Note on conservation laws based upon traceless energy-momentum tensors in flat space-time

In this note we prove the following theorem. If in a flat space-time with metric g_ij(x) treferred to general coordinates xⁱ a vector ξⁱ(x) satisfies (Tⁱ_jξ^j)_;i=0 (semicolon denotes covariant differentiation) for all energy-momentum tensors of the set $\text{{}\text{T}{}^{\mathrm{ij}}\text{T}{}^{\mathrm{i}}{}_{\mathrm{j;i}}\text{=0;g}{}_{\mathrm{ij}}\text{T}{}^{\mathrm{ij}}\text{=0}$; T^ij = T^ji; T^iju_iu_j > 0 (where u_i is a time-like vector)}, then the vector ξⁱ defines a conformal motion. This theorem, which may be considered as a converse (in flat space-time) to a well-known result of Trautman, is a generalization of a result obtained by J. T. ?opuszański and J. Szczucka-Soko?owska [Reports on Mathematical Physics 11 (1977), 153] in which they assumed the vector ξⁱ was a polynomial in Minkowski coordinates.     

Etude des proprietes thermodynamiques d'un groupement tetranucleaire: Application au compose Na3RuO4

The exact eigenvalues spectrum of the spin hamiltonian $\text{H}\text{= ?2}\text{∑}\text{(i, j)}\text{J}{}_{\mathrm{ij}}\text{S}\text{?}{}_{\mathrm{i}}\text{S}\text{?}{}_{\mathrm{j}}$ have been calculated for a tetranuclear cluster formed by four spins 3/2 at the vertices of a lozenge. Two isotrope exchange interactions J₁ and J₂ are able to explain the thermodynamic properties (magnetic susceptibility, entropy, specific heat). A ground state transition from singlet to triplet state occurs when the $\text{J}{}_2\text{J}{}_1$ ratio reaches the value $\text{4}\text{3}$. The magnetic susceptibility data of Na₃RuO₄ fit well with the theoretical values proposed for $\text{J}{}_1\text{K}\text{= (?19,5 K)}$ and J₂/k (?22,5 K).     

On the asymptotic approximations of the solutions of a system of two non-linearly coupled harmonic oscillators

A procedure, closely related to the averaging method, is given for the construction of asymptotic approximations for the solutions of the Lagrangian system

$\text{d}\text{x}{}_1\text{d}\text{t}\text{=x}{}_2\text{,}\text{d}\text{x}{}_2\text{d}\text{t}\text{=?x}{}_1\text{+ε}\text{∑}\text{i, j=1}\text{4}\text{α}{}_{\mathrm{ij}}\text{x}{}_{\mathrm{i}}\text{x}{}_{\mathrm{j}}\text{,}\text{d}\text{x}{}_3\text{d}\text{t}\text{=x}{}_4\text{,}\text{d}\text{x}{}_4\text{d}\text{t}\text{=?4(1+δ)x}{}_3\text{+ε}\text{∑}\text{i, j=1}\text{4}\text{β}{}_{\mathrm{ij}}\text{x}{}_{\mathrm{i}}\text{x}{}_{\mathrm{j}}\text{, x}{}_1\text{(0)=a}{}_0\text{, x}{}_2\text{(0)=0, x}{}_3\text{(0)=b}{}_0\text{, x}{}_4\text{(0)=0,}$

where ε > 0 and δ > 0 are small parameters, a_ij = a_ji and β_ij = β_ji are real constants. The solutions can be represented as follows:

$\text{x}{}_1\text{=a}\text{cos}\text{(t+ξ), x}{}_2\text{=a}\text{sin}\text{(t+ξ), x}{}_3\text{=b}\text{cos}\text{(2t+ψ), x}{}_4\text{=2b}\text{sin}\text{(2t+ψ).}$

The asymptotic approximations (in a certain well-defined sense) of a, b, ξ and ψ are given. It is shown that a rapid variation of the phase, ψ(t), will take place if b → 0 for the case that δ ≈ ε or δ ? ε. In addition for the case δ ≈ ε the phenomenon of bifurcation will be discussed.     

Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.     

Lie algebraic aspects of quantum statistics. parafermi statistics

We study in detail the Lie-algebraical properties of the quantization condition for spinor fields

$\text{[a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{,a}{}^{\mathrm{?}}{}_{\mathrm{j}}\text{],a}{}^{\mathrm{\pm }}{}_{\mathrm{i}}\text{= ±2δ}{}_{\mathrm{ij}}\text{a}{}^{\mathrm{\pm }}{}_{\mathrm{j}}$

.It turns out that the parafermi statistics is one particular solution of this relation: it is the minimal rank simple Lie algebra generated by the operators a^±_i entering into the above relation. We point out some other solutions.     

Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions

This paper is concerned with the competitive-diffusive systems

$\text{u}{}_{\mathrm{t}}\text{=d}{}_{\mathrm{l}}\text{u}{}_{\mathrm{xx}}\text{+(a}{}_{\mathrm{l}}\text{?b}{}_{\mathrm{l}}\text{u?c}{}_{\mathrm{l}}\text{v)u}\text{v}{}_{\mathrm{t}}\text{=d}{}_2\text{v}{}_{\mathrm{xx}}\text{+(a}{}_2\text{?b}{}_2\text{u?c}{}_2\text{u)v}\text{(x, t) ? (0, 1) × (0, ∞)}$

, with homogeneous Dirichlet boundary conditions. From a global bifurcation view point, the dependency of steady-states on the parameters a_i, b_i, c_i and d_i (i = 1, 2) is investigated. In particular, bifurcation of coexist ence solutions amd their stabilities are our main interests.     

Polariton modes at the interface between two conducting or dielectric media

A review of polariton modes at interfaces composed of two semiinfinite, homogeneous, and isotropic media is given. Both media are characterized by frequency-dependent dielectric functions ?_i(ω), i = 1, 2, and may become “interface-wave-active” in different frequency regions. The conditions for the existance of propagation windows are analyzed and applied to two particular cases: an interface composed of (a) two dielectrics with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{?\infty i}}\text{(}\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>Li</mtext>}}{}^2\text{ω}{}^2\text{ω}{}_{\mathrm{<mtext>T</mtext><mtext>i</mtext>}}{}^2$, where ?_t8i are the dielectric constants for very large frequencies and ωTi and ωLi are the transverse and longitudinal phonon frequencies; (b) two conductors with dielectric functions $\text{?}{}_{\mathrm{i}}\text{= ?}{}_{\mathrm{\infty i}}\text{(}\text{1 ?ω}{}_{\mathrm{i}}{}^2\text{ω}{}^2\text{)}$, where ω_iare the plasma frequencies. In the first case there exist two propagation windows in the infrared region, while in the second case there is one propagation window in the ultraviolet, visible, or infrared region. The dispersion relations of the modes and their decay distances into the two media are presented, and various damping effects are discussed. The review is concluded with theoretical results on the optical excitation and detection (ATR) of the interface modes.     

12C(7Li,t)16O and stellar helium fusion

The reaction ¹²C(⁷Li, t)¹⁶O has been studied at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$ with the LASL tandem accelerator and QDDD magnetic spectrometer. Angular distributions to levels with E_x < 11 MeV have been obtained from 0° to 90°, including 0°. The results have been analyzed with finite-range distorted-wave Born approximation theory. The α-particle spectroscopic factors and reduced widths obtained are compared with those calculated with group theory (SU(3)) and other models. The analysis of data for the 7.1 and 9.6 MeV J^π = 1^? levels, which are of great importance in stellar helium buring, yields a ratio, R, of dimensionless reduced α-widths $\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(7.1}\text{MeV}\text{)}\text{θ}{}^2{}_{\mathrm{<mtext>a</mtext>}}\text{(9.6}\text{MeV}\text{)}\text{= 0.35b ± 0.13}$. The observed line width of the 9.6 MeV level (Γ_c.m. = 390 ± 60 keV) is less than the accepted value (Γ_c.m. = 510 ± 60 keV) and implies θ²_a(9.6 MeV) ≈ 0.6. These results as well as data for the 6.92 MeV J^π = 2⁺ and 10.35 MeV J^π = 4⁺ “α-cluster” states indicate 0.09 < θ²_a(7.1 MeV) < 0.33 with a mean value θ²_a(7.1 MeV) = 0.14 ± 0.04. The implication for stellar helium burning is discussed.     

Monte Carlo study on dynamical behaviour of spins and spin clusters in the 2D ± J Ising spin-glass

To investigate dynamical (time-dependent) behavior of spins and spin clusters in the two-dimensional ± J Ising spin-glass, we have evaluated the relaxation time τ_i of individual spins by the Monte Carlo simulation. An interesting finding is that, at least in the temperature range $\text{T ? 0.8J}$, most of τ_i are described by $\text{τ}{}_{\mathrm{i}}\text{∝}\text{exp}\text{{}\text{E}{}_{\mathrm{i}}\text{(T ? T}{}_0\text{}}$ with T₀?0.5J (E_i being a constant), which suggests that the system undergoes a glass transition obeying Fulcher's law.     

Magnetostatic modes of gyrotropic cylinder and bar

We present a theory of magnetostatic modes which are wavelike in the direction parallel to the axis of an infinitely long, ferromagnetic bar of square cross-section and are localized at the faces and edges of the bar. We write H = ?▽?, where φ is a magnetic scalar potential, and obtain as the equations determining ?, $\text{Σ}\text{μ}{}_{\mathrm{\alpha \beta }}\text{?}{}^2\text{σ}\text{?X}{}_{\mathrm{\alpha }}\text{?X}{}_{\mathrm{\beta }}\text{=0}$ for the interior of the bar, and ▽²? = 0 for the exterior, where μ_αβ(ω) is the magnetic permeability tensor of the bar. We transform to cylindrical coordinates and solve the resulting second order partial differential equations by assuming a solution for ? of the form ?(r, θ, z) = e^iqxf(r, θ). The use of cylindrical coordinates allows us to project out of our expressions for ? the parts which belong to each of the irreducible representations of C₄, the group of proper rotations which leave the bar invariant. This has the consequence that the boundary conditions need to be applied along only one side of the bar, and are then automatically satisfied along the remaining three sides as well. The boundary conditions that ? and the normal component of B be continuous across the bar surfaces are satisfied at a discrete set of points along one side of the bar, and two coupled eigenvalue equations are obtained which are solved simultaneously for the frequencies of the corresponding magnetostatic modes. The convergence of this method is found to be quite good. We also present the dispersion curves for the magnetostatic modes of a gyrotropic right circular cylinder which are localized at the surface of the cylinder.     

Zero field steps in short Josephson junction

A theoretical investigation is carried out on the zero field current steps of a short Josephson junction under both the d.c. voltage V_d.c. and a.c. voltage V_a.c. cos ωt. The steps occur when the condition $\text{Ω + pω = 2Nω}{}_{\mathrm{n}}$ is fulfilled, where $\text{Ω = 2eV}{}_{\mathrm{d.c.}}\text{/}\text{h}\text{?}$, ω_n is the nth eigenfrequency in the eigenfrequency in the junction cavity, p and N are integers.     

Ground state spectroscopic constants of isothiocyanic acid,HNCS, from its microwave and millimeter wave spectra combined with far infrared data

The microwave and millimeter wave spectra of isothiocyanic acid, HNCS, in the ground vibrational state have been investigated in the frequency region 8–300 GHz. The a-type R-branch transitions have been assigned up to J = 25 and K_a = 4, and the a-type ^qQ₁ branch transitions up to J = 45. No b-type transitions could be identified in the frequency region covered. The far infrared data reported by Krakow, Lord, and Neely [J. Mol. Spectrosc., 27, 148 (1968)] were combined with our millimeter wave data in order to determine reliable spectroscopic constants. The rotational Hamiltonian, Watson's formalism with S reduction, has been extended empirically to higher order to facilitate the fitting of the large centrifugal distortion effects. The obtained constants are:

$\text{A = 1357.3 GHz; B = 5883.4627 MHz; C = 5845.6113 MHz; D}{}_{\mathrm{J}}\text{= 1.19393 kHz; D}{}_{\mathrm{JK}}\text{= ?1025.37 kHz; D}{}_{\mathrm{K}}\text{= 51.57 GHz; d}{}_1\text{= ?13.781 Hz; d}{}_2\text{= ?4.59 Hz.}$

The ¹⁴N quadrupole coupling constant has also been determined: χ_aa = 1.114 MHz.     

Inelastic neutron scattering study of magnetic excitations in the helimagnetic and antiferromagnetic phases of NiBr2

The spin wave dispersion in NiBr₂ has been studied by medium and long wavelength inelastic neutron scattering in the [1 1 0], [1 0 0] and [0 0 1] directions at 4.2 and 30 K, i.e. in the incommensurate helical and collinear antiferromagnetic phases. The values of the intralayer Heisenberg exchange constant J_ij and XY anisotropy constant D at 4.2(30) K are J₀₁ 0.379(1)(0.379(1)), J₀₂ 0.0036(50)(0.0036(50)), J₀₃ - 0.105(5) (?0.105(5)), J′ - 0.0423(50)(?0.389(50))D 0.0364(50)(0.0290(50)), where J′; is the interlayer exchange constant. In fitting the 4.2 K data account is taken of the co-existence of three equivalent domains and of intensity arising from $\text{ω(}\text{q}\text{)}$ and $\text{ω(}\text{q ± k}{}_0\text{)}$ where $\text{k}{}_0$ is the wavevector of the helix. In the low frequency region of the dispersion curve such peaks are resolved. The results reinforce the hypothesis that in zero-field the commensurate-incommensurate phase transition is driven by fluctuations.     

Dual model for dislocation and disclination melting

We show that defect melting involving dislocations and disclinations is dually equivalent to an extension of an XY model with an energy of the type Σ_{i, j}{[cos(?_iu_j + ?_ju_i) + ? cos ?_iω_j] }, where $\text{ω}{}_{\mathrm{t}}\text{=}\text{1}\text{2}\text{?}{}_{\mathrm{tjk}}\text{?}{}_{\mathrm{j}}\text{u}{}_{\mathrm{k}}$ is the local rotation field. The. model clarifies the proper choice of defect core energies arising from nonlinear elasticity. These permit the pile-up of dislocations to disclinations which is essential for the first order of the melting transition.     

Temperature dependence of N2-broadened halfwidths of ozone

The temperature dependence of N₂-broadened halfwidths of ozone has been studied over a temperature range of 200–500 K. Assuming the form $\text{γ}\text{(T) =}\text{γ}\text{(T}{}_0\text{)(}\text{T}{}_0\text{T}\text{)}{}^{\mathrm{n}}$, the exponent n has been determined from QFT-ID calculations for 126 ro-vibrational transitions of ozone selected to consider a wide range of the rotational quantum number J″ (1 to 35), the full manifold of K″_a for particular J″, values and transitions important to stratospheric studies. The results give an average temperature exponent of n = 0.77 for nitrogen-broadening. The temperature exponents are transition dependent but the fluctuation about the average value is small (±6%). The value on n as a function of J″ and K″_a is investigated. Comparison of the present results with experiment and other theoretical calculations shows good agreement. Based on the results an average temperature exponent for air-broadening of n = 0.76 is suggested.     

Conductivity of a quasi-one-dimensional metal at finite temperatures

The longitudinal conductivity of a quasi-one-dimensional metal is calculated for the case T?ω_D (ω_D being the limiting phonon frequency) and ω_Dl¹/v?1 where l¹ is the effective mean free path determined by impurity and phonon scattering: $\text{l}{}^1\text{= (l}{}^{\mathrm{?1}}{}_{\mathrm{ph}}\text{+ l}{}^{\mathrm{?1}}{}_{\mathrm{i}}\text{)}{}^{\mathrm{?1}}\text{, l}{}_{\mathrm{ph}}\text{= v/λT, l}{}_{\mathrm{i}}$ is the impurity mean free path. The conductivity is σ = (c₁e²/πS)l³_iv^?2ω_DλT for l_i?l_ph, σ = (c₂e²/πS)vω_D(λT)^?2 for l_i?l_ph, λ being the dimensionless electron-phonon interaction constant, c₁, c₂ ～ 1, S = a_xa_y is the (xy) area per one chain.     

On the physical basis for Urbach's rule

The low-energy tail of the E 6 a exciton in GeS obeys Urbach's rule, with Urbach parameters σ₀ = 1.45 ± 0.05, and $\text{h}\text{?}\text{ω}{}_{\mathrm{p}}\text{= 8.7 ± 0.6 meV}$. The energy ?ω_p corresponds to a previously measured rigid-layer vibrational mode which has no associated electric field. This finding is inconsistent with Dow and Redfield's unified theory of Urbach and exponential absorption edges. Our results are consistent with Sumi and Toyazawa's theory of Urbach edges, and with Fivaz and Mooser's model for electron-phonon interactions in layered compounds.     

The external field problem for QCD

In lattice gauge theory, many computations such as the strong coupling expansions, mean field theory, or the few plaquette models require the evaluation of the one-link integral in the presence of an arbitrary N × N complex matrix source (J). For SU(N) gauge theories, we express our general solution to the external field problem as an integral over the maximal abelian subgroup [U(1)]^N?1

where S₀ = 2Σ_kz_k cos(φ_k ? θ), z_j are eigenvalues of √JJ⁺, e^2iNθ=detJ/detJ⁺, and G is an appropriate jacobian determinant. Our explicit solution follows from differential Schwinger-Dyson equations cast in a separable form by using fermionic variables, and the special cases of N = 2, 3 and ∞ agree with earlier derivations.     

A further contribution to the theory of the transient hot-wire technique for thermal conductivity measurements

We study the density of states of a one-dimensional tightbinding electron model with random hopping elements. The Hamiltonian is $\text{H = -∑}{}_{\mathrm{i}}\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i+1}}\text{+a}{}^{\mathrm{+}}{}_{\mathrm{i+1}}\text{a}{}_{\mathrm{i}}\text{)}$, where the $\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}$'s are independent identically distributed random variables. It is proved that the single particle density of states D(E) diverges near E = 0 as $\text{1}\text{|(E}\text{log}{}^3\text{|E|)|}$.     

Intermittent incommensurate chaos

Near the onset of intermittent chaos from quasiperiodic motion lying on an attracting 2D torus with rotation number ρ=ω₂/ω₁=(√5?1)/2, the power spectrum of the cartesian coordinate of the intersection point on the Poincaré section is studied. The Poincaré section is distorted from the ellipse near the onset of chaos. Then a sequence of spectral lines are excited at frequencies $\text{Ω}{}_{\mathrm{i}}\text{= ρ}{}^{\mathrm{i}}\text{Ω}{}_2\text{, (i=1,2,…)}$. Their intensities are found to obey the power law $\text{Ω}{}^4{}_{\mathrm{i}}\text{or}\text{Ω}{}^2{}_{\mathrm{i}}\text{for}\text{i ? 1}$ according as the Poincaré section has a sharp wrinkle or not. A similar spectrum is obtained also in the chaotic regime ε > 0. The mean value of time intervals of quasiperiodic states between two consecutive bursts and the square root of their variance are found to be inversely proportional to ε near the onset point g3 = 0.