Misleading signposts along the de Broglie-Bohm road to quantum mechanics

Eighty years after de Broglie's, and a little more than half a century after Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics), which is presumably the simplest theory which explains the orthodox quantum mechanics formalism, has reached an exemplary state of conceptual clarity and mathematical integrity. No other theory of quantum mechanics comes even close. Yet anyone curious enough to walk this road to quantum mechanics is soon being confused by many misleading signposts that have been put up, and not just by its detractors, but unfortunately enough also by some of its proponents. This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted for publication in Foundations of Physics. A "slip of pen" in the bibliography has been corrected -- thanks go to Oliver Passon for catching it

Thermal conductivity of amorphous polymers and its dependence on molecular weight

Thermal conductivity is an important transport property governing the performance of polymers in non-isothermal conditions. Nevertheless, its dependence on molecular weight M has not been the subject of as much attention as other properties of polymeric materials. We determine the thermal conductivity of polystyrene and polyisobutylene for a wide range of molecular weight by measuring the density, heat capacity and thermal diffusivity. Using coarse-graining and reverse mapping methods, we were able to produce molecular melts to study the thermal conductivity of polystyrene using molecular dynamics simulations over a similar range of molecular weight. We find satisfactory agreement between the experimental and simulation results. However, all of our results show that thermal conductivity depends only slightly on molecular weight up the entanglement limit and it is independent thereafter. Our results put into question the few previous experimental studies on this topic by showing that the previously accepted proportionality to $\sqrt{M}$ does not hold. Our findings could have significant implications for the understanding of complex phenomena such as anisotropic thermal conductivity in polymers subjected to flow.Marie Skłodowska-Curie IF MTCIATTP 750985

Radiolarian faunal characteristics in Oligocene of the Kerguelen Plateau, Leg 183, Site 1138

Three sites from Ocean Drilling Program (ODP) Leg 183 (Kerguelen Plateau) have been analyzed to document faunal change in high-latitude radiolarians and to compare the faunal change to Eocene-Oligocene climatic deterioration. Radiolarians are not preserved in Eocene sediments. In Oligocene sediments, radiolarian preservation improves in a stepwise manner toward the Miocene. A total of 115 species were found in lower Oligocene samples from Site 1138; all are documented herein. Radiolarian preservation is presumably linked to productivity triggered by climatic cooling during the early Oligocene. Similar patterns of improving preservation through the Eocene/Oligocene boundary are documented from several Deep Sea Drilling Project and ODP sites in the Southern Ocean, indicating a general pattern. In contrast to the Southern Kerguelen Plateau, however, proxies for productivity are more divergent at Site 1138 (Central Kerguelen Plateau). Whereas carbonate dissolution, as indicated by poor preservation of foraminifers and common hiatuses, is very pronounced in the upper Eocene-lowermost Oligocene, the quality of radiolarian and diatom preservation does not significantly increase until the uppermost lower Oligocene. Multiple measures of radiolarian diversity in the Oligocene from Site 1138 closely parallel radiolarian preservation, indicating that preserved radiolarian diversity is controlled by productivity

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a few minor technical fixes. Modified title slightl

Galaxy alignments: An overview

The alignments between galaxies, their underlying matter structures, and the cosmic web constitute vital ingredients for a comprehensive understanding of gravity, the nature of matter, and structure formation in the Universe. We provide an overview on the state of the art in the study of these alignment processes and their observational signatures, aimed at a non-specialist audience. The development of the field over the past one hundred years is briefly reviewed. We also discuss the impact of galaxy alignments on measurements of weak gravitational lensing, and discuss avenues for making theoretical and observational progress over the coming decade.Comment: 43 pages excl. references, 16 figures; minor changes to match version published in Space Science Reviews; part of a topical volume on galaxy alignments, with companion papers at arXiv:1504.05546 and arXiv:1504.0546

The Vlasov continuum limit for the classical microcanonical ensemble

For classical Hamiltonian N-body systems with mildly regular pair interaction potential it is shown that when N tends to infinity in a fixed bounded domain, with energy E scaling quadratically in N proportional to e, then Boltzmann's ergodic ensemble entropy S(N,E) has the asymptotic expansion S(N,E) = - N log N + s(e) N + o(N); here, the N log N term is combinatorial in origin and independent of the rescaled Hamiltonian while s(e) is the system-specific Boltzmann entropy per particle, i.e. -s(e) is the minimum of Boltzmann's H-function for a perfect gas of "energy" e subjected to a combination of externally and self-generated fields. It is also shown that any limit point of the n-point marginal ensemble measures is a linear convex superposition of n-fold products of the H-function-minimizing one-point functions. The proofs are direct, in the sense that (a) the map E to S(E) is studied rather than its inverse S to E(S); (b) no regularization of the microcanonical measure Dirac(E-H) is invoked, and (c) no detour via the canonical ensemble. The proofs hold irrespective of whether microcanonical and canonical ensembles are equivalent or not.Comment: Final version; a few typos corrected; minor changes in the presentatio

Nonperturbative calculation of Born-Infeld effects on the Schroedinger spectrum of the hydrogen atom

We present the first nonperturbative numerical calculations of the nonrelativistic hydrogen spectrum as predicted by first-quantized electrodynamics with nonlinear Maxwell-Born-Infeld field equations. We also show rigorous upper and lower bounds on the ground state. When judged against empirical data our results significantly restrict the range of viable values of the new electromagnetic constant which is introduced by the Born-Infeld theory. We assess Born's own proposal for the value of his constant.Comment: 4p., 2 figs, 1 table; submitted for publicatio

Galaxy alignments: Observations and impact on cosmology

Galaxy shapes are not randomly oriented, rather they are statistically aligned in a way that can depend on formation environment, history and galaxy type. Studying the alignment of galaxies can therefore deliver important information about the physics of galaxy formation and evolution as well as the growth of structure in the Universe. In this review paper we summarise key measurements of galaxy alignments, divided by galaxy type, scale and environment. We also cover the statistics and formalism necessary to understand the observations in the literature. With the emergence of weak gravitational lensing as a precision probe of cosmology, galaxy alignments have taken on an added importance because they can mimic cosmic shear, the effect of gravitational lensing by large-scale structure on observed galaxy shapes. This makes galaxy alignments, commonly referred to as intrinsic alignments, an important systematic effect in weak lensing studies. We quantify the impact of intrinsic alignments on cosmic shear surveys and finish by reviewing practical mitigation techniques which attempt to remove contamination by intrinsic alignments.Comment: 52 pages excl. references, 16 figures; minor changes to match version published in Space Science Reviews; part of a topical volume on galaxy alignments, with companion papers arXiv:1504.05456 and arXiv:1504.0554