Optimization of the Ballistic Guide Design for the SNS FNPB 8.9 A Neutron Line

The optimization of the ballistic guide design for the SNS Fundamental Neutron Physics Beamline 8.9 A line is described. With a careful tuning of the shape of the curve for the tapered section and the width of the straight section, this optimization resulted in more than 75% increase in the neutron flux exiting the 33 m long guide over a straight m=3.5 guide with the same length.Comment: 21 pages, 13 figures; added a paragraph on existing ballistic guides to respond to referee comments; accepted for publication in Nuclear Inst. and Methods in Physics Research,

Momentum-resolved electron-phonon interaction in lead determined by neutron resonance spin-echo spectroscopy

Neutron resonance spin-echo spectroscopy was used to monitor the temperature evolution of the linewidths of transverse acoustic phonons in lead across the superconducting transition temperature, $T_c$, over an extended range of the Brillouin zone. For phonons with energies below the superconducting energy gap, a linewidth reduction of maximum amplitude $\sim 6 \mu$eV was observed below $T_c$. The electron-phonon contribution to the phonon lifetime extracted from these data is in satisfactory overall agreement with {\it ab-initio} lattice-dynamical calculations, but significant deviations are found

Landau damping of Bogoliubov excitations in optical lattices at finite temperature

We study the damping of Bogoliubov excitations in an optical lattice at finite temperatures. For simplicity, we consider a Bose-Hubbard tight-binding model and limit our analysis to the lowest excitation band. We use the Popov approximation to calculate the temperature dependence of the number of condensate atoms $n^{\rm c 0}(T)$ in each lattice well. We calculate the Landau damping of a Bogoliubov excitation in an optical lattice due to coupling to a thermal cloud of excitations. While most of the paper concentrates on 1D optical lattices, we also briefly present results for 2D and 3D lattices. For energy conservation to be satisfied, we find that the excitations in the collision process must exhibit anomalous dispersion ({\it i.e.} the excitation energy must bend upward at low momentum), as also exhibited by phonons in superfluid $^4\rm{He}$. This leads to the sudden disappearance of all damping processes in $D$-dimensional simple cubic optical lattice when $U n^{\rm c 0}\ge 6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element. Beliaev damping in a 1D optical lattice is briefly discussed.Comment: 28 pages, 9 figure

The mixing time of the switch Markov chains: a unified approach

Since 1997 a considerable effort has been spent to study the mixing time of switch Markov chains on the realizations of graphic degree sequences of simple graphs. Several results were proved on rapidly mixing Markov chains on unconstrained, bipartite, and directed sequences, using different mechanisms. The aim of this paper is to unify these approaches. We will illustrate the strength of the unified method by showing that on any $P$-stable family of unconstrained/bipartite/directed degree sequences the switch Markov chain is rapidly mixing. This is a common generalization of every known result that shows the rapid mixing nature of the switch Markov chain on a region of degree sequences. Two applications of this general result will be presented. One is an almost uniform sampler for power-law degree sequences with exponent $\gamma>1+\sqrt{3}$. The other one shows that the switch Markov chain on the degree sequence of an Erd\H{o}s-R\'enyi random graph $G(n,p)$ is asymptotically almost surely rapidly mixing if $p$ is bounded away from 0 and 1 by at least $\frac{5\log n}{n-1}$.Comment: Clarification

Interrelations Between the Neutron's Magnetic Interactions and the Magnetic Aharonov-Bohm Effect

It is proved that the phase shift of a polarized neutron interacting with a spatially uniform time-dependent magnetic field, demonstrates the same physical principles as the magnetic Aharonov-Bohm effect. The crucial role of inert objects is explained, thereby proving the quantum mechanical nature of the effect. It is also proved that the nonsimply connectedness of the field-free region is not a profound property of the system and that it cannot be regarded as a sufficient condition for a nonzero phase shift.Comment: 18 pages, 1 postscript figure, Late

Approximate Sampling of Graphs with Near-PP-stable Degree Intervals

The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current result about the well-studied switch Markov chain is that it is rapidly mixing on P-stable degree sequences (see DOI:10.1016/j.ejc.2021.103421). The switch Markov chain does not change any degree sequence. However, there are cases where degree intervals are specified rather than a single degree sequence. (A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed.) Rechner, Strowick, and M\"uller-Hannemann introduced in 2018 the notion of degree interval Markov chain which uses three (separately well-studied) local operations (switch, hinge-flip and toggle), and employing on degree sequence realizations where any two sequences under scrutiny have very small coordinate-wise distance. Recently Amanatidis and Kleer published a beautiful paper (arXiv:2110.09068), showing that the degree interval Markov chain is rapidly mixing if the sequences are coming from a system of very thin intervals which are centered not far from a regular degree sequence. In this paper we extend substantially their result, showing that the degree interval Markov chain is rapidly mixing if the intervals are centred at P-stable degree sequences.Comment: Fixed the titl

Accumulation of three-body resonances above two-body thresholds

We calculate resonances in three-body systems with attractive Coulomb potentials by solving the homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved by using the Coulomb-Sturmian separable expansion approach. This approach provides an exact treatment of the threshold behavior of the three-body Coulombic systems. We considered the negative positronium ion and, besides locating all the previously know $S$-wave resonances, we found a whole bunch of new resonances accumulated just slightly above the two-body thresholds. The way they accumulate indicates that probably there are infinitely many resonances just above the two-body thresholds, and this might be a general property of three-body systems with attractive Coulomb potentials.Comment: 4 pages, 3 figure

Rooted NNI moves on tree-based phylogenetic networks

We show that the space of rooted tree-based phylogenetic networks is connected under rooted nearest-neighbour interchange (rNNI) moves.Comment: Fixed typos and references to labels in the last subsectio