Hydrodynamics of Quantum Matter

Professor: Thomas Scaffidi

Description: Imagine preparing a set of qubits in a simple product state, and time evolving it under a given Hamiltonian which couples them. The state of the system is going to become more and more complex as entanglement building up. If one wanted to store information about the system on a classical computer, the number of bits required would increase exponentially with time. Yet, after a while one expects the system to reach a thermal equilibrium, that should be describable in terms of a few macroscopic quantities, like temperature. In the field of quantum dynamics, the goal is to understand this extremely rich process, from the microsopic quantum chaos at short times, to the emergent hydrodynamics at long times.
The project concerns a new regime of electronic transport in which electrons behave like a viscous fluid, and for which the ubiquitous Ohm’s law is replaced by the much richer Navier-Stokes equation. Interest in this regime was recently amplified by a series of experiments in 2D materials like graphene. The goal of the project is to calculate from first-principles the precise form of the scattering operator between electrons in realistic models for novel quantum materials, in order to predict hydrodynamic behavior and discover novel phenomena. In practice, this involves the derivation of scattering properties using perturbation theory and the calculation of high-dimensional integrals using a variety of numerical methods.

Preferred Qualifications: Experience with numerical physics (in python, julia or other languages) is a plus.