Two charges on a plane in a magnetic field: II. Moving neutral quantum system across a magnetic field

The moving neutral system of two Coulomb charges on a plane subject to a constant magnetic field B$B$ perpendicular to the plane is considered. It is shown that the composite system of finite total mass is bound for any center-of-mass momentum P$P$ and magnetic field strength; the energy of the ground state is calculated accurately using a variational approach. Its accuracy is cross-checked in a Lagrange-mesh method for B=1$B=1$  a.u. and in a perturbation theory at small B$B$ and P$P$. The constructed trial function has the property of being a uniform approximation of the exact eigenfunction. For a Hydrogen atom and a Positronium a double perturbation theory in B$B$ and P$P$ is developed and the first corrections are found algebraically. A phenomenon of a sharp change of energy behavior for a certain center-of-mass momentum and a fixed magnetic field is indicated.     

Fermion entropy of non-uniformly rectilinearly accelerating black hole with electric and magnetic charges

Using the thin film brick-wall model, we calculate the fermion entropy on event horizon and the surface density of the entropy on the Rindler Horizon to a rectilinearly accelerating non-stationary black hole with electric and magnetic charges. The conclusion that black hole entropy is proportional to its area can still be applied by regulating the cut-off factor ?$?$ and the film's thickness δ$\delta$, which are time dependent.     

Site–bond percolation on triangular lattices: Monte Carlo simulation and analytical approach

A generalization of the pure site and pure bond percolation problems called site–bond percolation on a triangular lattice is studied. Motivated by considerations of cluster connectivity, two distinct schemes (denoted as S∩B$S\cap B$ and S∪B$S\cup B$) for site–bond percolation are used. In S∩B$S\cap B$ (S∪B$S\cup B$), two points are said to be connected if a sequence of occupied sites and (or  ) bonds joins them. By using finite-size scaling theory, data from S∩B$S\cap B$ and S∪B$S\cup B$ are analyzed in order to determine (i$i$) the phase boundary between the percolating and non-percolating regions and (ii$ii$) the numerical values of the critical exponents of the phase transition occurring in the system. A theoretical approach, based on exact calculations of configurations on finite triangular cells, is applied to study the site–bond percolation on triangular lattices. The percolation processes have been monitored by following the percolation function, defined as the ratio between the number of percolating configurations and the total number of available configurations for a given cell size and concentration of occupied elements. A comparison of the results obtained by these two methods has been performed and discussed.     

Axial charges of octet baryons in two-flavor lattice QCD

We evaluate the strangeness-conserving NN, ΣΣ, ΞΞ, ΛΣ and the strangeness-changing ΛN, ΣN, ΛΞ, ΣΞ axial charges in lattice QCD with two flavors of dynamical quarks and extend our previous work on pseudoscalar-meson–octet-baryon coupling constants so as to include πΞΞ, KΛΞ and KΣΞ   coupling constants. We find that the axial charges have rather weak quark mass dependence and the breaking in SU(3)$\mathrm{SU}(3)$-flavor symmetry is small at each quark-mass point we consider.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

The spatial distribution of clusters and the formation of mixed languages in bilingual competition

We use cellular automata simulation methods to study the competition between two languages (language A$A$ and B$B$). We assume each of the two languages consists of F$F$ independent features and define an individual as two F$F$-length “identity level” integer strings. The value of each integer of the strings indicates whether the individual is willing or unwilling to express a certain feature and how his willingness or unwillingness is. In our model, individuals who speak either language A$A$ or B$B$ are randomly placed on a square lattice initially and programmed to evolve under the communication and interaction methods. First, we consider the situation that the competition occurs between two languages with only one feature. We find the differences between short-time coexistence processes and long-time coexistence processes and discuss how the spatial distribution of languages evolves. We observe that periodic line-shaped boundaries take shape in some simulations and lead to long-time coexistence between the two languages. Then we study the multi-feature cases when F=10$F=10$ and find the correlation among the evolution of different features decreases with time. We also observe the extinction of two primitive languages and formation of mixed languages.     

Paramagnetic susceptibility of ferrite and cementite obtained from ab initio calculations

Paramagnetic susceptibility of BCC ferrite (α$\mathrm{\alpha }$-Fe) and of cementite (Fe₃C), was calculated in a temperature range above the Curie point, using a density functional-based method in conjunction with statistical approximations. The electronic structure and the magnetic energy of both systems were calculated using the full potential linear augmented plane wave (FPLAPW) method as implemented in the Wien2k Code. The temperature effect was captured by introducing the Boltzmann statistical distribution to describe the orientation perturbation of the magnetic moments caused by thermal agitation. The magnetic moment was calculated in the temperature range from 1045 to 1175 K for alpha-iron and from 540 to 640 K for cementite. The modeling was performed for applied magnetic fields ranging from 1–2 T. The main assumption was that the effect of temperature and that of the applied magnetic field can be decoupled and, consequently, be treated separately. The calculated moments were used to estimate the paramagnetic susceptibility according to the linear relation χ=M/B$\chi =M/B$ well established for paramagnetic systems. The calculated values were compared with published experimental measurements for iron and with values obtained from the Curie–Weiss law for cementite.     

Euler–Heisenberg effective action and magnetoelectric effect in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field B$B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field E$E$ at E/B?1$E/B?1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field E$E$ and the lowest order correction to it due to the magnetic field (B/E?1$B/E?1$).     

A case of subdominant/suppressed “high energy” contribution to the baryon asymmetry of the Universe in flavoured leptogenesis

The CP-violation necessary for the generation of the baryon asymmetry of the Universe YB$Y_B$ in the “flavoured” leptogenesis scenario can arise from the “low energy” PMNS neutrino mixing matrix U   and/or from the “high energy” part of neutrino Yukawa couplings, which can mediate CP-violating phenomena only at some high energy scale. The possible interplay between these two types of CP-violation is analysed. The type I see-saw model with three heavy right-handed Majorana neutrinos having hierarchical spectrum is considered. We show that in the case of inverted hierarchical light neutrino mass spectrum, there exist regions in the corresponding leptogenesis parameter space where the relevant “high energy” phases have large CP-violating values, but the purely “high energy” contribution in YB$Y_B$ plays a subdominant role in the production of baryon asymmetry compatible with the observations. In some of these regions the purely “high energy” contribution in YB$Y_B$ is so strongly suppressed that one can have successful leptogenesis only if the requisite CP-violation is provided by the Majorana phase(s) in the neutrino mixing matrix.     

Dirac oscillator in perpendicular magnetic and transverse electric fields

We study (2+1)$(2+1)$ dimensional massless Dirac oscillator in the presence of perpendicular magnetic and transverse electric fields. Exact solutions are obtained and it is shown that there exists a critical magnetic field B_c$B_c$ such that the spectrum is different in the two regions B>B_c$B>B_c$ and B<B_c$B<B_c$. The situation is also analyzed for the case B=B_c$B=B_c$.     

Atomic resolution and vortex lattice studies of magnetic superconductors: A first approach in the nickel borocarbide TmNi2B2C

We present new scanning tunneling microscopy measurements in the superconductor TmNi₂B₂C. The topography shows in some areas flat surfaces, where atomic size modulations can be identified. We find a hexagonal vortex lattice between 0.15 T and 1.4 T, when the magnetic field is applied along the basal plane of the tetragonal crystal structure (B⊥c)$(B\perp c)$, and a hexagonal to square transition around 0.15 T when the field is applied along the c  -axis (B‖c)$(B\Vert c)$. Measured intervortex distance are smaller than expected at high field, due to the internal field being larger than the applied field.     

Symmetry breaking of a Bose–Fermi mixture in a triple-well potential

We investigate the properties of a one-dimensional Bose–Fermi mixture in a triple-well potential with two equally populated spin components at zero temperature. Based on the coupled equations for a Bose–Fermi mixture, we illustrate the symmetry breaking of the Bose–Fermi mixture with different strengths of interspecies and intraspecies interactions that are induced by changing the particle numbers of bosons and fermions. The several novel density profiles of symmetric and asymmetric ground states in the phase diagram of the (_NF,_NB$N_F,N_B$) plane are demonstrated. In addition, the variation of density as a function of _NB$N_B$ at fixed _NF$N_F$, which clearly shows the transition among distinct types of symmetric and asymmetric ground states, is illustrated.     

Electronic spectra of one-dimensional nano-quasi-periodic systems under bias

We investigate the properties of the energy spectra of quantum one-dimensional nano-quasi-crystals in the presence of external electric fields. These systems are modelled by means of finite sequences, ordered according to a Fibonacci rule which constituted of two blocks A$A$ (constant potentials of different heights defined on finite intervals) and B$B$ (delta potentials of different intensities). We use the electric field ability of producing Stark ladders in periodic systems to obtain well separated energy levels and to study the evolution of these levels when disorder is introduced. We show that this effect also allows us to predict the approximate position of the levels in the disordered system, in spite of its chaotic appearance at first view. We show, against the usual belief, that the n$n$th Stark ladder in general is not formed exclusively from the levels of the n$n$th band. The disorder is introduced in two different ways: by changing the distribution of the blocks or by changing the values of the delta potential intensities. In both cases we start from electrified periodic structures which are gradually perturbed to obtain electrified quasi-periodic structures. We show that the use of Fibonacci sequences as a particular case is not crucial and one can use the electric field to analyze any other type of quasi-periodic systems.     

Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B   decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ$B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3)$\mathrm{SU}(3)$ sum rule for pairs of B→Kπ$B\to K\pi$ and B→Kη₈$B\to K{\eta }_8$, generalized to pairs of B→Kπ$B\to K\pi$, B→Kη$B\to K\eta$ and B→Kη^′$B\to K{\eta }^{\prime }$.     

SL(2,R) duality-symmetric action for electromagnetic theory with electric and magnetic sources

For the SL(2,R) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials A^μ$A^{\mu }$ and B^μ$B^{\mu }$ in a judicious way. On the two potentials A^μ$A^{\mu }$ and B^μ$B^{\mu }$ the SL(2,R) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,Z)-invariant action. Also given is a Zwanziger-type action for SL(2,R) duality-invariant Born–Infeld electrodynamics which can be important for D-brane dynamics in string theory.     

Naturally light sterile neutrinos from theory of R-parity

The fate of R-parity is one of the central issues in the minimal supersymmetric standard model (MSSM). Gauged B−L$B-L$ symmetry provides a natural framework for addressing this question. Recently, it was pointed out that the minimal such theory does not need any additional Higgs if the B−L$B-L$ breaking is achieved through the VEVs of right-handed sneutrinos, which ties the new physics scale to the scale of the MSSM. We show here that this immediately leads to an important prediction of two light sterile neutrinos, which can play a significant role in the BBN and neutrino oscillations. We also discuss some new relevant phenomenology for the LHC, in the context of the minimal supersymmetric left–right symmetric theory which provides a natural setting for the gauged B−L$B-L$ symmetry.     

Number-theory dark matter

We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)_B–L gauge symmetry, Z₂(B–L)$Z_2(\mathrm{B}\text{–}\mathrm{L})$. We introduce a set of chiral fermions charged under the U(1)_B–L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)_B–L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z₂(B–L)$Z_2(\mathrm{B}\text{–}\mathrm{L})$.