230 research outputs found
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 . This conjecture is proved here. We also recall our
1991 extension of the Wehrl map to a quantum channel from to , with corresponding to the Wehrl map to classical densities.
For each and we show that the minimal output entropy for
these channels occurs for a 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
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