Gauge fixing in lattice gauge theory simulations is crucial for many calculations e.g. the study of gauge dependent quantities such as the gluon propagator [1]. However, the standard lattice Landau gauge condition [2] is the same as the continuum condition, ∑ μ ∂μAμ = 0, only to leading order in the lattice spacing, a. The focus of this talk is to use mean-fieldimproved perturbation theory [3] ...

We obtain expressions for the current operator in the lowest Landau level (L.L.L.) field theory, where higher Landau level mixing due to various external and interparticle interactions is sytematically taken into account. We consider the current operators in the presence of electromagnetic interactions, both Coulomb and time-dependent, as well as local four-fermi interactions. The importance of...

We compare the energies of different electron solids, such as bubble crystals with triangular and square symmetry and stripe phases, to those of correlated quantum liquids in partially filled intermediate Landau levels. Multiple transitions between these phases when varying the filling of the top-most partially filled Landau level explain the observed reentrance of the integer quantum Hall effe...

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 derive the fractional generalization of the Ginzburg–Landau equation from the variational Euler–Lagrange equation for fractal media. To describe fractal media we use the fractional integrals considered as approximations of integrals on fractals. Some simple solutions of the Ginzburg–Landau equation for fractal media are considered and different forms of the fractional Ginzburg–Landau equatio...

In 1957 Abrikosov published his work on periodic solutions to the linearized Ginzburg-Landau equations. Abrikosov’s analysis assumes periodic boundary conditions, which are very different from the natural boundary conditions the minimizer of the Ginzburg-Landau energy functional should satisfy. In the present work we prove that the global minimizer of the fully non-linear functional can be appr...

We study, via bosonization, the Landau fixed point for the problem of interacting spinless fermions near the Fermi surface in dimensions higher than one. We rederive the bosonic representation of the Fermi operator and use it to find the general form of the fermion propagator for the Landau fixed point. Using a generalized Bogoliubov transformation we diagonalize exactly the bosonized hamiltoni...

We develop an approach to apply Wang-Landau algorithm to multicomponent alloys in semigrand-canonical ensemble. Although the Wang-Landau algorithm has great advantages over conventional sampling methods, there are few applications to alloys. This is because calculating compositions in semi-grand-canonical ensemble using the Wang-Landau algorithm requires a multidimensional density of states in ...

The reduction of the energy gap due to Landau level mixing, characterized by the dimensionless parameter λ = (e/ǫl0)/h̄ωc, has been calculated by variational Monte Carlo for the fractional quantum Hall effect at filling fractions ν = 1/3 and 1/5 using a modified version of Jain’s composite fermion wave functions. These wave functions exploit the Landau level mixing already present in composite f...

The so-called Ginzburg-Landau formalism applies for parabolic systems which are defined on cylindrical domains, which are close to the threshold of instability, and for which the unstable Fourier modes belong to non-zero wave numbers. This formalism allows to describe an attracting set of solutions by a modulation equation, here the Ginzburg-Landau equation. If the coefficient in front of the c...