Can slow roll inflation induce relevant helical magnetic fields?

We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with $B^2(k) \propto k$, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the evolution of the correlation length and the field amplitude during the inverse cascade and viscous damping of the helical magnetic field in the radiation era after inflation. We conclude that except for low scale inflation with very strong coupling, the magnetic fields generated by such an axial coupling in single field slow roll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies and clusters.Comment: 33 pages 6 figures; v4 to match the accepted version to appear in JCA

Configuration of a Smectic A Liquid Crystal Due to an Isolated Edge Dislocation

We discuss the static configuration of a smectic A liquid crystal subject to an edge dislocation under the assumption the the director and layer normal fields ( n and a , respectively) defining the smectic arrangement are not, in general, equivalent. After constructing the energy density for the smectic, we obtain exact solutions to the equilibrium equations which result from its minimisation at quadratic order in the variables which describe the distortion, and hence a complete description of the smectic configuration across the domain of the sample. We also examine the effect of relaxing the constraint n ≡ a for different values of the constants which characterise the response of the material to distortions, and compare these results with the "classical" case considered by previous authors, in which equivalence of n and a is enforced

A correlated source-sink-potential model consistent with the Meir–Wingreen formula

We model a molecular device as a molecule attached to a set of leads treated at the tight-binding level, with the central molecule described to any desired level of electronic structure theory. Within this model, in the absence of electron–phonon interactions, the Landauer–Büttiker part of the Meir–Wingreen formula is shown to be sufficient to describe the transmission factor of the correlated device. The key to this demonstration is to ensure that the correlation self-energy has the same functional form as the exact correlation self-energy. This form implies that nonsymmetric contributions to the Meir–Wingreen formula vanish, and hence, conservation of current is achieved without the need for Green’s Function self-consistency. An extension of the Source-Sink-Potential (SSP) approach gives a computational route to the calculation and interpretation of electron transmission in correlated systems. In this picture, current passes through internal molecular channels via resonance states with complex-valued energies. Each resonance state arises from one of the states in the Lehmann expansion of the one-electron Green’s function, hole conduction derived from ionized states, and particle conduction from attached states. In the correlated device, the dependence of transmission on electron energy is determined by four structural polynomials, as it was in the tight-binding (Hückel) version of the SSP method. Hence, there are active and inert conduction channels (in the correlated case, linked to Dyson orbitals) governed by a set of selection rules that map smoothly onto the simplest picture

Missing Links: Referrer Behavior and Job Segregation

How does referral recruitment contribute to job segregation, and what can organizations do about it? Current theory on network effects in the labor market emphasizes the job-seeker perspective, focusing on the segregated nature of job-seekers’ information and contact networks, and leaves little role for organizational influence. But employee referrals are necessarily initiated from within a firm by referrers. We argue that referrer behavior is the missing link that can help organizations manage the segregating effects of referring. Adopting the referrer’s perspective of the process, we develop a computational model which integrates a set of empirically documented referrer behavior mechanisms gleaned from extant organizational case studies. Using this model, we compare the segregating effects of referring when these behaviors are inactive to the effects when the behaviors are active. We show that referrer behaviors substantially boost the segregating effects of referring. This impact of referrer behavior presents an opportunity for organizations. Contrary to popular wisdom, we show that organizational policies designed to influence referrer behaviors can mitigate most if not all of the segregating effects of referring

Maple User Manual

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