Towards quantum simulation of fingering instabilities in quantum Hall droplets
Cristiano Muzzi (Université Libre de Bruxelles)
Systems of charged particles in a nonuniform magnetic field can exhibit growth processes analogous to those observed for interfaces between two immiscible incompressible fluids with different viscosities, a phenomenon known as Laplacian growth. In particular, a quantum Hall droplet can develop cusps driven by gradients of magnetic fields. This phenomenon is known as fingering instability and has been deeply studied in classical fluid dynamics.
In this seminar, I will show how the shape of the droplet can be predicted through a random matrix theory (plasma analogy) and to probe this phenomenon, in quantum Hall fluids. I will address this phenomenon dynamically by deforming an initially isotropic droplet by turning on magnetic fields far away from it. Studying this phenomenon in a lattice model, beyond the limit of Aharonov-Casher wavefunctions, I will show that the formation of such patterns is a genuine feature of quantum Hall states. Lattice effects and sudden deformations of the droplet are also studied. To conclude, I will discuss a quantum simulation setup in the continuum to observe this phenomenon in cold atomic gases in artificial gauge fields.