The energy spectrum of an electron confined to an arbitrary surface of revolution in an external magnetic field, parallel to the symmetry axis, is studied analitycally and numerically. The problem is reduced via conformal mapping to one on the surface of a sphere. The case of a spheroid is considered in details, and the dependence on parameters is discussed. In the high magnetic field limit a r...

The Ginzburg–Landau (GL) equations of superconductivity provide a computational model for the study of magnetic flux vortices in type-II superconductors. In this article we show through numerical examples and rigorous mathematical analysis that the GL model reduces to the frozen-field model when the charge of the Cooper pairs (the superconducting charge carriers) goes to zero while the applied ...

The synthesis and crystallographic, thermodynamic, and transport properties of single crystalline Rh 9 In 4 S 4 were studied. The resistivity, magnetization, and specific heat measurements all clearly indicate bulk superconductivity with a critical temperature, T c ∼ 2.25 K. The Sommerfeld coefficient γ and the Debye temperature(Θ D) were found to be 34 mJ mol −1 K −2 and 217 K, respectively. T...

In this note we consider a Landau Hamiltonian perturbed by a random magnetic potential of Anderson type. For a given number of bands, we prove the existence of both strongly localized states at the edges of the spectrum and dynamical delocalization near the center of the bands in the sense that wave packets travel at least at a given minimum speed. We provide explicit examples of magnetic pertu...

The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum are investigated. For two flux quanta per unit cell of the periodic potential, interactions open a gap in each Landau level with the smallest gap in the n=1 Landau level. For more flux quanta through the unit cell, where the noninteracting energy spectra have many gaps in ea...

We study the asymptotic limit of solutions of the Ginzburg-Landau equations in two dimensions with or without magnetic field. We first study the Ginzburg-Landau system with magnetic field describing a superconductor in an applied magnetic field, in the “London limit” of a Ginzburg-Landau parameter κ tending to ∞. We examine the asymptotic behavior of the “vorticity measures” associated to the v...

The various uncommon properties of magnetic nanoparticles (Stoner nanoparticles) and molecular magnets have attracted much attention in industry as well as in the academic community. In this review we begin with going through important experiments in this field and possible applications of these materials. Then we introduce the theoretic models currently used for Stoner nanoparticles and molecu...

Let Ω be a 2D domain with a hole ω. In the domain A = Ω \ ω consider a class J of complex valued maps having degrees 1 and 1 on ∂Ω, ∂ω respectively. In a joint work with P. Mironescu we show that if cap(A) ≥ π (subcritical domain), minimizers of the Ginzburg-Landau energy E κ exist for each κ. They are vortexless and converge in H(A) to a minimizing S-valued harmonic map as the coherency length...

We discuss how to use Wang-Landau simulations in an efficient manner to investigate the statistical mechanics of individual lattice polymers and peptides adsorbed at a planar surface. For nearest neighbor interactions, we show that a single Wang-Landau simulation, recording the density of states as a function of numbers of internal contacts and of surface beads, is sufficient to give a full des...

Using mirror pairs (M3,W3) in type II superstring compactifications on Calabi-Yau threefols, we study, geometrically, F-theory duals of M-theory on seven manifolds with G2 holonomy. We first develop a new way for getting Landau Ginzburg (LG) CalabiYau threefols W3, embedded in four complex dimensional toric varieties, mirror to sigma model on toric Calabi-Yau threefolds M3. This method gives di...