This essay is a review of the topic of vortices in rapidly rotating BECs, where the system is in a quantum Hall-like regime and the density profile is of the Thomas-Fermi form. Also, in this paper, deviations from a triangular lattice is being considered while the system condensates into the lowest Landau levels.

A generalized Ginzburg–Landau–Devonshire (GLD) theory is used to study the properties of ferroelectric thin films sandwiched between two metal electrodes with a first-order phase transition. By taking into account the effect of the imperfect surface layer and a natural boundary condition, the temperature and film-thickness dependence of the spontaneous polarization and the dielectric susceptibi...

Adhesion of microorganisms to various interfaces has been explained by the classical Derjaguin–Landau–Verwey– Overbeek (DLVO) theory of colloid stability. The theory has been used as a qualitative model, but also in a quantitative way to calculate adhesion free energy changes involved in microbial adhesion. In this paper some important investigations will be review that show how the DLVO theory...

We calculate the complex phase of chiral determinant by the vacuum overlap formula with configurations of two-dimensional U(1) gauge field fixed in Landau and Laplacian gauge. The complex phase fluctuates over the Gribov copies, which appear in the process of Landau gauge fixing and contain vortex-like singularities. In the Laplacian gauge, the fluctuation can be reduced and the phase can be de...

We report the observation of an acute sensitivity of the anisotropic longitudinal resistivity of twodimensional electron systems in half-filled high Landau levels to the magnitude and orientation of an in-plane magnetic field. In the third and higher Landau levels, at filling fractions n 9 2, 11 2, etc., the in-plane field can lead to a striking interchange of the “hard” and “easy” transport di...

Stationary structures in two-dimensional Heisenberg ferromagnets. Abstract Stationary structures in a classical isotropic two-dimensional Heisenberg ferromagnetic are studied in the framework of the (2+1)-dimensional Landau-Lifshitz model. It is established that in the case of S(r, t) = S(r − vt) the Landau-Lifshitz equation is closely related to the Ablowitz-Ladik hierarchy. This relation is u...

We have measured the quantum-Hall activation gaps in graphene at filling factors nu=2 and nu=6 for magnetic fields up to 32 T and temperatures from 4 to 300 K. The nu=6 gap can be described by thermal excitation to broadened Landau levels with a width of 400 K. In contrast, the gap measured at nu=2 is strongly temperature and field dependent and approaches the expected value for sharp Landau le...

We study the Schrödinger operator with a constant magnetic field in the exterior of a two-dimensional compact domain. Functions in the domain of the operator are subject to a boundary condition of the third type (Robin condition). In addition to the Landau levels, we obtain that the spectrum of this operator consists of clusters of eigenvalues around the Landau levels and that they do accumulat...

We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling. Higher dimensional generalizations of flat Landau levels are obtained in the Landau-like gauge. The 2D helical Dirac modes with opposite helicities and 3D Weyl modes with opposite chiralities are spa...

‎In this paper‎, ‎we obtain exact solutions involving parameters of some nonlinear PDEs in mathmatical physics; namely the one-‎dimensional modified complex Ginzburg-Landau equation by using the $ (G'/G) $ expansion method‎, homogeneous balance method, extended F-expansion method‎. ‎By ‎using homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by j...