Anisotropic Quantum Hall Droplets

I will present recent developments on two-dimensional droplets of free electrons in a strong magnetic field, confined by generally anisotropic electrostatic potentials. Having developed a semiclassical expansion scheme to obtain approximate Gaussian eigenstates of the one-body Hamiltonian, I will apply it to "edge-deformed" potentials of particular interest. I will explain how these one-particle insights can be extended to full many-body droplets, and be used to compute the ground state correlation function near the droplet's boundary and derive the corresponding low-energy effective field theory. Finally, I will propose a scheme to measure the anisotropy by subjecting the droplet to microwave radiation.