A bstract Scattering amplitudes in quantum field theories have intricate analytic properties as functions of the energies and momenta scattered particles. In perturbation theory, their singularities are governed by a set nonlinear polynomial equations, known Landau equations , for each individual Feynman diagram. The singularity locus associated integral is made precise with notion discriminant...

We study equilibrium liquid crystal configurations in three-dimensional domains, within the continuum Landau-De Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-De Gennes predictions match and the temperature regimes where the Landau-D...

We study the three-dimensional topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The three-dimensional lowest Landau level wave functions exhibit the quaternionic analyticity as a generalization of the complex analyticity of ...

The initial-boundary value problem for the time-dependent Ginzburg-Landau equa, tions that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented. Keywords-Superconductivity, Timedependent Ginzburg-Landau equa...

Using a variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy– state diagram of small quantum dots is studied in the magnetic-field range where the density of magnetic flux quanta just exceeds the density of electrons. An accurate analytical many-body wave function is constructed for various angular momentum and spin states in the lowest Landau level, an...

The commensurability condition is applied to determine the hierarchy of fractional fillings of Landau levels in monolayer and in bilayer graphene. The filling rates for fractional quantum Hall effect (FQHE) in graphene are found in the first three Landau levels in one-to-one agreement with the experimental data. The presence of even denominator filling fractions in the hierarchy for FQHE in bil...