Half‐Space Neutron Transport with Linearly Anisotropic Scattering

The method developed by Case is used to solve four time‐independent, one‐speed problems for neutron transport in a homogeneous medium where the scattering function is linear in the cosine of the scattering angle. The solutions to the albedo, Milne, Green's function, and constant isotropic source problems for a half‐space are facilitated by the use of half‐range bi‐orthogonality relations between the eigenfunctions of the homogeneous transport equation. Expressions are also derived for the emerging angular densities and the densities and net currents on the surface of the half‐space.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70296/2/JMAPAQ-6-12-1939-1.pd

Time‐Dependent One‐Speed Albedo Problem for a Semi‐Infinite Medium

A Laplace transformation technique is used to determine the neutron distribution in a semi‐infinite medium which has been irradiated by a neutron pulse. The result is given in terms of known solutions of Milne's problem and of the steady‐state albedo problem, which in turn are expressed by aid of Case's X‐function. Simple asymptotic approximations, valid for t ≫ 1, are deduced from the exact result.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71087/2/JMAPAQ-6-7-1125-1.pd

Closure Relations for the Eigenfunctions of the One‐Speed Transport Equation

Orthogonality relations for the eigenfunctions of the one‐speed transport equation are used to derive the corresponding closure relations. These express in a concise form the completeness properties previously proved by Case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69771/2/JMAPAQ-8-4-823-1.pd

Relaxation rates and collision integrals for Bose-Einstein condensates

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $\mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $\mathcal{G}^{22}$ and $\mathcal{G}^{12}$. In this work, we show that the third collision integral $\mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/201

Photoinduced IR absorption in (La(1-x)Sr(x)Mn)(1-\delta)O3: changes of the anti-Jahn-Teller polaron binding energy with doping

Photoinduced IR absorption was measured in (La(1-x)Sr(x)Mn)(1-\delta)O3. A midinfrared peak centered at ~ 5000 cm$^{-1}$ was observed in the x=0 antiferromagnetic sample. The peak diminishes and softens as hole doping is increased. The origin of the photoinduced absorption peak is atributted to the photon assisted hopping of anti-Jahn-Teller polarons formed by photoexcited charge carriers, whose binding energy decreases with increasing hole doping. The shape of the peak indicates that the polarons are small.Comment: 5 pages, 3 figures, submitted to PR

Kinetic theory of diffusion in liquids: A hydrodynamic approximation

Diffusion in simple classical liquids is analyzed in terms of the test-particle phase-space density, with emphasis upon its long-time behavior. The Green's function of the generalized Fokker-Planck equation is used to define auxiliary quantities, in particular the transport mean path that enters solutions of the Chapman-Enskog type. Approximations for the lowest eigenvalues and eigenfunctions of the Fourier- and Laplace-transformed F.-P. operator σ_(ks) are constructed, and an expansion for the resolvent operator (s + ik · v – σ_(ks))^(-1) proposed. With the additional assumption that branch-points on the negative real axis of s are the only singularities of the transformed F.-P. operator, a Laplace inversion is tentatively carried out, so that the general form of the solution is obtained. This is found to agree with the solution derived by hydrodynamic arguments. Only in a limited sense is the latter method equivalent to that of mode-mode coupling