The N → ∞ limit of the edges of finite planar electron densities is discussed for higher Landau levels. For full filling, the particle number is correlated with the magnetic flux, and hence with the boundary location, making the N → ∞ limit more subtle at the edges than in the bulk. In the nth Landau level, the density exhibits n distinct steps at the edge, in both circular and rectangular samp...

We present some mathematical aspects of Landau-Ginzburg string vacua in terms of toric geometry. The one-to-one correspondence between toric divisors and some of (−1, 1) states in Landau-Ginzburg model is presented for superpotentials of typical types. The Landau-Ginzburg interpretation of non-toric divisors is also presented. Using this interpretation, we propose a method to solve the so-calle...

The charge carriers in graphene are massless Dirac fermions and exhibit a relativistic Landau-level quantization in a magnetic field. Recently, it has been reported that, without any external magnetic field, quantized energy levels have been also observed from strained graphene nanobubbles on a platinum surface, which were attributed to the Landau levels of massless Dirac fermions in graphene f...

We extend topological Landau-Ginsburg models with boundaries to Quaternion Landau-Ginsburg models that satisfy the axioms for open-closed topological field theories. Later we prove that moduli spaces of Quaternion Landau-Ginsburg models are non-commutative Frobenius manifolds in means of [J. Geom. Phys, 51 (2003),387-403.].

Low-temperature, electronic transport in Landau levels N > 1 of a twodimensional electron system is strongly anisotropic. At half-filling of either spin level of each such Landau level the magnetoresistance either collapses to form a deep minimum or is peaked in a sharp maximum, depending on the in-plane current direction. Such anisotropies are absent in the N = 0 and N = 1 Landau level, which ...

Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the proper...

Configurational-bias Monte Carlo has been incorporated into the Wang-Landau method. Although the Wang-Landau algorithm enables the calculation of the complete density of states, its applicability to continuous molecular systems has been limited to simple models. With the inclusion of more advanced sampling techniques, such as configurational-bias, the Wang-Landau method can be used to simulate ...

In this paper we discuss correlation functions in certain A-twisted Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been discussed extensively in the literature, virtually no work has been done on A-twisted theories. In particular, we study examples of Landau-Ginzburg models over topologically nontrivial spaces – not just vector spaces – away from large-radius limits, so ...

From a variational perspective, we derive a series of magnetization and quantum spin current systems coupled via an “s-d” potential term, including Schrödinger-Landau-LifshitzMaxwell system, Pauli-Landau-Lifshitz system, and Schrödinger-Landau-Lifshitz system with successive simplifications. For the latter two systems, we propose to use the time splitting spectral method for the quantum spin cu...

We study the Landau level localization and scaling properties of a disordered twodimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with parameterized potentials. Using a transfer matrix for a finite-width strip geometry, we calculate the localization length as a function of system size and electron e...