Physica最新文献

Many-particle systems with a hamiltonian of the form H = A + hB, h being a parameter, are discussed. In particular, for a certain class of these systems, a criterion is derived for the asymptotic equality of the isolated and the adiabatic susceptibility or, equivalently, for the ergodicity of B. This criterion states that, for sufficiently large particle number, any hermitian operator polynomial in h of any degree J that commutes with H(h) can be written as a linear combination of the powers H⁰, …, H^J with polynomial coefficients.

An exposition of the renormalization-group equations for the hierarchical model is given. Attention is drawn to some properties of the spin distribution functions which are conserved under the action of the renormalization group.

A simple formalism is presented here which describes low-resolution low-frequency depolarized light scattering from binary mixtures of fluids of nonspherical molecules and from pure fluids of nonrigid molecules, each one containing two segments. It is shown that when the k dependent features are negligible these spectra can contain two lorentzians because only dissipative modes are possible. The results presented here can also be used to describe dielectric relaxation from similar systems.

The generalization of the Faxén theorem for the force on a sphere in an incompressible fluid to the general nonstationary case derived in a previous paper, is further extended to the case of a compressible fluid.

The spherical approximation is considered for dipole—dipole interactions. Numerical calculations of the critical temperature of two compounds, Ce₂Mg₃(NO₃)₁₂⋯24H₂O and Dy(C₂H⋯SO₄)₃ ⋯9H₂O, are presented. Good agreement with experimental data is found. The Luttinger—Tisza calculations are shown to give the exact classical ground state in these two compounds, whereas this calculation is shown to fail in Er(C₂H₅⋯SO₄)₃⋯9H₂O.

It is found that in some systems the longe-range effects can be described by introducing an extra degree of freedom in the system, and the critical behaviour is therefore similar to that of a system with short-range interactions on a four-dimensional lattice.

A phenomenological linear Boltzmann equation is derived to study the classical motion of a rigid linear test molecule in a gaseous medium. The state of the molecule is defined by its center- of-mass coordinate and velocity, rotation frequency, orientation of its angular momentum and a rotor phase angle. The thermal-neutron scattering cross section is derived from a Fourier transform of a density distribution function which satisfies the Boltzmann equation with a suitable initial condition. Cross sections are calculated for some models to indicate the effect of coupling of center of mass and internal behavior.

Density-gradient terms may play a role in controlling density fluctuations in a fluid. It is shown that if these terms depend on the square of the density gradient they diminish in importance as the critical point is approached, in ordinary fluids and in the two-dimensional Ising lattice, but not in the three-dimensional Ising lattice or in four-dimensional systems. However, with a slight deviation from the square-gradient law, the gradient term may parallel the compressibility term, and it seems probable that this does occur, in conformity with Widom's hypothesis that the correlation length parallels the thickness of an interface between two phases. Critical-exponent relationships involved are discussed, and possible effects on the correlation length are considered. The introduction of a new critical singularity is discussed.

The perturbation of a uniformly decaying equilibrium is studied within the framework of resistive magnetodynamics. If the time of decay of the equilibrium state is large, the eigenmodes are the same as in nonresistive MHD. Nonresistive instabilities persist but the oscillating displacements have an increasing amplitude and an increasing period.

The experimental study of the coupling between the magnetizations and the high-frequency field h allows us to observe four resonances R₁, R₂, R₃, R₄ (at increasing resonance fields) with various polarizations. At hyperfrequencies, R₁ and R₄ are elliptically polarized in a plane normal to the cristallographic plane bc; the intersection of these two planes depends of the orientation of the d.c. field H. The polarization of the lines R₂ and R₃ is linear along c. This direction is independent of the orientation of H, within the experimental errors. At radio frequencies, the elliptical polarization of RR₁ and RR₄ is reduced to linear polarization in bc along the major axis of the ellipse. The resonances R₂ and R₃ remain polarized along c. The behaviour of these four resonances is studied as a function of the temperature and the frequency. At 1.91 K and at radio frequencies, the line shape depends strongly of the frequency.