Incompressibility Estimates for the Laughlin Phase

Incompressibility Estimates for the Laughlin Phase

This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level. When repulsive interactions are strong enough in this model, highly correlated states emerge, built on Laughlin’s famous wave function. We investigate a model...

Incompressibility Estimates for the Laughlin Phase, Part Ii

We consider fractional quantum Hall states built on Laughlin’s original Nbody wave-functions, i.e., they are of the form holomorphic × gaussian and vanish when two particles come close, with a given polynomial rate. Such states appear naturally when looking for the ground state of 2D particles in strong magnetic fields, interacting via repulsive forces and subject to an external potential due t...

A Posteriori Modeling Error Estimates for the Assumption of Perfect Incompressibility in the Navier-Stokes Equation

We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible NavierStokes equation: Real fluids are never perfectly incompressible, but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible Navier-Stokes equation, the pressure being a steep function of the density. ...

Laughlin the Probability - Resultant

Hyperdeterminantal computation for the Laughlin wave function

The decomposition of the Laughlin wave function in the Slater orthogonal basis appears in the discussion on the second-quantized form of the Laughlin states and is straightforwardly equivalent to the decomposition of the even powers of the Vandermonde determinants in the Schur basis. Such a computation is notoriously difficult and the coefficients of the expansion have not yet been interpreted....