Continuum mechanics for quantum many-body systems

by Prof. Giovanni Vignale

Tuesday 22 Jun 2010, 16:00 → 18:00 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

The dynamics of quantum many-body systems poses a major challenge to computational physicists and chemists. While the Schroedinger equation contains the formal solution of the problem, physical understanding requires that we develop effective equations of motion for the variables of interest. At stake is the possibility of understanding processes like ionization, dissociation, tunneling, scattering, and chemical reactions. Time-dependent density functional theory(TDDFT) has long offered a relatively simple method for including many-body effects in the description of the dynamics. However, in recent years some limitations of TDDFT have come to light, which have prompted the introduction of a higher version of the theory, the so-called time-dependent current density functional theory (TDCDFT). In this talk I review the original motivation and early successes of TDCDFT. I then proceed to describe a very recent spinoff of this theory, which we call Quantum Continuum Mechanics. 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, 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 Schroedinger 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 density- and current-density functional 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.