Non-Equilibrium Physics 1

Course goals

Upon completing this course, the student will:
 

• Understand hydrodynamic behavior in metals and graphene and its consequences for transport properties.
• Be able to derive the Boltzmann Transport Equation and use it as a basis to derive the Navier-Stokes equation.
• Solve the Boltzmann Transport Equation in linear response for simplified cases.
• Formulate (elasto)hydrodynamic equations and perform dimensional analysis on these to understand the regimes wherein non-linearities play a role.
• Know how to solve Stokes flows using Green’s functions and the potential-flow formalism and understand the dynamics of suspended particles therein.
• Know basic properties of active matter systems and how active matter and hydrodynamic theory interact.

Content

The course aims to introduce how hydrodynamic theory can be used to describe the behavior in non-equilibrium systems, whether this involves classical (active) or quantum physics. The student will be shown the origin of the mesoscale Boltzmann Transport Equation (BTE) and how this gives rise to hydrodynamic equations for sufficiently long length and time scales. This formalism impacts many fields in physics and the course will provide students with an overview of the scope. We will also introduce the basic tools to make progress in analyzing the BTE and Stokes flow for basic systems and simple geometries. We will consider electron transport in the hydrodynamic regime, as well as classical elastohydrodynamic flows and active matter systems. All of these have gained popularity over the past decades, and we will emphasize how the course material is relevant to current research efforts.