Th.J. Siskens

On a soluble model of an antiferromagnetic chain with alternating interactions and magnetic moments

The one-dimensional anisotropic XY model with alternating nearest-neighbour interactions and magnetic moments is investigated. The singularities of the susceptibility χzz in the ground state are studied in detail. In the general anisotropic case χzz can exhibit two logarithmic singularities at two different values of the applied magnetic field b. If the interactions satisfy a certain relation which will be reffered to as the pseudoisotropic condition (which includes the isotropic case), χzz can have two power-12 singularities at the upper side of the lower critical field and the lower side of the upper critical field. Deviations from this behaviour which occur for special values of the interaction constants are discussed in some detail. Finally the specific heat is studied in the low- and high-temperature limits.

On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. II

Time-dependent properties of the one-dimensional XY model with Dzyaloshinsky interactions in the presence of a magnetic field in the z direction are investigated. Explicit expressions are derived for the time correlation functions of the z components of two spins and the time auto-correlation functions of Mz (= the z component of the magnetization). The ergodic behaviour of Mz in the thermodynamic limit is discussed in some detail. Furthermore an exact expression is derived for the time dependence of the average of Mz in a typical nonequilibrium situation. Finally the frequency-dependent susceptibility is evaluated.

Time correlation functions and ergodic properties in the alternating XY-chain

Explicit expressions for the time-dependent spin correlation functions are derived for the one-dimensional alternating XY-model in zero field. The ergodic properties of the wave-number dependent magnetization are discussed. It is found that the magnetization is ergodic, apart from exceptional cases, such as e.g. the homogeneous XY-model.

Relativistic kinetic theory of quantum systems: IV. Transport equation for the neutrino component of an eeνeνe-mixture

Abstract The transport equation for a neutrino system derived previously is extended to include binary collisions involving electrons, positrons and antineutrinos. The transition amplitudes for these collision processes are specified in terms of an effective Hamiltonian density following from the Weinberg-Salam theory. The resulting equation incorporates the reactive processes e e ↔ ν ν and exhibits the electron and positron spins explicitly. It is shown to be form invariant under Lorentz transformations.

The weak interaction and the isotropy of the universe

Abstract We consider viscous dissipation of anisotropy and the corresponding entropy production during the lepton era of the universe, and investigate their sensitivity to the viscosity coefficients of the cosmological fluid.

Transition amplitudes and probabilities for the Weinberg-Salam model

Transition probabilities for the processes vv↔vv, vv, vv↔vv, and spin-dependent transition amplitudes for the processes ve↔ve, vē↔vē, ve↔ve, ve↔ve and vv↔eē are calculated in lowest order for the Weinberg-Salam model.

Transport coefficients for the cosmological fluid during the lepton era

Abstract The coefficients of heat conductivity, diffusion, thermal diffusion, shear and bulk viscosity are evaluated for a non-degenerate (eν e ) mixture in which the particles interact in accordance with Weinberg-Salam model.

Relativistic kinetic theory of quantum systems: V. Transport equations for the massive components of an eeveve-mixture

Covariant transport equations are derived for the Wigner function matrices describing the massive components of a non-degenerate eeveve-mixture. The collision terms pertaining to the various collision processes involve spin-dependent transition amplitudes which are specified in terms of an effective Hamiltonian density obtained from the Weinberg-Salam theory.

Antiferromagnetic chain with Dzyaloshinsky interactions

Abstract Some exact results for a one-dimensional anisotropic XY-model with antisymmetric exchange are presented.

Relativistic kinetic theory of quantum systems: VII. Transport coefficients for (eve) and (evμ) mixtures

Abstract For (e v e ) and (e v μ ) binary mixtures the transport coefficients are evaluated as functions of the temperature and composition of the system. The particles are assumed to interact according to the Weinberg-Salam model. Results for the two mixtures are compared, and are contrasted to corresponding results obtained on the basis of a mean free path model.