An analytical solver for the multi-group two-dimensional neutron-diffusion equation by integral transform techniques

In this work, we present an analytical solver for neutron diffusion in a rectangular two-dimensional geometry by a two-step integral transform procedure. To this end, we consider a regionwise homogeneous problem for two energy groups, i.e. fast and thermal neutrons, respectively. Each region has its specific physical properties, specified by cross-sections and diffusion constants. The problem is set up by two coupled bi-dimensional diffusion equations in agreement with general perturbation theory. These are solved by integral transforms Laplace transform and generalized integral transform technique yielding analytical expressions for the scalar neutron fluxes. The solutions for neutron fluxes are presented for fast and thermal neutrons in the four regions

Proof of an entropy conjecture for Bloch coherent spin states and its generalizations

Wehrl used Glauber coherent states to define a map from quantum density matrices to classical phase space densities and conjectured that for Glauber coherent states the mininimum classical entropy would occur for density matrices equal to projectors onto coherent states. This was proved by Lieb in 1978 who also extended the conjecture to Bloch SU(2) spin-coherent states for every angular momentum $J$. This conjecture is proved here. We also recall our 1991 extension of the Wehrl map to a quantum channel from $J$ to $K=J+1/2, J+1, ...$, with $K=\infty$ corresponding to the Wehrl map to classical densities. For each $J$ and $J<K\leq \infty$ we show that the minimal output entropy for these channels occurs for a $J$ coherent state. We also show that coherent states both Glauber and Bloch minimize any concave functional, not just entropy.Comment: Version 2 only minor change

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

The inclusive 56Fe(nu_e,e-)56Co cross section

We study the 56Fe(nu_e,e^-)56Co cross section for the KARMEN neutrino spectrum. The Gamow-Teller contribution to the cross section is calculated within the shell model, while the forbidden transitions are evaluated within the continuum random phase approximation. We find a total cross section of 2.73 x 10^-40 cm^2, in agreement with the data.Comment: 4 pages, 1 figure. Replaced due to new improved calculation

Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field

The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator. A non-linear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary-value problem. The semiclassical spin dynamics is thus readily amenable to numerical methods.Comment: 16 pages, submitted to Journal of Physics

On the Density Dependent Nuclear Matter Compressibility

In the present work we apply a quantum hadrodynamic effective model in the mean-field approximation to the description of neutron stars. We consider an adjustable derivative-coupling model and study the parameter influence on the dynamics of the system by analyzing the full range of values they can take. We establish a set of parameters which define a specific model that is able to describe phenomenological properties such as the effective nucleon mass at saturation as well as global static properties of neutron stars (mass and radius). If one uses observational data to fix the maximum mass for neutron stars by a specific model, we are able to predict the compression modulus of nuclear matter K = 257,2MeV