Basic ideas about noncommuting coordinates are summarized, and then coordinate noncommutativity, as it arises in the Landau problem, is investigated. I review a quantum solution to the Landau problem, and evaluate the coordinate commutator in a truncated state space of Landau levels. Restriction to the lowest Landau level reproduces the well known commutator of planar coordinates. Inclusion of ...

We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to conve...

We construct a phenomenological Landau theory for the two-dimensional helical Fermi liquid found on the surface of a three-dimensional time-reversal invariant topological insulator. In the presence of rotation symmetry, interactions between quasiparticles are described by ten independent Landau parameters per angular momentum channel, by contrast with the two (symmetric and antisymmetric) Landa...

In this paper, we will describe the mathematical foundation of topological Landau–Ginzburg (LG) models coupled to gravity at genus 0 in terms of primitive forms. In particular, we can give a natural explanation for the large phase space. We also discuss the mirror symmetry for Calabi–Yau manifolds and CP1 in our context. We see that the mirror partner of CP1 is the theory of primitive form asso...

The effects of Landau-level mixing and finite thickness of the two-dimensional electron gas on the relative stability of Skyrmion and single spin-flip excitations at Landau-level filling factor n51 have been investigated. Landau-level mixing is studied by fixed-phase diffusion Monte Carlo, and finite thickness is included by modifying the effective Coulomb interaction. Both Landau-level mixing ...

A formal asymptotic expansion is used to simplify the Ginzburg-Landau model of superconductivity in the limit of large values of the Ginzburg-Landau parameter and high applied magnetic field strengths. The convergence of solutions of the full Ginzburg-Landau equations to solutions of the leading order equations in the hierarchy is demonstrated for both boundary value and periodic problems. The ...

In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e. nonlinear sigma models on nontrivial noncompact manifolds with superpotential, generalizing old computations in Landau-Ginzburg models over (orbifolds of) vector spaces. For Landau-Ginzburg models in the same universality class as nonlinear sigma models, we explicitly ...

We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians under a condition on the decay of the Fermi projections. This condition and continuity of the integrated density of states are shown to imply continuity of the Hall conductance. In addition, we prove the existence of delocalization near each Landau level for these two-dimensional Hamiltonians. More precisel...

1 University Koblenz-Landau, Institute for Integrated Natural Sciences, Germany 2 Leibniz Universität Hannover, Forschungszentrum Küste, Germany 3 University Koblenz-Landau, Institute for Integrated Natural Sciences, Germany 4 University Stuttgart, Institute for Institute for Modelling Hydraulic and Environmental Systems, Germany 5 University Koblenz-Landau, Institute for Environmental Sciences...

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different ...