Schedule Nov 04, 2009
Continuum Mechanics for Quantum Many-Body Systems
Giovanni Vignale (Univ. Missouri)

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 fluid mechanics. A similar description is possible for quantum many-body systems, 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. Several approximation schemes for this functional are discussed. The simplest scheme allows us to bypass the solution of the time-dependent Schr"odinger equation, resulting in an equation of motion for the displacement field that requires only ground-state properties as an input. This approach may have significant advantages over conventional wave function approaches for large systems, particularly for systems that exhibit strongly collective behavior. I illustrate the formalism by applying it to the calculation of excitation energies in simple one- and two-electron systems.

Other video options

To begin viewing slides, click on the first slide below. (Or, view as pdf.)

[01] [02] [03] [04] [05] [06] [07] [08] [09] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

Author entry (protected)