Self,nitrogen and oxygen broadening of the 115-GHz line of carbon monoxide

Self nitrogen, oxygen and air-broadened half-widths of the 115-GHz line of CO have been measured at various temperatures between 293 K (room temperature) and 220 K. The temperature dependence of the broadening parameter CCO-XW is described by a power law CCO-XW (T) = CCO-XW(293 K)(T/293)-n co-x. The values of CCOW (293 K) and nCO-X are presented for each broadening gas X, X - CO, N2 and O2. The usual relation CCO-airW (T) = 0.78CCO−N2W(T) + 0.21CCO−O2 W(T) is found to be valid in the temperature and pressure ranges of the present experiments.     

On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Crystal symmetry groups and their representations I lattice extensions of point groups in R2 and R3

We classify all point groups in R² and R³ according to their decomposition into m-fold semidirect products of cyclic groups. This product is characterized completely by means of m?1 matrices α⁽¹⁾,…, α^(m?1) with non-negative integer elements. For any arithmetic class [Pⁿ_i] in Rⁿ (n=2, 3) we define the set D(Pⁿ_i, T) of representative translations with the following properties: (a) The elements of D(Pⁿ_i, T) are in one-to-one correspondence with defining relations of Pⁿ_i; (b) D(Pⁿ_i, T) determines uniquely all equivalence classes of the factors of Pⁿ_i over T.We present: (i) a construction of all sets D(Pⁿ_i, T) in R² and R³; (ii) a construction of all algebraic classes of space groups and a derivation of all group operations which transform one algebraic class into another; (iii) a derivation of formulas expressing the multiplication table of any space group by means of the representative translations and matrices α⁽¹⁾,…, α^(m?1). The results (i), (ii) and (iii) are obtained without making use of the notion of non-primitive translations.     

Free-field realization of theWKP(N) algebra

TheW _KP ^(N) algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW _KP ^(N) can also be decomposed toN independent copies ofW _KP ⁽¹⁾ algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW _KP ⁽¹⁾ . In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW _KP ^(N) in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R) _k algebras with levelk = 1. By reductions, we give similar results forW ^(N) andW ₃ ⁽²⁾ algebra.     

Normal and antinormal ordering of field operators in quantum optics

The relations between the probability distributionp n _vt of the number of photonsn _vt in a volumeV at timet and the probability distributions P_N(W) and P_A(W) of the integrated intensityW related to the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containingM modes. As the normally ordered correlations are measured with photodetectors and the antinormally ordered correlations are measured with quantum counters the relations betweenn _vt , P_N(W) and P_A(W) permit the statistical behaviour of light to be determined from measurements with photodetectors and quantum counters. The results obtained here are used for the superposition of coherent and thermal fields. It is also shown that the antinormal correlations depend explicitly on the number of modes and that in the classical limit, when the average photon occupation number per mode becomes large, the distributionsn _vt , P_N(W) and P_A(W) become equal.     

Analysis of the twist-four two-quark process by renormalization mixing

We discuss the renormalization of the twist-four operators (both the two-quark operator and the four-quark operator) and how the anomalous dimensions are calculated in a fairly compact way. Especially, we calculate large spin (n) behaviour of the anomalous dimensions which are relevant for the two-quark process. The most singular behaviour turns out to be 2″ up to some power of n. By using them, we find that, in the twist-four level, W_L ∞ (1 - x)⁰ and W_T(vW₃) ∞ (1 - x)¹ for the pion, and W_L ∞ (1 - x)² and W_T(vW₃) ∞ (1 - x)³ for the nucleon, up to radiative corrections. These are the results which remain after the kinematical target mass effects are taken into account. Target and current dependence is also discussed.     

Sound propagation anomalies and phase diagram of chromium alloys

Calculations of the complex elastic moduli Ĉ(T) in dilute Cr alloys are compared to measurements of the velocity and damping of sound near T _N and at high temperatures T>T _N (T _N — Néel temperature). The thermodynamic calculation is based on the covalent bond model of 3d ions in a state with different numbers n of covalent electrons. The parameters A _ij ⁽ⁿ⁾ of indirect exchange between the ions of the i and j sublattices are expressed in terms of the covalent bond energy Γ _ij ⁽ⁿ⁾ . The stability of the charge and spin density waves (CDWs and SDWs) is found by a variational method and is determined by the dispersion of Γ _ij ⁽ⁿ⁾ and by the Coulomb parameters U _n. For a small structural vector Q the phase diagram contains a superantiferromagnetic phase (SAFM) at temperatures T _N<T≲2T _N. The peak of the defect |ΔE(T)| of the modulus and of the sound damping Δ_h(T _N) near the first-order SDW-SAFM transition is determined by the structure of the transitional domain. Measurements of the anomalous growth of E(T) at temperatures T>T _N make it possible to determine the magnetostriction constants λ(T) of Ce alloys in the SAFM phase on the basis of the SAFM theory. Fiz. Tverd. Tela (St. Petersburg) 41, 1467–1472 (August 1999)     

Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Distribution function of the number of particles in the condensate of an ideal Bose gas confined by a trap

The distribution function W₀(n₀) of the number n₀ of particles in the condensate of an ideal Bose gas confined by a trap is found. It is shown that at the temperature below the critical temperature T_c this function has a Gaussian shape and depends on the trap potential via two parameters only. The center of this function shifts to larger values of n₀ with decreasing temperature and its width tends to zero, which corresponds to the suppression of fluctuations. In the narrow vicinity of the critical temperature \(\left| {T - {T_c}} \right| \leqslant {T_c}/\sqrt N \), where N is the number of particles in the trap, the distribution function changes and at the temperature above the critical one it takes the usual form W₀(n₀) = [1 ? exp(μ)]exp(μn₀), where μ is the chemical potential in temperature units. In the limit N→∞, this change occurs at a jump.     

n体聚集过程和联合聚集过程的集团尺寸分布

本文研究n体聚集过程和联合聚集过程的集团分布演化。从广义Smoluchovki方程出发,给出聚集核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B(A,B均为常数)的显解;利用聚集核K(i₁,i₂,…,i_n)=(Ai₁+B)(Ai₂+B)…(Ai_n+B)和核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B的方程之间的联系,得出核K(i₁,i₂,…,i_n)=S_(i1)S_(i2)…S_(in)(S_K=AK+B)的凝前解。而且,根据联合聚集动力学方程,讨论了聚集和型核分别为K₂(i,j)=i+j,K₃(i,j,k)=i+j+k的集团尺寸分布C_m(t)的长时行为,并将结论推广到一般的联合聚集过程。 关键词：     

Kondo anomalies of heat conductivity and Lorenz ratio in normal state (La,Ce) Al2

The thermal conductivity of LaAl₂ and of two dilute (La, Ce)Al₂ alloys was measured in the normal state between 0.4 and 8 K. From the lattice conductivity of LaAl₂ a high dislocation densityN _d caused by the arc melting process can be inferred. After annealingN _d is reduced by an order of magnitude. For the (La, Ce)Al₂ samples minima are observed at 5 K in theW ^e ·T vs.T curves (W ^e =electronic thermal resistivity). Below 1 K the quantityW ^e ·T is linear in (— lnT). The electronic Lorenz ratioL ^e (T)=ρ(T)/W ^e (T) ·T shows a maximum at 2 K with a value 23% aboveL ^e (0). It is for the first time that this Kondo anomaly is established in its full temperature dependence.     

DC conductivity of new single and mixed alkali oxyfluorovanadate glasses

New glasses have been prepared according to these formulas (70-x)V₂O₅-30BaF₂-xAF, where AF=LiF or NaF and (60-x)V₂O₅-30BaF₂-10LiF-xAF, where AF=NaF and x=10, 15, 20, 25 and 30 mol%. Density of the glasses was measured and molar volume calculated and they correlated with the AF content. The dc conductivity has been measured in the temperature range from 302 to 453 K. The dc conductivity increases with temperature and V₂O₅ content, while it decreases with the alkali fluoride content. Conductivity has been correlated with the calculated polaron distance, R, and glass transition temperature, T_g. The activation energy, W, increases with the increase in the alkali fluoride, while it decreases with the V₂O₅ content. Some parameters like polaron distance, R, polaron radius, r_p, ion concentrations, n(V), n(Li) or n(Na), hopping energy, W_H, density of localized states at Fermi level, N(E_F), polaron coupling constant, γ_p, polaron band width, J, hopping mobility, μ, and carrier density for electronic conduction, N_c, were calculated to explain the conduction mechanism and behavior of the present glasses.     

On the entropy of systems undergoing time evolution

The aim of the present paper is to discuss the behaviour of entropy of physical systems undergoing time evolution. We discuss the case of an infinite-dimensional separable Hilbert space $\text{H}$ where the entropy of a microstate ? is given by the formula s(?) = ?Tr(?ln?). Information about a physical system is given by the mean values Tr(?A_i) = m, i = 1, …, N, of N self-adjoint (not necessarily bounded) operators A_i.     

On spectral representations for the functions Wi(v, q2) (i = 1, 2) describing electroproduction process

It is shown that the Deser, Gilbert, Sudarshan representation (DGSR) does not follow from microcausality and spectrality only. Examples of the functions W_i(v, q²) satisfying the microcausality and spectrality conditions are given which cannot be written as the DGSR with spectral function h(a, α) that is a temperature distribution. Instead of the DGSR the spectral representation for W_i(v, q²) has been proved (eq. (3)) which follows only from microcausality and spectrality.     

Minimal number of operators for observability ofN-level quantum systems

This paper discusses the minimal numbern _min of operatorsA ₁,...,A _n , whose expectation values at some instants determine the statistical state of anN-level quantum system. We assume that the macroscopic information about the system in question is given by the mean values Tr[ρ(t _j )A _i ]=m _i (t _j ) ofn self-adjoint operatorsA ₁,...,A _n at some instantst ₁<t ₂t _s , wheres ²?1.     

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).     

Bootstrap calculation of the dynamical quark mass in QCD4 at finite temperature

Nonperturbative calculations of the dynamical quark mass m(T) are given in QCD₄, based on the bootstrap solution of the Schwinger-Dyson equation for the quark Green function at finite temperatures. A closed nonlinear equation is obtained for m(T) whose solution is found under some simplifying assumptions. We used a particular approximation for the effective charge and the nonperturbative expressions of the gluon magnetic and electric masses. The singular behavior of m(T) is established and its parameters are determined numerically. The singularity found is shown to correctly reproduce the chiral phase transition and the temperature limits obtained for m(T) are qualitatively correct. The complete phase diagram of QCD₄ in the (μ, T) plane is briefly discussed.     

Influence of an adsorbing gas on the layering transitions in crystal growth

The influence of an adsorbing gas on the layering transition of a film is studied. In agreement with an earlier publication, we find that the adsorbate lowers the critical temperature T_c(n) for the nth layer. We also find that a system which is dry near T = 0 may undergo an apparent wetting transition due to the adsorbate. Indirect evidence is given that the sequence T_c(n) ends at T_R, the roughening temperature, as conjectured by de Oliviera and Griffiths. Re-entrant behavior in the layering transitions is observed for sufficiently strong adsorption energy; similar behavior also appears in the roughening transition, for which there exists some experimental evidence.     

Measurement of collision broadening of the P1(5) line of (0,0) band of OH AΣ←XΠ transition at high temperatures

Even for the well-studied and ubiquitous species, OH, the current state of theoretical development of broadening theory does not allow extrapolation from low-temperature laboratory measurements to the range of practical combustion devices. We performed a series of experiments at typical combustion conditions to determine the collision broadening of the P₁(5) line of the (0,0) band of OH A²Σ⁺←X²Π transition by Ar in shock-heated H₂-O₂-Ar mixtures and by air in H₂-air flames over a wide range of stoichiometry (φ=0.01-10.0), temperature (T=780-2440 K), and pressure (p=0.7-10.0 atm). The values of the collision width, Δν_C, were acquired by fitting Voigt profiles to the measured spectral line shapes in flames and to the peak absorption coefficients (k_ν0) in shock tube experiments. Collision broadening parameters (2γ_Ar, 2γ_N2, and 2γ_H2O) were then calculated assuming the linear dependence of Δν_C with pressure—the 2γ_N2 and 2γ_H2O values were inferred from 2γ_Air and the equilibrium concentration of N₂ and H₂O of a given flame. The temperature dependences of 2γ_i in our temperature range are, respectively, 1.0, 0.75, and 0.87 for Ar, N₂, and H₂O. The collision broadening cross sections (σ) deduced from 2γ_i values are expressed with an assumed form, σ_i(T)=σ_i,₀(T₀/T)^k, T₀=1000 K: for Ar, σ_Ar,0=63.3 (Ų), k=0.50; for N₂, σ_N2,0=68.0 (Ų), k=0.25; for H₂O, σ_H2O,0=188.8 (Ų), k=0.37.     

Supercovariant derivatives,super-Weyl groups,and N = 2 supergravity

We analyze the kinematic constraints for N = 2 Poincaré supergravity within the context of “superconformal symmetry breakdown”. We find that N = 2 supergravity is described in terms of two independent supertensors: W_αβij and T_αi. We also discuss general properties of superspace covariant derivatives to derive the relation of superspace to component approaches.