Toward a Mean Field Formulation of the Babcock-Leighton Type Solar Dynamo. I. α-Coefficient versus Durney's Double-Ring Approach

We develop a model of the solar dynamo in which, on the one hand, we follow the Babcock-Leighton approach to include surface processes, such as the production of poloidal field from the decay of active regions, and, on the other hand, we attempt to develop a mean field theory that can be studied in quantitative detail. One of the main challenges in developing such models is to treat the buoyant rise of the toroidal field and the production of poloidal field from it near the surface. A previous paper by Choudhuri, Schüssler, & Dikpati in 1995 did not incorporate buoyancy. We extend this model by two contrasting methods. In one method, we incorporate the generation of the poloidal field near the solar surface by Durney's procedure of double-ring eruption. In the second method, the poloidal field generation is treated by a positive α-effect concentrated near the solar surface coupled with an algorithm for handling buoyancy. The two methods are found to give qualitatively similar results.

Renormalization of noncommutative quantum field theories

We report on a comprehensive analysis of the renormalization of noncommutative phi(4) scalar field theories on the Groenewold-Moyal plane. These scalar field theories are twisted Poincare invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative Lehmann-Symanzik-Zimmermann formalism. DOI: 10.1103/PhysRevD.87.064014

Feshbach resonance in a synthetic non-Abelian gauge field

We study the Feshbach resonance of spin-1/2 particles in a uniform synthetic non-Abelian gauge field that produces spin-orbit coupling and constant spin potentials. We develop a renormalizable quantum field theory including the closed-channel boson which engenders the resonance. We show that the gauge field shifts the Feshbach field where the low-energy scattering length diverges. In addition the Feshbach field is shown to depend on the center-of-mass momentum of the particles. For high-symmetry gauge fields which produce a Rashba spin coupling, we show that the system supports two bound states over a regime of magnetic fields when the background scattering length is negative and the resonance width is comparable to the energy scale of the spin-orbit coupling. We discuss interesting consequences useful for future theoretical and experimental studies, even while our predictions are in agreement with recent experiments.

Branes and supersymmetric quantum field theories

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.

One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.

First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

Possible antigravity regions in F (R) theory?

We construct an F(R) gravity theory corresponding to the Weyl invariant two scalar field theory. We investigate whether such F (R) gravity can have the antigravity regions where the Weyl curvature invariant does not diverge at the Big Bang and Big Crunch singularities. It is revealed that the divergence cannot be evaded completely but can be much milder than that in the original Weyl invariant two scalar field theory. (C) 2014 The Authors. Published by Elsevier B.V.

The effect of the scalar-isovector meson field on hyperon-rich neutron star matter

We investigate the effect of the calar-isovector delta-meson field on the equation of state (EOS) and composition of hyperonic neutron star matter, and the properties of hyperonic neutron stars within the frame work of the relativistic mean field theory. The influence of the delta-field turns out to be quite different and generally weaker for hyperonic neutron star matter as compared to that for npe mu neutron star matter. We find that inclusion of the delta-field enhances the strangeness content slightly and consequently moderately softens the EOS of neutron star matter in its hyperonic phase. As for the composition of hyperonic star matter, the effect of the delta-field is shown to shift the onset of the negatively-charged (positively-charged) hyperons to slightly lower (higher) densities and to enhance (reduce) their abundances. The influence of the delta-field on the maximum mass of hyperonic neutron stars is found to be fairly weak, where as inclusion of the delta-field turns out to enhance sizably both the radii and the moments of inertia of neutron stars with given masses. It is also shown that the effects of the delta-field on the properties of hyperonic neutron stars remain similar in the case of switching off the Sigma hyperons.

Relativistic Mean Field Study of the Z=117 Isotopic Chain

The properties of the Z = 117 isotopic chain are studied within the framework of the axially deformed relativistic mean field theory (RMFT) in the blocked BCS approximation. The ground-state properties, such as binging energies, deformations as well as the possible.. decay energies and lifetimes are calculated with the parameter set of NL-Z2 and compared with results from the finite range droplet model. The analysis by RMFT shows that the isotopes in the range of mass number A = 291 similar to 300 exhibit higher stability, which suggests that they may be promising nuclei to be hopefully synthesized in the lab among the nuclei Z = 117.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Atomic parity nonconservation, neutron radii, and effective field theories of nuclei

Accurately calibrated effective field theories are used to compute atomic parity nonconserving (APNC) observables. Although accurately calibrated, these effective field theories predict a large spread in the neutron skin of heavy nuclei. Whereas the neutron skin is strongly correlated to numerous physical observables, in this contribution we focus on its impact on new physics through APNC observables. The addition of an isoscalar-isovector coupling constant to the effective Lagrangian generates a wide range of values for the neutron skin of heavy nuclei without compromising the success of the model in reproducing well-constrained nuclear observables. Earlier studies have suggested that the use of isotopic ratios of APNC observables may eliminate their sensitivity to atomic structure. This leaves nuclear structure uncertainties as the main impediment for identifying physics beyond the standard model. We establish that uncertainties in the neutron skin of heavy nuclei are at present too large to measure isotopic ratios to better than the 0.1% accuracy required to test the standard model. However, we argue that such uncertainties will be significantly reduced by the upcoming measurement of the neutron radius in 208^Pb at the Jefferson Laboratory.

A new efficient approach to the direct restricted active space self-consistent field method

An implicitly parallel method for integral-block driven restricted active space self-consistent field (RASSCF) algorithms is presented. The approach is based on a model space representation of the RAS active orbitals with an efficient expansion of the model subspaces. The applicability of the method is demonstrated with a RASSCF investigation of the first two excited states of indole

Finite-stretching corrections to the Milner-Witten-Cates theory for polymer brushes

This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance $\mu \propto L^{-1}$ from the substrate, where $L$ is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance $\xi \propto L^{-1/3}$. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.