Theory for the reduction of products of spin operators

In this study we show that the sum of the powers of arbitrary products of quantum spin operators such as $(S^+)^l(S^-)^m(S^z)^n$ can be reduced by one unit, if this sum is equal to 2S+1, S being the spin quantum number. We emphasize that by a repeated application of this procedure \em all \em arbitrary spin operator products with a sum of powers larger than 2S can be replaced by a combination of spin operators with a maximum sum of powers not larger than 2S. This transformation is exact. All spin operators must belong to the same lattice site. By use of this procedure the consideration of single-ion anisotropies and the investigation of the magnetic reorientation within a Green's function theory are facilitated. Furthermore, it may be useful for the study of time dependent magnetic properties within the ultrashort (fsec) time domain.Comment: 11 pages, 1 table, uses rotatin

Multistatic Specular Meteor Radar Network in Peru: System Description and Initial Results

The mesosphere and lower thermosphere (MLT) region is dominated globally by dynamics at various scales: planetary waves, tides, gravity waves, and stratified turbulence. The latter two can coexist and be significant at horizontal scales less than 500 km, scales that are difficult to measure. This study presents a recently deployed multistatic specular meteor radar system, SIMONe Peru, which can be used to observe these scales. The radars are positioned at and around the Jicamarca Radio Observatory, which is located at the magnetic equator. Besides presenting preliminary results of typically reported large-scale features, like the dominant diurnal tide at low latitudes, we show results on selected days of spatially and temporally resolved winds obtained with two methods based on: (a) estimation of mean wind and their gradients (gradient method), and (b) an inverse theory with Tikhonov regularization (regularized wind field inversion method). The gradient method allows improved MLT vertical velocities and, for the first time, low-latitude wind field parameters such as horizontal divergence and relative vorticity. The regularized wind field inversion method allows the estimation of spatial structure within the observed area and has the potential to outperform the gradient method, in particular when more detections are available or when fine adaptive tuning of the regularization factor is done. SIMONe Peru adds important information at low latitudes to currently scarce MLT continuous observing capabilities. Results contribute to studies of the MLT dynamics at different scales inherently connected to lower atmospheric forcing and E-region dynamo related ionospheric variability

Quantum Monte Carlo simulation of thin magnetic films

The stochastic series expansion quantum Monte Carlo method is used to study thin ferromagnetic films, described by a Heisenberg model including local anisotropies. The magnetization curve is calculated, and the results compared to Schwinger boson and many-body Green's function calculations. A transverse field is introduced in order to study the reorientation effect, in which the magnetization changes from out-of-plane to in-plane. Since the approximate theoretical approaches above differ significantly from each other, and the Monte Carlo method is free of systematic errors, the calculation provides an unbiased check of the approximate treatments. By studying quantum spin models with local anisotropies, varying spin size, and a transverse field, we also demonstrate the general applicability of the recent cluster-loop formulation of the stochastic series expansion quantum Monte Carlo method.Comment: 9 pages, 12 figure

Schwinger boson theory of anisotropic ferromagnetic ultrathin films

Ferromagnetic thin films with magnetic single-ion anisotropies are studied within the framework of Schwinger bosonization of a quantum Heisenberg model. Two alternative bosonizations are discussed. We show that qualitatively correct results are obtained even at the mean-field level of the theory, similar to Schwinger boson results for other magnetic systems. In particular, the Mermin-Wagner theorem is satisfied: a spontaneous magnetization at finite temperatures is not found if the ground state of the anisotropic system exhibits a continuous degeneracy. We calculate the magnetization and effective anisotropies as functions of exchange interaction, magnetic anisotropies, external magnetic field, and temperature for arbitrary values of the spin quantum number. Magnetic reorientation transitions and effective anisotropies are discussed. The results obtained by Schwinger boson mean-field theory are compared with the many-body Green's function technique.Comment: 14 pages, including 7 EPS figures, minor changes, final version as publishe

Kasner and Mixmaster behavior in universes with equation of state w \ge 1

We consider cosmological models with a scalar field with equation of state $w\ge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1$. We generalize the results to theories where the scalar field couples to p-forms and show that there exists a finite value of $w$, depending on the p-forms, such that chaotic oscillations are suppressed. We show that $Z_2$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde

Did transit through the galactic spiral arms seed crust production on the early Earth?

Although there is evidence for periodic geological perturbations driven by regular or semi-regular extra-terrestrial bombardment, the production of Earth’s continental crust is generally regarded as a function of planetary differentiation driven by internal processes. We report time series analysis of the Hf isotopic composition of zircon grains from the North Atlantic and Pilbara cratons, the archetypes of Archean plate tectonic and non-plate tectonic settings, respectively. An ~170–200 m.y. frequency is recognized in both cratons that matches the transit of the solar system through the galactic spiral arms, where the density of stars is high. An increase in stellar density is consistent with an enhanced rate of Earth bombardment by comets, the larger of which would have initiated crustal nuclei production via impact-driven decompression melting of the mantle. Hence, the production and preservation of continental crust on the early Earth may have been fundamentally influenced by exogenous processes. A test of this model using oxygen isotopes in zircon from the Pilbara craton reveals correlations between crust with anomalously light isotopic signatures and exit from the Perseus spiral arm and entry into the Norma spiral arm, the latter of which matches the known age of terrestrial spherule beds. Our data support bolide impact, which promoted the growth of crustal nuclei, on solar system transit into and out of the galactic spiral arms

On the magnetic stability at the surface in strongly correlated electron systems

The stability of ferromagnetism at the surface at finite temperatures is investigated within the strongly correlated Hubbard model on a semi-infinite lattice. Due to the reduced surface coordination number the effective Coulomb correlation is enhanced at the surface compared to the bulk. Therefore, within the well-known Stoner-picture of band ferromagnetism one would expect the magnetic stability at the surface to be enhanced as well. However, by taking electron correlations into account well beyond the Hartree-Fock (Stoner) level we find the opposite behavior: As a function of temperature the magnetization of the surface layer decreases faster than in the bulk. By varying the hopping integral within the surface layer this behavior becomes even more pronounced. A reduced hopping integral at the surface tends to destabilize surface ferromagnetism whereas the magnetic stability gets enhanced by an increased hopping integral. This behavior represents a pure correlation effect and can be understood in terms of general arguments which are based on exact results in the limit of strong Coulomb interaction.Comment: 6 pages, RevTeX, 4 eps figures, accepted (Phys. Rev. B), for related work and info see http://orion.physik.hu-berlin.d

On the Regularizability of the Big Bang Singularity

The singularity for the big bang state can be represented using the generalized anisotropic Friedmann equation, resulting in a system of differential equations in a central force field. We study the regularizability of this singularity as a function of a parameter, the equation of state, $w$. We prove that for $w >1$ it is regularizable only for $w$ satisfying relative prime number conditions, and for $w \leq 1$ it can always be regularized. This is done by using a McGehee transformation, usually applied in the three and four-body problems. This transformation blows up the singularity into an invariant manifold. The relationship of this result to other cosmological models is briefly discussed.Comment: 22 pages, 0 figure