general, these dispersion relations starting from the second one. As a corollary these equations do not preserve, in general, the decay rate faster than |x|^?3 for initial data from the Schwartz class.     

On the free energy of the hopfield model

The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS _i andp random patterns ξ^μ=(ξ ₁ ^μ ,ξ ₂ ^μ ,...,ξ _N ^μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ _μ ^p h^μμξ _i=1 ^N ξ _i ^μ S_i, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh ^μ1 andh ^μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref ^cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ _i ^μ =±1}=(1/2)±?, we obtain the lower bound 1+4?²(p?1) for the temperatureT _c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T_*=1?4?² and T_c=1+4?² where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T _* marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T_*=max{1?4?²(p?1),0}.     

Iodine as a donor in CdS

Iodine doped single crystals of CdS were grown from the vapor phase. High temperature Hall effect measurements for the crystals equilibrated with Cd and S₂ vapors at temperatures between 700 and 1000°C gave the free electron concentration as a function of p_Cd or p_S2 and temperature. The results can be explained on the basis of a model in which the CdS is saturated with iodine at low p_Cd (=high p_S2) but unsaturated at high p_Cd.The solubility of iodine in CdS is given by c_t=1·73×10²²p_S2^?1/8 exp (?1·045 eV/kT) cm^?3 atm^?1/8=4·62×10¹⁹p_Cd^1/4 exp (?0·195 eV/kT) cm^?3 atm^1/4The formation of pairs (I_SV_Cd)′ from I_S^· and V_Cd″ is governed by the equilibrium constant K_{P(I, V)}=4 exp (≤1·1 eV/kT)If Cd diffusion occurs primarily by free vacancies, the Cd^* tracer self diffusion leads to a vacancy mobility of (1·2±0·5)×10^?5 cm² sec^?1 at 900°C, in agreement with results reported by Woodbury [12], but (7±3) times larger than reported by Kumar and Kroger [10].     

A novel method for determining the single particle potential directly from the measured single particle density: Application to the charge density difference between the isotones <Superscript>206</Superscript>Pb–<Superscript>205</Superscript>Tl

We present a novel method, based on the single particle Schroedinger equation, to determine the central potential (mean-field) directly from the single particle matter density and its first and second derivatives. As an example, we consider the experimental data for the charge density difference between the isotones ²⁰⁶Pb–²⁰⁵Tl, deduced by phase shift analysis of elastic electron scattering cross-section measurements and corresponds to the shell model 3s_1/2 proton orbit, and determine the corresponding single particle potential. We also present results of least-square fits to parametrized single particle potentials. The 3s_1/2 wave functions of the determined potentials reproduce fairly well the experimental data within the quoted errors. More accurate experimental data, with uncertainty smaller by a factor of two or more, may answer the question how well can the data be reproduced by a calculated 3s_1/2 wave function.     

Lifshits Tails Caused by Anisotropic Decay: The Emergence of a Quantum-Classical Regime

We investigate Lifshits-tail behaviour of the integrated density of states for a wide class of Schrödinger operators with positive random potentials. The setting includes alloy-type and Poissonian random potentials. The considered (single-site) impurity potentials f: ?^d→[0,∞[ decay at infinity in an anisotropic way, for example, \(f(x_{1},x_{2})\sim (|x_{1}|^{\alpha_{1}}+|x_{2}|^{\alpha_{2}})^{-1}\) as |(x₁,x₂)|→∞. As is expected from the isotropic situation, there is a so-called quantum regime with Lifshits exponent d/2 if both α₁ and α₂ are big enough, and there is a so-called classical regime with Lifshits exponent depending on α₁ and α₂ if both are small. In addition to this we find two new regimes where the Lifshits exponent exhibits a mixture of quantum and classical behaviour. Moreover, the transition lines between these regimes depend in a nontrivial way on α₁ and α₂ simultaneously.     

Local potentials phase equivalent to separable two-nucleon interactions

Local energy-dependent potentials have been constructed phase equivalent to members of a family of phase-equivalent separable two-nucleon potentials in the¹ S ₀-state. It has been shown that these potentials obey the known off-shell constraints in the¹ S ₀-state and can therefore not be regarded as unrealistic in this sense. They have the same shape as the energy-independent local Kermode potentials. However we also find that the off-shell behaviour of a separable¹ S ₀ potential and its local equivalent can differ considerably.     

Electron hopping and optic phonons in Eu3S4

Raman scattering on single crystals of Eu₃S₄ does not show the allowed q=o phonon modes in the cubic phase and exhibits no new modes in the distorted low temperature phase (T<186 K). Above the Curie temperature T_c=3.8 K the scattering is dominated by a spin-disorder induced one-phonon density of states allowing for the observation of the zone boundary phonon breathing mode of the S^2?ions. This mode does not show any anomaly near the charge order -disorder phase transition T_t=186 K. Temperature tunable spin fluctuations associated with the temperature activated Eu²⁺→Eu³⁺ electron hopping are detected in the scattering intensity, superimposed on the usual thermal spin disorder.     

Classical stability of direct products of spheres in gravitational systems

Classical stability of Einstein spaces S^d₁ ×?×S^d_n(d_j ? 2) against all fluctuations is investigated in euclidean gravity with a cosmological constant. It is shown that S^d is classically stable, while S^d₁ ×?× S^d_n(n ? 2) is classically unstable. As a generalization of this analysis it is proved that a compact Einstein space B₁ ×?× B_n(n ? 2) which is a direct product of each Einstein space is classically unstable. Non-Einstein spaces M² × S⁴ (M² × S² × S²) are also considered in six- dimensional Einstein-Maxwell theory and are shown to be classically stable (unstable).     

Classical calculation of proton collisions with ethylene

Single electron capture and single ionization total cross sections in collisions of proton with ethylene are calculated for an energy range 25 keV ≤ E ≤ 150 keV, using the classical trajectory Monte Carlo method. Multi-center model potentials are employed to represent the interaction of the active electron on each molecular orbital with the C₂H₄⁺_{4}^{+} core. The results are compared with experimental results for single electron capture.     

Inversion of conductivity type in Bi2Te3−xSx crystals

Transport parameters and optical properties of Bi₂Te_3?xS_x single-crystals with x=0–0.18 were studied. With increasing sulphur content the concentration of free current carriers decreases up to x=0.12, due to the interaction of S^x_Te defects with antisite defects Bi^′_Te, and then the p-type conductivity changes to the n-type. The optical gap of Bi₂Te_3?xS_x crystals increases with increasing S content. The obtained results led to the preparation of Bi₂Te₃-Bi₂Te_3?xS_xp–n junction by the heat treatment of p-type Bi₂Te₃ in S vapours.     

ESR spectra of Eu centers in defect Ga2S3 single crystals

In this paper, the author presents the results of measurements of the low-temperature and angular dependences of the ESR spectra of Eu²⁺ centers in defect Ga₂S₃ single crystals in the temperature range 8–29 K and for 0–180° orientations of the static magnetic field. The electron structure of impurity ¹⁵¹Eu atoms in Ga₂S₃:Eu single crystals has been studied by using the ESR method at different doping proportions of Eu atoms. Ga₂S₃ single crystals were grown from the melt using the Bridgman method. The Eu concentration was determined by atomic absorption analysis and X–ray fluorescence analysis (XRFA). By investigation on the ESR spectra, the author has first determined the values of charge states for Eu, which have turned out to be a Eu²⁺(4f⁷) ion with spin S=7/2, g=4.18±0.02 and concentration of the states of Eu N=6.3×10¹⁴ cm⁻³.     

Separable expansion of the t-matrix in the 3S1-3D1 channel

A recently proposed separable expansion for the t-matrix for local potentials is extended to the coupled channel of nucleon-nucleon interactions. The simple method yields a rather convergent separable expansion, with simple form factors, and the requirements of two particle unitarity and time reversal symmetry are maintained for approximations of any rank. The method is illustrated for the simplified Reid soft-core potential in the ³S₁-³D₁ channel, and the results compared with a recent calculation of Pieper.     

Measurement of light scalar mesons in many-body decays in the PHENIX experiment at the Relativistic Heavy-Ion Collider

The unique design of the PHENIX detector at the Relativistic Heavy-Ion Collider allows one to detect neutral and charged particles produced in high-energy collisions of heavy ions. This circumstance made it possible to measure many-particle decays of light mesons, such as K _S ⁰ →π⁰π⁰, η→π⁰π^?π⁺, and η→γγ in p + p, d + Au and Au + Au collisions at the energy \(\sqrt {S_{NN} }\) = 200 GeV. The latest results of measuring the differential production cross sections, ratios of particle yields (K _S ⁰ /π⁰ and η/π⁰), and the nuclear modification factors (\(R_{dA}^{K_S }\), R _dA ^η , R _AA ^η ) in a wide range of transverse momenta (from 2 to 12 GeV s^?1) are reported.     

Quantenstatistik des Hochtemperatur-Plasmas im thermodynamischen Gleichgewicht

High temperature plasmas are investigated on the basis of quantum theory. A new method for the calculation of the thermodynamic properties is developed. According to the method of Morita effective potentials are introduced. They permit the evaluation of the partition function with the well-known formalism of classical statistical mechanics. The first corrections added to Debye's limiting law of the free energy are expressed by the two particle Slater sum S₂(r). A Bloch equation for S₂(r) is derived and is solved in the Fourier representation by a development according to the interaction parameter ζ = e²/kTλ, λ being the thermal wavelength. The effects of symmetry are taken into account. The free energy is calculated explicitely up to the order of ζ². In the case of small concentrations our results agrees with that derived by Trubnikow and Elesin. Effects of symmetry neglected, up to the order of ζ² the formula of DeWitt is obtained.