Recorded 13 April 2022. Giovanni Vignale of University of Missouri-Columbia, Physics, presents "Quantum continuum mechanics for many-body systems" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: Classical continuum mechanics is a theory of the dynamics of classical liquids and solids in which the state of the body is described by a small set of collective fields, such as the displacement field in elasticity theory; density, velocity, and temperature in hydrodynamics. A similar description is possible for quantum many-body systems, at all length scales, and indeed its existence is guaranteed by the basic theorems of time-dependent current density functional theory. In this talk I show how the exact Heisenberg equation of motion for the current density of a many-body system can be closed by expressing the quantum stress tensor as a functional of the current density. I then introduce an \anti-adiabatic" approximation scheme for this functional. I show that this approximation schemes emerges naturally from a variational Ansatz for the time-dependent many-body wave function. The anti-adiabatic approximation scheme allows us to bypass the solution of the time-dependent Schrodinger equation, resulting in an equation of motion for the displacement field that requires only ground-state properties as input. This approach may have significant advantages over the conventional Kohn-Sham density- and current-density functional approaches for large systems, particularly for systems that exhibit strongly collective behavior, such as quantum condensates. I illustrate the formalism by applying it to the calculation of excitation energies in a few model systems. I discuss strategies for improvement and generalizations, for example, to include dissipation, ion dynamics and electron-ion coupling, electromagnetic fields. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/workshop-ii-model-reduction-in-quantum-mechanics/?tab=schedule