Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and AC conductivity of a homogeneous superconductor with arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers--Kronig transforms. A number of applications illustrates its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.Comment: 20 pages, 7 figures, calculation of Casimir energy adde

Technical note: statistical generation of climate-perturbed flow duration curves

Assessing the robustness of a water resource system's performance under climate change involves exploring a wide range of streamflow conditions. This is often achieved through rainfall–runoff models, but these are commonly validated under historical conditions with no guarantee that calibrated parameters would still be valid in a different climate. In this note, we introduce a new method for the statistical generation of plausible streamflow futures. It flexibly combines changes in average flows with changes in the frequency and magnitude of high and low flows. It relies on a three-parameter analytical representation of the flow duration curve (FDC) that has been proved to perform well across a range of basins in different climates. We rigorously prove that, for common sets of streamflow statistics mirroring average behaviour, variability, and low flows, the parameterisation of the FDC under this representation is unique. We also show that conditions applied to these statistics for a solution to exist are commonly met in practice. These analytical results imply that streamflow futures can be explored by sampling wide ranges of three key flow statistics and by deriving the corresponding FDC in relation to model basin response across the full spectrum of flow conditions. We illustrate this method by exploring in which hydro-climatic futures a proposed run-of-river hydropower plant in eastern Turkey is financially viable. Results show that, contrary to approaches that modify streamflow statistics using multipliers applied uniformly throughout a time series, our approach seamlessly represents a large range of futures with increased frequencies of both high and low flows. This matches expected impacts of climate change in the region and supports analyses of the financial robustness of the proposed infrastructure to climate change. We conclude by highlighting how refinements to the approach could further support rigorous explorations of hydro-climatic futures without the help of rainfall–runoff models

Taking Blockchain Seriously

In the present techno-political moment it is clear that ignoring or dismissing the hype surrounding blockchain is unwise, and certainly for regulatory authorities and governments who must keep a grip on the technology and those promoting it, in order to ensure democratic accountability and regulatory legitimacy within the blockchain ecosystem and beyond. Blockchain is telling (and showing) us something very important about the evolution of capital and neoliberal economic reason, and the likely impact in the near future on forms and patterns of work, social organization, and, crucially, on communities and individuals who lack influence over the technologies and data that increasingly shape and control their lives. In this short essay I introduce some of the problems in the regulation of blockchain and offer counter-narratives aimed at cutting through the hype fuelling the ascendency of this most contemporary of technologies

Analytic Approach to Perturbative QCD

The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q^2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD beta-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.Comment: Latex-file, 19 pages, 2 tables, 51 references, to be published in Int. J. Mod. Phys.

Calculating Casimir Energies in Renormalizable Quantum Field Theory

Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been studied by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension $D$ not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for $D\ne1$. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in $D$ and three dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B and Appendix, and other minor correction

Casimir energy in the MIT bag model

The vacuum energies corresponding to massive Dirac fields with the boundary conditions of the MIT bag model are obtained. The calculations are done with the fields occupying the regions inside and outside the bag, separately. The renormalization procedure for each of the situations is studied in detail, in particular the differences occurring with respect to the case when the field extends over the whole space. The final result contains several constants undergoing renormalization, which can be determined only experimentally. The non-trivial finite parts which appear in the massive case are found exactly, providing a precise determination of the complete, renormalized zero-point energy for the first time, in the fermionic case. The vacuum energy behaves like inverse powers of the mass for large masses.Comment: 19 pages, Latex, 1 Postscript figure, submitted to J. Phys.

One Loop Multiphoton Helicity Amplitudes

We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for $n$-photon scattering and electron-positron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow {\it all}\ of the integrations to be performed explicitly. For $n$-photon scattering, we find that unless $n=4$, the amplitudes for the helicity configurations (+++...+) and (-++...+) vanish to one-loop order.Comment: 27 pages + 4 uuencoded figures (included), Fermilab-Pub-93/327-T, RevTe

Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation

We investigate the effective conductivity ($\sigma_e$) of a class of amorphous media defined by the level-cut of a Gaussian random field. The three point solid-solid correlation function is derived and utilised in the evaluation of the Beran-Milton bounds. Simulations are used to calculate $\sigma_e$ for a variety of fields and volume fractions at several different conductivity contrasts. Relatively large differences in $\sigma_e$ are observed between the Gaussian media and the identical overlapping sphere model used previously as a `model' amorphous medium. In contrast $\sigma_e$ shows little variability between different Gaussian media.Comment: 15 pages, 14 figure

Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, $\sum\frac12\hbar\omega$, seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, $\langle T_{00}\rangle$, typically diverge near boundaries. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein's equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Ros

Extensive complex neocortical movement topography devolves to simple output following experimental stroke in mice

The neocortex encodes complex and simple motor outputs in all mammalian species that have been tested. Given that changes in neocortical reorganization (and corresponding corticospinal output) have been implicated in long term motor recovery after stroke injury, there remains a need to understand this biology in order to expedite and optimize clinical care. Here, changes in the neocortical topography of complex and simple movement outputs were evaluated in mice following experimental middle cerebral artery occlusion (MCAo). Neocortical motor output was defined using long-duration parameters of intracortical microstimulation (LD-ICMS) based on area and spatial coordinates of separate motor output types to build upon our recent report in uninjured mice. LD-ICMS test sites that elicited complex (multi-joint) movement, simple (single skeletal joint) movement, as well as co-elicited FORELIMB + HINDLIMB responses were detected and recorded. Forelimb reaching behavior was assessed using the single pellet reaching (SPR) task. At 6 weeks post-surgery, behavioral deficits persisted and neocortical territories for separate movements exhibited differences in neocortical area, and spatial location, and differed between MCAo-Injured animals (i.e., the MCAo group) and Sham-Injured animals (i.e., the Control group). MCAo-Injury reduced neocortical area of complex movements while increasing area of simple movements. Limited effects of injury were detected for spatial coordinates of neocortical movements. Significant positive correlations were detected between final SPR performance and either area of complex retract or area of co-occurring FORELIMB + HINDLIMB sites