Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.Comment: 23 pages, Plain TeX, no figure

Teaching Integration outside the Traditional Classroom

Today\u27s educational environment is being transformed by online technologies that open new venues for teaching and make education accessible far beyond the traditional classroom environment. How rrught these changes affect the ways we teach the integration of psychology and Christianity? Three faculty members dialogue about such integration opportunities, advantages, and potential disadvantages

Low-velocity anisotropic Dirac fermions on the side surface of topological insulators

We report anisotropic Dirac-cone surface bands on a side-surface geometry of the topological insulator Bi$_2$Se$_3$ revealed by first-principles density-functional calculations. We find that the electron velocity in the side-surface Dirac cone is anisotropically reduced from that in the (111)-surface Dirac cone, and the velocity is not in parallel with the wave vector {\bf k} except for {\bf k} in high-symmetry directions. The size of the electron spin depends on the direction of {\bf k} due to anisotropic variation of the noncollinearity of the electron state. Low-energy effective Hamiltonian is proposed for side-surface Dirac fermions, and its implications are presented including refractive transport phenomena occurring at the edges of tological insulators where different surfaces meet.Comment: 4 pages, 2 columns, 4 figure

Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Splitting The Gluon?

In the strongly correlated environment of high-temperature cuprate superconductors, the spin and charge degrees of freedom of an electron seem to separate from each other. A similar phenomenon may be present in the strong coupling phase of Yang-Mills theories, where a separation between the color charge and the spin of a gluon could play a role in a mass gap formation. Here we study the phase structure of a decomposed SU(2) Yang-Mills theory in a mean field approximation, by inspecting quantum fluctuations in the condensate which is formed by the color charge component of the gluon field. Our results suggest that the decomposed theory has an involved phase structure. In particular, there appears to be a phase which is quite reminiscent of the superconducting phase in cuprates. We also find evidence that this phase is separated from the asymptotically free theory by an intermediate pseudogap phase.Comment: Improved discussion of magnetic nature of phases; removed unsubstantiated speculation about color confinemen

Integration in the Classroom: Ten Teaching Strategies

Teaching integration involves engaging students as active participants in the unfolding relationship of psychology and Christianity, with a particular focus on integration. Ten specific teaching strategies are offered to help students enter into the challenges and opportunities of integration. The teaching strategies are organized according to Moon\u27s (1997) four directions for integration: practical, personal, classic, and contemporary

Adjacency labeling schemes and induced-universal graphs

We describe a way of assigning labels to the vertices of any undirected graph on up to $n$ vertices, each composed of $n/2+O(1)$ bits, such that given the labels of two vertices, and no other information regarding the graph, it is possible to decide whether or not the vertices are adjacent in the graph. This is optimal, up to an additive constant, and constitutes the first improvement in almost 50 years of an $n/2+O(\log n)$ bound of Moon. As a consequence, we obtain an induced-universal graph for $n$-vertex graphs containing only $O(2^{n/2})$ vertices, which is optimal up to a multiplicative constant, solving an open problem of Vizing from 1968. We obtain similar tight results for directed graphs, tournaments and bipartite graphs

Bag Formation in Quantum Hall Ferromagnets

Charged skyrmions or spin-textures in the quantum Hall ferromagnet at filling factor nu=1 are reinvestigated using the Hartree-Fock method in the lowest Landau level approximation. It is shown that the single Slater determinant with the minimum energy in the unit charge sector is always of the hedgehog form. It is observed that the magnetization vector's length deviates locally from unity, i.e. a bag is formed which accommodates the excess charge. In terms of a gradient expansion for extended spin-textures a novel O(3) type of effective action is presented, which takes bag formation into account.Comment: 13 pages, 3 figure

Recursive solutions for Laplacian spectra and eigenvectors of a class of growing treelike networks

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing treelike networks. The two interesting quantities are determined through the recurrence relations derived from the structure of the networks. Beginning from the rigorous relations one can obtain the complete eigenvalues and eigenvectors for the networks of arbitrary size. The analytical method opens the way to analytically compute the eigenvalues and eigenvectors of some other deterministic networks, making it possible to accurately calculate their spectral characteristics.Comment: Definitive version accepted for publication in Physical Reivew

Evolution of thin-wall configurations of texture matter

We consider the free matter of global textures within the framework of the perfect fluid approximation in general relativity. We examine thermodynamical properties of texture matter in comparison with radiation fluid and bubble matter. Then we study dynamics of thin-wall selfgravitating texture objects, and show that classical motion can be elliptical (finite), parabolical or hyperbolical. It is shown that total gravitational mass of neutral textures in equilibrium equals to zero as was expected. Finally, we perform the Wheeler-DeWitt's minisuperspace quantization of the theory, obtain exact wave functions and discrete spectra of bound states with provision for spatial topology.Comment: intermediate research on nature of dual-radiation matter; LaTeX, 12 pages, 1 figure and epsfig style file included; slightly shortened version was published in December issue of GR