Vortex configurations on a thin superconducting spherical shell in the presence of a magnetic dipole

In this work we study vortex configurations on a thin superconducting spherical shell of radius R and thickness d  (R?d?ξ)$(R?d?\xi )$ with a magnetic dipole inside it. The point magnetic dipole (with magnetic moment, m_z$m_z$) is oriented along one of the sphere main axis. It is placed a distance z₀$z_0$ from the center of the sphere. Due to the symmetry of the sample, there are vortices and antivortices pancakes on the shell resulting in zero total vorticity. The vortex interactions with the shielding currents produced by the external fields – as well as with other vortices – are calculated within the London limit. The vortex configurations are obtained by solving numerically the Bardeen–Stephen equation of motion for the vortices. For z₀≈0$z_0\approx 0$ the most frequent vortex configurations present equal arrangements of vortices and antivortices on the north and south hemispheres. For z₀≈0.5R$z_0\approx 0.5R$, the diversity of vortex configurations increases, with a higher number of configurations (in comparison to smaller z₀$z_0$) having different vortices and antivortices distributions on each shell hemisphere. We also study the equilibrium states dependence on the magnetic dipole strength and position.     

Whistler instability in a semi-relativistic bi-Maxwellian plasma

Employing linearized Vlasov–Maxwell system of equations, the whistler instability is discussed for a semi-relativistic bi-Maxwellian distribution. The dispersion relations are analyzed analytically along with the graphical representation and the estimates of the growth rate and instability threshold condition are also presented in the limiting cases i.e., _ξ±=(ω?Ω)/_k∥vt‖?1${\xi }_{\pm }=(\omega ?\Omega )/k_{\parallel }{v}_{t_{\Vert }}?1$ (resonant case) and _ξ±?1${\xi }_{\pm }?1$ (non-resonant case). Further for field free case i.e., _B0=0$B_0=0$, the growth rates for Weibel instability in a semi-relativistic bi-Maxwellian plasma are presented for both the limiting cases.     

Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

Discrete gauge symmetries in discrete MSSM-like orientifolds

Motivated by the necessity of discrete _ZN${\mathbb{Z}}_N$ symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)$U(1)$?s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1)$U(1)$ factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)$U(1)$?s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1)$U(3)\times U(2)\times U(1)\times U(1)$ and U(3)×Sp(2)×U(1)×U(1)$U(3)\times \mathit{Sp}(2)\times U(1)\times U(1)$ configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5)$\mathit{SU}(5)$ GUT models. We find examples of models with _Z2${\mathbb{Z}}_2$ (R-parity) and _Z3${\mathbb{Z}}_3$ symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.     

Three ways to solve the Poisson equation on a sphere with Gaussian forcing

Motivated by the needs of vortex methods, we describe three different exact or approximate solutions to the Poisson equation on the surface of a sphere when the forcing is a Gaussian of the three-dimensional distance, ∇²ψ=exp(-2?²(1-cos(θ))-C^Gauss(?)${\nabla }^2\psi =\exp (-2{?}^2(1-\cos (\theta ))-C^{\mathit{Gauss}}(?)$. (More precisely, the forcing is a Gaussian minus the “Gauss constraint constant”, C^Gauss$C^{\mathit{Gauss}}$; this subtraction is necessary because ψ$\psi$ is bounded, for any type of forcing, only if the integral of the forcing over the sphere is zero [Y. Kimura, H. Okamoto, Vortex on a sphere, J. Phys. Soc. Jpn. 56 (1987) 4203–4206; D.G. Dritschel, Contour dynamics/surgery on the sphere, J. Comput. Phys. 79 (1988) 477–483]. The Legendre polynomial series is simple and yields the exact value of the Gauss constraint constant, but converges slowly for large ?$?$. The analytic solution involves nothing more exotic than the exponential integral, but all four terms are singular at one or the other pole, cancelling in pairs so that ψ$\psi$ is everywhere nice. The method of matched asymptotic expansions yields simpler, uniformly valid approximations as series of inverse even powers of ?$?$ that converge very rapidly for the large values of ?  (?>40)$(?>40)$ appropriate for geophysical vortex computations. The series converges to a nonzero O(exp(-4?²))$O(\exp (-4{?}^2))$ error everywhere except at the south pole where it diverges linearly with order instead of the usual factorial order.     

Jack polynomial fractional quantum Hall states and their generalizations

In the study of fractional quantum Hall states, a certain clustering condition involving up to four integers has been identified. We give a simple proof that particular Jack polynomials with α=−(r−1)/(k+1)$\alpha =-(r-1)/(k+1)$, (r−1)$(r-1)$ and (k+1)$(k+1)$ relatively prime, and with partition given in terms of its frequencies by [n₀^0(r−1)sk^0r−1k^0r−1k?^0r−1m]$[n_0{0}^{(r-1)s}k{0}^{r-1}k{0}^{r-1}k?0^{r-1}m]$ satisfy this clustering condition. Our proof makes essential use of the fact that these Jack polynomials are translationally invariant. We also consider nonsymmetric Jack polynomials, symmetric and nonsymmetric generalized Hermite and Laguerre polynomials, and Macdonald polynomials from the viewpoint of the clustering.     

Comment on reparametrization invariance of quark–lepton complementarity

We study the complementarity between quark and lepton mixing angles (QLC), the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4$\pi /4$. Experimentally in the standard PDG parametrization, two such relations exist approximately. These QLC relations are accidental which only manifest themselves in the PDG parametrization. We propose reparametrization invariant expressions for the complementarity relations in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that |_Vus/_Vud|+|_Ve2/_Ve1|+|_Vus/_Vud||_Ve2/_Ve1|=1$|V_{us}/V_{ud}|+|V_{e2}/V_{e1}|+|V_{us}/V_{ud}||V_{e2}/V_{e1}|=1$ and |_Vcb/_Vtb|+|_Vμ3/_Vτ3|+|_Vcb/_Vtb||_Vμ3/_Vτ3|=1$|V_{cb}/V_{tb}|+|V_{\mu 3}/V_{\tau 3}|+|V_{cb}/V_{tb}||V_{\mu 3}/V_{\tau 3}|=1$. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.     

Strange attractor in the Potts spin glass on hierarchical lattices

The spin-glass q-state Potts model on d  -dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension _dl(q)$d_l(q)$ for q>2$q>2$, the coupling constants probability distribution flows to a low-temperature strange attractor   or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature _Tc(q,d)$T_c(q,d)$. The strange attractor was investigated considering four initial different distributions for q=3$q=3$ and d=5$d=5$ presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.     

Fermi matrix element with isospin breaking

Prompted by the level of accuracy now being achieved in tests of the unitarity of the CKM matrix, we consider the possible modification of the Fermi matrix element for the β  -decay of a neutron, including possible in-medium and isospin violating corrections. While the nuclear modifications lead to very small corrections once the Behrends–Sirlin–Ademollo–Gatto theorem is respected, the effect of the u−d$u-d$ mass difference on the conclusion concerning V_ud$V_{ud}$ is no longer insignificant. Indeed, we suggest that the correction to the value of |V_ud|²+|V_us|²+|V_ub|²${|V_{ud}|}^2+{|V_{us}|}^2+{|V_{ub}|}^2$ is at the level of ¹⁰⁻⁴${10}^{-4}$.     

The propagation kernel for strong coupling gravity

The strong coupling limit of Einstein gravity in d+1$d+1$ dimensions gives rise to a quantum theory where after factorization of the conformal factor mode SL(d,R)/SO(d)$\mathrm{SL}(d,\mathbb{R})/\mathrm{SO}(d)$ nonlinear sigma-models are spatially coupled by the diffeomorphism constraint. A functional integral representation for the theory?s propagation kernel is derived in completions of the proper time gauge which manifestly invokes only physical gauge invariant degrees of freedom. In the weak field limit it reduces to the propagation kernel of massless and transversal-traceless free fields. For strong fields a covariant normal coordinate expansion is developed which covers the configuration manifold globally. Its leading order approximant resembles a semiclassical propagation kernel but without the need to solve the classical constraints. The results have implications for the ground state structure of quantum gravity.     

The anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of a longitudinal field on a bcc lattice

In this work we study the critical behavior of the quantum spin-1/2 anisotropic Heisenberg antiferromagnet in the presence of a longitudinal field on a body centered cubic (bcc) lattice as a function of temperature, anisotropy parameter (Δ)$(\Delta )$ and magnetic field (H  ), where Δ=0$\Delta =0$ and 1 correspond the isotropic Heisenberg and Ising models, respectively. We use the framework of the differential operator technique in the effective-field theory with finite cluster of N  =4 spins (EFT-4). The staggered _ms=(_mA−_mB)/2$m_s=(m_A-m_B)/2$ and total m=(_mA+_mB)/2$m=(m_A+m_B)/2$ magnetizations are numerically calculated, where in the limit of _ms→0$m_s\to 0$ the critical line _TN(H,Δ)$T_N(H,\Delta )$ is obtained. The phase diagram in the T−H$T-H$ plane is discussed as a function of the parameter Δ$\Delta$ for all values of H∈[0,_Hc(Δ)]$H\in [0,H_c(\Delta )]$, where _Hc(Δ)$H_c(\Delta )$ correspond the critical field (_TN=0)$(T_N=0)$. Special focus is given in the low temperature region, where a reentrant behavior is observed around of H=_Hc(Δ)≥_Hc(Δ=1)=8J$H=H_c(\Delta )\ge H_c(\Delta =1)=8J$ in the Ising limit, results in accordance with Monte Carlo simulation, and also was observed for all values of Δ∈[0,1]$\Delta \in [\mathrm{0,1}]$. This reentrant behavior increases with increase of the anisotropy parameter Δ$\Delta$. In the limit of low field, our results for the Heisenberg limit are compared with series expansion values.