Physica最新文献

It is shown that constant-α force-free magnetic fields are very preserved by velocity fields satisfying an equation of the form ∇ × ξ = αξ, where $\text{ξ = ∇ × (}\text{v}\text{×}\text{B}\text{) = (}\text{∂}\text{∂}\text{t}\text{− λ∇}{}^2\text{)}\text{B}$, and $\text{λ =}\text{1}\text{μσ}$. Explicit expressions are derived for the velocity fields preserving cylindrically symmetric force-free magnetic fields of interest in controlled thermonuclear fusion studies as well as astrophysics. Such velocity fields include the form of observed astrophysical features reported in the literature as well as those invoked in other studies, thus lending them further support and a firm foundation.

Classical binary-encounter calculations have been performed for the K-shell ionization cross section of Al and Ni target atoms by ¹₁H, ⁴₂He and ⁷₃Li projectiles. The binding-energy correction due to the interaction of the projectile with target K electrons has been incorporated along with the correction due to Coulomb repulsion. It is found that the simple BEA theory can account for the experimentally observed deviation of the cross section from a Z²₁ dependence.

The dependence of the longitudinal dynamic susceptibility on the static magnetic field is studied theoretically. The susceptibility is expressed in terms of the collision operator. Eigenvectors of the collision operator with respect to zero eigenvalue are investigated by using perturbation theory. It is shown that the real part of the susceptibility coincides with the adiabatic susceptibility at harmonic fields and its dependence on the magnetic field near harmonic fields is of the Lorentz type.

A magnetic system is considered, which consists of domains with submagnetizations m_r (r = 1, 2, …, M). Equations describing the evolution of m_r(t) are studied and it is shown that there is a rapid transition towards a “scaling state”, followed by a slow approach to equilibrium. Near the critical temperature these effects are most pronounced.

A two-component decorated lattice model is introduced to study critical phenomena and phase equilibrium in binary fluids. For certain ranges of interaction parameters, the model demonstrates gas-gas equilibria of the first and second types. Since no assumption of analyticity is made, the model yields non-classical critical behavior. In particular, at the critical double point (the coalescence of two critical points), the exponent β which, before the coalescence, describes the shape of the isothermal coexistence curves in the pressure-mole fraction plane, is changed to 2β. It is shown that this renormalization of β is in agreement with the phenomenological theory of Griffiths and Wheeler.

The effect of the electron-phonon interactions on the states of a single tightly bound electron in a one-dimensional crystal in an external electric field F is discussed with the help of a master equation for the occupation probabilities of electron states. It is found that the occupation probabilities of the Stark ladder states usually do not provide a good description of the state of the system despite the fact that these were eigenstates in the absence of the interactions. A good description is possible in terms of the occupation probabilities of time-dependent band states with $\text{k(t) = k}{}_{\mathrm{o}}\text{+ eFt/}\text{h}\text{̵}$ since these probabilities satisfy a markoffian master equation.

We study the time evolution of a large system consisting of two kinds of particles that can be transformed into each other by an external field. Hydrodynamic equations are derived. The approach to equilibrium of densities and correlation functions is oscillatory with a slowly decaying amplitude like t^{−$\text{1}\text{2}$} for large times t. Generalized $\text{H}$ theorems hold, but for large t the $\text{H}$ quantity again oscillates around the new equilibrium value. Possible removal of these oscillations by coarse-graining is discussed.

A thermodynamically equivalent hamiltonian is constructed for a general spin-$\text{1}\text{2}$ system including infinitely long-range interaction of a ferromagnetic type. A rigorous proof is given for the thermodynamical equivalence.

We give a new generalization of the Foldy-Wouthuysen transformation and show a simple and elegant method of obtaining explicit forms of the Foldy-Wouthuysen transformation and its generalizations by using the U-matrix method of Ramakrishnan. We also show how this method can be used to obtain the transformation which connects the Dirac equation to the non-covariant form of the Dirac equation recently discussed in the literature.