Physica最新文献

The Heisenberg ferromagnet with exchange and crystal-field anisotropies is studied. The free energy and magnetization are calculated by means of a method developed by Wortis.

The boson formulation of superconductivity is derived quite generally without resorting to power-series expansions in the momentum. An exact form for the boson characteristic function is given in terms of the boson energy. An exact equation for the boson energy is also derived. By solving this equation one can compute the boson characteristic function in the entire domain of momentum. This result implies that one can describe spatial variations of the order parameter and of the magnetic field without any practical restriction.

A new covariant derivation is given for the relativistic symmetry group of a uniform electromagnetic field. The symmetry group of the equations of motion of a charged (classical, Klein-Gordon or Dirac) particle in such a field and its irreducible representations are determined. Using the representations the solutions of the equations of motion are discussed. Exact solutions can be given for the motion of a charged particle in an arbitrary uniform field.

Using Dirac's method of constraints we study the problem of a gauge-invariant hamiltonian formulation of a relativistic plasma. In particular we get a hamiltonian formulation strictly in terms of the electric and magnetic fields, and the mechanical momenta of the particles. The explicit Lie-bracket relations between the fundamental microscopic variables is no longer canonical. These Lie-bracket relations and the equations of motion are given by Dirac's modified Poisson bracket.

A solution method is developed for nonlinear differential equations having the following two properties. Their coefficients are stochastic through their dependence on a Markov process. The magnitude of the fluctuations, multiplied with their auto-correlation time, is a small quantity. Under these conditions, the solution is also approximately a Markov process. Its probability distribution obeys a master equation, whose kernel is found as an expansion in that small quantity. The general formula is derived. Applications will be given in the second part of this work.

A new method for evaluating the path integral corresponding to the harmonic oscillator with time-dependent frequency Ω(t) and acted on by a time-dependent perturbative force is given. The advantage of the present method consists in the fact that our analytical expression for this path integral can immediately be expanded as a series in the eigenfunctions of the corresponding Schrödinger equation.

The boson characteristic function is computed in the entire region of momenta. A comparison with the BCS kernel is discussed.

Isotopic thermal-diffusion factors have been determined for neon, in the temperature range from 139.6 up to 302.3 K.

In our previous observations, a wide temperature range from about 140 to 803 K has been experimentally covered and used to test the exponential-six model. Theoretical calculations with other properties (viscosity, thermal conductivity, self-diffusion and second virial coefficient) have been also considered within the frame-work of the model.

We use a model due to Kac to investigate some properties of the generalized entropy proposed by the Brussels group. We show that the entropy production is positive-definite and that the entropy and entropy production per particle are finite in the limit of an infinite system.

The generalized $\text{H}$ theorem is a dynamical theorem and describes the approach to equilibrium of the whole system: generally, correlations play a role in its formulation and cannot be forgotten even if macroscopic variables satisfy the chaos condition. However, a detailed investigation of the evolution equations for the moments shows that correlations reach their equilibrium value faster than the one-particle reduced distribution function and that, asymptotically, there is a regime where one recovers Boltzmann's results.

The Luttinger-Tisza method and generalizations of this method for determining the minimum energy spin arrangement in a crystal subject to certain strong conditions are reviewed. It is shown that one can always replace the strong conditions by a set of additional conditions which in the simplest cases is identical with the single weak condition introduced in the Luttinger-Tisza method. A general method of calculating the minimum energy spin arrangement, based on the space group symmetry of the magnetic atom arrangements, is given, and the method of Niemeyer, based on permutation groups, is shown to be equivalent to this method. It is also known that the Luttinger-Tisza conjecture concerning the periodicity of the minimum energy spin arrangement is equivalent to a sufficient, but not necessary, condition for a minimum of the energy.