Beam extraction and delivery at compact neutron sources

The beam performance of a source of radiation is primarily characterized by its brightness, which remains constant in a conservative force field along the propagation of the beam. The neutron flux at an area with direct view to a homogenous radiation emitting moderator surface will just depend on the solid angle of beam divergence as determined by the moderator size. Recently it was found that by reducing the size of neutron moderators their brightness can be enhanced by a factor in the range of up to 3–6. In direct view of such moderators from sizable distances often required in neutron scattering applications the beam divergence will become reduced. Supermirror based neutron optical guide systems allow us to deliver neutron beam divergences independently of distance from the source. Due to the low radiation fields at compact sources such systems can be placed close to the neutron emitting moderators, a specific advantage and a new design feature. Focusing type neutron guides with phase space acceptance properly matched to the phase space to be delivered over distance can provide for beam delivery with small losses of brightness within a convenient and flexible range of beam parameters

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

Shape functions of dipolar ferromagnets at the Curie point

We present a complete mode coupling theory for the critical dynamics of ferromagnets above the Curie point with both short range exchange and long range dipolar interaction. This theory allows us to determine the full Kubo relaxation functions at the critical point. In particular, we are able to explain recent spin echo measurements

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

Damping of Bogoliubov Excitations in Optical Lattices

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to coupling to a thermal cloud of such excitations. For simplicity, we consider a 1D Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion'', analogous to phonons in superfluid $^4\rm{He}$. This leads to the disappearance of all damping processes when $U n^{\rm c 0}\ge 6t$, where $U$ is the on-site interaction, $t$ is the hopping matrix element and $n^{\rm c 0}(T)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in 2D and 3D optical lattices. The disappearance of Beliaev damping above a threshold wavevector is noted.Comment: 4pages, 5figures, submitted to Phys. Rev. Let

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

PTAS for Sparse General-Valued CSPs

We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker's approach gives a PTAS on planar graphs, excluded-minor classes, and beyond. For Max-CSPs, and even more generally, maximisation finite-valued CSPs (where constraints are arbitrary non-negative functions), Romero, Wrochna, and \v{Z}ivn\'y [SODA'21] showed that the Sherali-Adams LP relaxation gives a simple PTAS for all fractionally-treewidth-fragile classes, which is the most general "sparsity" condition for which a PTAS is known. We extend these results to general-valued CSPs, which include "crisp" (or "strict") constraints that have to be satisfied by every feasible assignment. The only condition on the crisp constraints is that their domain contains an element which is at least as feasible as all the others (but possibly less valuable). For minimisation general-valued CSPs with crisp constraints, we present a PTAS for all Baker graph classes -- a definition by Dvo\v{r}\'ak [SODA'20] which encompasses all classes where Baker's technique is known to work, except possibly for fractionally-treewidth-fragile classes. While this is standard for problems satisfying a certain monotonicity condition on crisp constraints, we show this can be relaxed to diagonalisability -- a property of relational structures connected to logics, statistical physics, and random CSPs

Successive shortest paths in complete graphs with random edge weights

Consider a complete graph Kn with edge weights drawn independently from a uniform distribution U(0,1). The weight of the shortest (minimum-weight) path P1 between two given vertices is known to be ln n/n, asymptotically. Define a second-shortest path P2 to be the shortest path edge-disjoint from P1, and consider more generally the shortest path Pk edge-disjoint from all earlier paths. We show that the cost Xk of Pk converges in probability to 2k/n + ln n/n uniformly for all k ≤ n − 1. We show analogous results when the edge weights are drawn from an exponential distribution. The same results characterize the collectively cheapest k edge-disjoint paths, that is, a minimum-cost k-flow. We also obtain the expectation of Xk conditioned on the existence of Pk