arXiv subjects
Publications and source records attributed to A. Kull.
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated using a generalized version of Feynman's checkerboard model. They turn out to be closely related to the continuum propagator.
An analytic collapse model for the formation and density distribution of virialized cold dark matter halos is proposed. Hierarchical structure formation is taken into account explicitly. Monte Carlo methods are used to generate samples of mass histories of virialized halos. The mean density distribution found from the collapse model is in good agreement with numerical results in the mass range from $10^{11}M_\odot$ to $10^{15}M_\odot$ and in the radial range form $0.05 r_{200}$ to $r_{200}$.
We revisit the path integral description of the motion of a relativistic electron. Applying a minor but well motivated conceptional change to Feynman's chessboard model, we obtain exact solutions of the Dirac equation. The calculation is performed by means of a particular simple method different from both the combinatorial approach envisaged by Feynman and its Ising model correspondence.
We report on X-ray observations of the core of the Shapley Supercluster. Combining data from pointed observations of the ROSAT PSPC detector and data from the ROSAT All-Sky Survey, the observed region covers an area of $6^\circ \times 3^\circ$. It contains the central clusters A3562, A3558 and A3556. We find clear evidence for X-ray emission connecting the three clusters. This confirms the existence of a filamentary, physical structure embedding the three clusters A3562, A3558 and A3556. We also find evidence for faint emission westwards of A3556. In total, the extension of the filamentary X-ray emission of the core of the Shapley Supercluster amounts up to at least $\sim 17.5 h_{50}^{-1}$ Mpc. The total luminosity in the 0.1-2.4 keV energy band is $\sim 16\times10^{44} h_{50}^{-2}$ erg s$^{-1}$.
The statistical mechanical investigation of Violent Relaxation of phase space elements of different densities first derived by Lynden-Bell (1967) is re-examined. It is found that the mass independence of the equations of motion of Violent Relaxation calls for a constraint on the volume of the phase space elements used to formulate the statistical mechanical description of Violent Relaxation. In agreement with observations of astrophysical objects believed to have been subject to Violent Relaxation (e.g. clusters of galaxies), the coarse grained phase space distribution $\bar{f}$ of the final state in the non-degenerate limit turns into a superposition of Maxwellians of a common velocity dispersion. Thus, the velocity dispersion problem present in the investigation of Lynden-Bell (1967) is removed.
The statistical mechanical investigation of violent relaxation (Lynden-Bell 1967) is extended to indistinguishable objects. It is found that, coincidentally, the equilibrium distribution is the same as that obtained for classical objects. For massive neutrinos, the Tremaine \& Gunn (1979) phase space bound is revisited and reinterpretated as the limit indicating the onset of degeneracy related to the coarse-grained phase space distribution. In the context of one of the currently most popular cosmological models, the Cold and Hot Dark Matter (CHDM) model (Primack et al. 1995), the onset of degeneracy may be of importance in the core region of clusters of galaxies. Degeneracy allows the neutrino HDM density to exceed the limit imposed by the Tremaine \& Gunn (1979) bound while accounting for the phase space bound.