Partial inner product spaces. II. Operators

We study linear operators between nondegenerate partial inner product spaces and their relationships to selfadjoint operators in a “middle” Hilbert space.     

Linearformen in Logarithmen von U-Zahlen und Transzendenz von Potenzen II

Ohne Zusammenfassung     

Theoretical birefringence of ultraoriented polyethylene from model structure calculations

The birefringence of model structures of ultraoriented polyethylene has been calculated by using the point-dipole concept and the polarizability tensor of the methylene group derived recently by Pietralla. For well-oriented chains the birefringence is determined by the combination of a negative anisotropy of the polarizability tensor of the methylene group and a positive anisotropy of the Lorentz tensor, both with respect to the chain direction. As a consequence it decreases with increasing density. The results are in agreement with experimental values of Mead, Desper, and Porter. In the model the amorphous regions are regarded as a mixture of planar and helical segments arranged in nematiclike bundles which additionally may have a certain distribution of orientation. The birefringence is not much affected by defects which, on the other hand, strongly influence the ultimate mechanical properties.     

Dynamical correlations near instabilities in nonlinear chemical reaction systems

Projection operator techniques are applied to stochastic master equations for homogeneous chemical reaction systems to derive a continued fraction representation for dynamical correlations of the particle numbers. The formalism is applied to two simple nonlinear chemical reactions which exhibit first and second order phase transition analogies, respectively. Numerical results are obtained and various approximations are investigated to describe memory effects arising at the instability points. The method presented here provides a systematic way of investigating the dynamics of nonlinear chemically reacting systems showing unstable behaviour and enhanced fluctuations far from thermal equilibrium.     

Buchbesprechungen

Ohne Zusammenfassung

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Book reviews

     

Spectral properties of reduced Bloch Hamiltonians

Bloch Hamiltonians are defined, and the existence of bands is proven for a large class of periodic operators. The results are strong enough to include most of the reasonable physical models of a single electron in crystals. A notable exception is the Dirac Bloch Hamiltonian for a Coulombic crystal with high charge. Properties of the Bloch waves are briefly described and it is shown that “simple” Bloch Hamiltonians do not have Bloch waves with a finite number of Fourier coefficients. The asymptotic distribution of the bands is determined, and it is shown that for a large class of Hamiltonians, it is determined by the kinetic energy alone.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

Ionic Interactions in a Polarizable Dipolar Hard-Sphere Solvent

Potentials of mean forces of ions in infinitely diluted solutions are calculated by means of a general virial expansion for systems with short and long range interactions. The screened potentials are calculated by the MSA-approximation for the chain sum in the mixture model.     

The pair distribution function of moderately dense quantum fluids

The density expansion for the pair distribution functiong(r) and the structure factorS(k) for interacting quantum systems are given. These functions are thus represented by means of theT-matrices of the two-, three-,... body scattering problem. Possibly existing bound states are taken into account. Explicit expressions for the quantum virial coefficients in terms ofg(r) or ofT-matrices are derived.