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 fi elds, such as the displacement fi eld 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 signifi cant 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 fi elds.
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