Series expansions for a generalized XY hamiltonian: II. Tricritical behaviour of the Takagi model

The high-temperature series expansions for the square of the fluctuation in the order parameter, for the specific heat, the concentration and the concentration susceptibility for the Takagi model on an f.c.c. lattice are analysed in the field variables. We obtain for the critical exponent $\text{γ =}\text{4}\text{3}$ and the specific heat is possibly logarithmically divergent. If we take the tricritical point to be determined by γ_t = 1, the tricritical exponents α_t, λ_t and ω_t are found to be consistent with $\text{1}\text{2}$.     

On observability of N-level quantum systems

The purpose of this paper is to discuss necessary and sufficient conditions for observability of N-level quantum systems. We assume that the information about a physical system is given by the mean values Tr(?(t_j)A_i) = m_Ai(t_j), of n self-adjointoperators A₁,…,A_n on $\text{H}$ at some instants t₁ < t₂ <…<t_s. The question of theminimal number n of operators A₁,…,A_n (physical quantities $\text{A}{}_1\text{, …,}\text{A}{}_{\mathrm{n}}$) for which the quantum system $\text{S}$ is (A₁,…,A_n)-observableis discussed.     

Electron temperature measurements in low-density plasmas by helium spectroscopy

Methods of measuring the electron temperature in low-density plasmas by He spectroscopy are examined. These utilize either the relative intensities of singlet and triplet lines or the absolute intensities of single lines. Calculations from measured and theoretical data show that both methods are seriously influenced by secondary processes, the most important of which are excitation from the metastable levels 2¹S and 2³S, and excitation transfer in electron-atom collisions combined with imprisonment of resonance radiation. The calculations give parameter limits for the validity of different methods and combinations of lines. Due to the secondary processes, the determination of T_e from relative line intensities is restricted to low-density, short-duration plasmas (typically n_e < 2 × 10¹⁶ m^-3, t_ex < 5 × 10^-6 s) or to even lower densities that depend on the apparatus dimensions (typically n_e < 3 × 10¹⁵ m^-3, L ≈ 0.1 m). For the determination of T_e from absolute line intensities, the situation is more favourable and, with a suitable choice of lines, typical restrictions on n_e and t_ex are n_e < 5 × 10¹⁷ m^-3, t_ex < 10^-5 s or n_e < 10¹⁷ m^-3, L ≈ 0.1 m for electron temperatures above 10 eV. For temperatures below 10 eV and degrees of imprisonment below 7% measurements are possible for electron densities up to 10¹⁹–10²⁰ m^-3, without any limits on t_ex or L.     

Impurity transport in fractal media in the presence of a degrading diffusion barrier

We have analyzed the transport regimes and the asymptotic forms of the impurity concentration in a randomly inhomogeneous fractal medium in the case when an impurity source is surrounded by a weakly permeable degrading barrier. The systematization of transport regimes depends on the relation between the time t ₀ of emergence of impurity from the barrier and time t _* corresponding to the beginning of degradation. For t ₀ < t _*, degradation processes are immaterial. In the opposite situation, when t ₀ > t _*, the results on time intervals t < t _* can be formally reduced to the problem with a stationary barrier. The characteristics of regimes with t _* < t < t ₀ depend on the scenario of barrier degradation. For an exponentially fast scenario, the interval t _* < t < t ₀ is very narrow, and the transport regime occurring over time intervals t < t _* passes almost jumpwise to the regime of the problem without a barrier. In the slow power-law scenario, the transport over long time interval t _* < t < t ₀ occurs in a new regime, which is faster as compared to the problem with a stationary barrier, but slower than in the problem without a barrier. The asymptotic form of the concentration at large distances from the source over time intervals t < t ₀ has two steps, while for t > t ₀, it has only one step. The more remote step for t < t ₀ and the single step for t > t ₀ coincide with the asymptotic form in the problem without a barrier.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations

We study the behavior of 〈σ₀^x(t)σ_n^x(0)〉 and 〈σ₀^y(t)σ_n^y(0)〉 for the transverse Ising chain at the critical magnetic field at T = 0. Explicit results are obtained for the three distinct regions where t → ∞ and n → ∞with $\text{0 ?}\text{n}\text{t}\text{<1}$, $\text{1 <}\text{n}\text{t}$, or $\text{t = n + n}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{(}\text{z}\text{2}\text{)}$ where z is fixed of order one. In this latter region the general Painlevé V solution is shown to reduce to a Painlevé II function. We use our results to discuss the general problem of long-time behavior of Toda equations with slowly decaying initial values.     

Change in character of the paramagnetic to helimagnetic transition in CrAs upon MnAs substitution

The structural and magnetic characteristics of the para- (P) to helimagnetic (H_c) transition in Cr_1-tMn_tAs (0.00 ⩽ t ⩽ 0.67 ±0.01) have been studied by X-ray diffraction, differential scanning calorimetry and magnetic susceptibility measurements. The distinctly first order character of the P to H_c transition is retained at low substitution levels of Mn for Cr, as manifested by the observation of latent heat, temperature hysteresis and discontinuous jumps in the unit cell dimensions. All these effects decrease with increasing t, and in the vicinity of a pseudo tricritical point at t = 0.17 ± 0.02 the discontinuities in the a and c axes (Pnma setting of the MnP type unit cell) and the temperature hysteresis are no longer unambiguously detactable. However, the gradually diminishing discontinuity in the b axis is maintained, and, together with the behaviour of the heat capacity, this shows that the first order character of the P to H_c transition persists up to t = 0.32 ± 0.02. These unusual findings are discussed in terms of the concept of pseudo tricritical point, predicted by Bergman and Halperin for a compressible Ising system.     

Tsallis’ statistics in the variability of El Niño/Southern Oscillation during the Holocene epoch

Analysis of the Tsallis q-triplet for the variability of El Niño Southern Oscillation (ENSO) index during the Holocene epoch (last 11,000 years) is presented. Three periods are analyzed, 0-7000, 7000-9700, 9700-11,000 years before the present. During the first and the third periods, the q-index values have the expected usual relations between them (q_sens<1<q_stat<q_rel), and in the second one there is an inversion between q_stat and q_rel (q_stat>q_rel).     

Monte Carlo study of tricritical dynamics in two dimensions

The dynamical tricritical behavior for the spin-1 Ising model with single-ion interaction is investigated in two dimensions using Monte Carlo simulations. The nonlinear dynamical tricritical exponentz _t is determined from the asymptotic power-law relaxation of the magnetization. The valuez _t = 1.99 ± 0.04 reported here is the first estimate of the dynamical exponent at a multicritical point, in two dimensions.On leave from Departamento de Fisica, Universidade Federal de Pernambuco, Recife-PE, Brazil.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

The crossover behaviour of the susceptibility of the Ising model on anisotropic lattices

The behaviour of the reduced susceptibility χ′ of a d-dimensional Ising system in the limit t_d = tanhβJ_d → 0 is investigated. The critical exponent γ_n of (∂ⁿχ′/∂tⁿ_d)_td = 0 is, for n = 2,3, found to satisfy γ_n ? (n + 1)γ₀, and hence, by inequalities found by Liu and Stanley, γ_n = (n + 1) γ₀. For d = 2, the latter identify is valid for all n.     

Etude en fonction du temps de l'oxydation des magnetites substituees a l'aluminium et au chrome au moyen de la conductivite electrique

The oxidation of substituted magnetites (Fe²⁺Fe_2?x³⁺M_x³⁺O₄^2?(O < x < 2) into the lacunar phase γ(Fe_1?z³⁺M_z³⁺)O₃^{2 ?} (x = 3z) was followed over time by electrical conductivity over the temperature r Curves σ = f(t) are different according to whether we deal with an n or p-type spinel. However, for intermediate substitution rates (1,1 < x < 1,8), n-type ferrichromites are oxidized after an initial period in the same way as p-type semi-conductors.For the initial period, the chemisorption kinetics of oxygen upon these n-type samples, reduced under vacuum, was found to follow Elovich's law with an activation energy depending on the degree of coverage.     

The s-channel dual absorptive model as a consequence also of t-channel absorption

The dual absorptive model applied to t-channel predicts that Regge residues above threshold are I_n-functions which for t ? 0, for the leading trajectory, are simply J_n(R_o√−t). Thus s-channel absorptive models can be expressed entirely in terms of t-channel quantities. Implications to complex Regge poles is discussed.     

The Inviscid Burgers Equation with Initial Value of Poissonian Type

We study the discontinuities (shocks) of the solution to the Burgers equation in the limit of vanishing viscosity (the inviscid limit) when the initial value is the opposite of the standard Poisson process p. We show that this solution is only defined for t ε (0, 1). Let T ₀ = 0 and T _n , n≧1, be the successive jumps of p. We prove that for all M > 0 the inviscid limit is characterized on the region x ε (-∞, M], t ε (0, 1) by the increasing process $N(t) = \sup \{ n \in \mathbb{N} {\text{| }}M + nt > T_n \} $ and the random set I(x) = {n ε {0,..., N(t)}‖T _n -nt≦x<T _n+1 - nt}. The positions of shocks are given in a precise manner. We give the distribution of N(t) and also the distribution of its first jump. We also prove similar results when the initial value is u _μ(y, 0) = -μp(y/μ²) + μ^-1 max(y, 0), μ ε (0, 1).     

Boundary Conditions for the Dynamical Equations of Quantum Mechanics

We discuss the problem whether the time evolution in quantum physics should be represented by the time-symmetric unitary-group evolution, i.e., whether time t extends over???∞?<?t?<?+∞ or it is more realistic to describe quantum systems by a mathematical theory, for which time t starts from a finite value t ₀: t ₀?≤?t?<?+∞, for which the mathematicians would choose t ₀?=?0,¹ but which could be any finite value. If the quantum system in the lab should be described by some kind of quantum theory, one should also admit the possibility that the solution of the dynamical equations needs to be found under boundary conditions that admit a semigroup evolution. It is remarkable that results in lab experiments indicate the existence of an ensemble of finite beginnings of time $ t_0^{(i) } $ for an ensemble of individual quanta.     

Dynamical theory for photon and photoelectric pulse distributions in single molecule fluorescence

A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function w_N(t) and for the photoelectric pulse distribution function f_n(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. f_n(t) ≅ w_N(t). A relation between w_N(t) and f_n(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k.     

Spin dependence of inclusive reactions from proton-proton collisions at 7.9 GeV/c

The spin dependence of inclusive proton and pion production by 7.9 GeV/c protons has been measured using a polarized proton target, for nominal values of x = p_L^cm/p_max^cm = 0.7 in the transverse momentum range 0.4 GeV/c <pp_t < 1.2 GeV/c, and for p_t = 0.4 GeV/c in the range 0.1 < x < 0.96. The results indicate a positive asymmetry of +5% over this kinematic region, which corresponds to fragmentation of the unpolarized proton.     

Subnanosecond transient photocurrents in a-Si:H: A probe of thermalization within shallow band-tail states

The measurement of transient photocurrents in amorphous semiconductors has been shown to be a powerful way of exploring the thermalization of excess carriers within the manifold of localized states adjacent to the band edges. The extent to which thermalization within the shallowest states can be resolved in controlled by the experimental observation time. Reported here are measurements of transient photocurrents, using high-speed stripline techniques, in glow-discharge a-Si:H carried out in the time regime (0.6 ? 100 nsec) and the temperature range 150 ? 320K. We find an effective electron drift mobility of <μ_D(t)> = 1–3 cm²/Vsec at t=0.6 nsec and T=300K and a time-dependent activation energy, _?(t), for the photocurrent magnitude. The initial photocurrent decay (t < 100 nsec) can be fit to a power-law, t^?n, and the temperature dependence of the dispersion parameter, α=1?n, is given by α=α₀+βT. In view of these results the nature of the band-tail near the conduction band edge is discussed.     

Scaling function for order-parameter correlations in expansion to order 1/n: I. Short-range interactions

The order-parameter correlation function $\text{G}\text{?}\text{(}\text{q}\text{, ξ}{}_1\text{)}$ is calculated in the critical region of momentum space $\text{q}$ in terms of a second-moment correlation length ξ₁ by means of perturbation expansion to order 1/n, for an n-vector system with short-range interactions, in zero field above T_c, for 2 < d < 4. The scaling function of the $\text{q}$ dependence is obtained in closed form with a precisely identified cutoff-dependent factor which is the amplitude of the correlation-length dependence of the susceptibility. Both the exponents and the coefficients of the expansion for fixed q as t = (T?T_c)/T_c → 0 are given explicitly and the former are shown to be in accordance with the operator product expansion. The coefficients of order 1/n in the terms associated with a t^k(1?α) dependence of the energy density, for integer k ≥ 1, are expected to be explicitly cutoff-dependent and this is verified by the detailed calculations for k = 1. The behaviour for fixed t and q → 0 is shown to be markedly different from the Ornstein-Zernike approximation. Detailed comparison is provided with the scaling function of the t dependence of the correlations appearing in parallel work.