Dresden 2011 – wissenschaftliches Programm

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O: Fachverband Oberflächenphysik

O 87: Focussed session: Theory and computation of electronic structure: new frontiers VII (jointly with HL, DS)

O 87.1: Topical Talk

Donnerstag, 17. März 2011, 17:15–17:45, TRE Phy

Continuum mechanics for quantum many-body systems: the anti-adiabatic approximation — •Giovanni Vignale¹, Xianlong Gao², Jianmin Tao³, Stefano Pittalis¹, and Ilya Tokatly⁴ — ¹Department of Physics, University of Missouri, Columbia, MO 65211, USA — ²Department of Physics, Zhejiang Normal University, Jinhua, Zhejiang Province, 321004, China — ³Department of Chemistry, Rice University, 6100 Main Street Houston, TX 77005, USA — ⁴ETSF Scientific Development Centre, Dpto. Fisica de Materiales, Universidad del Pais Vasco, Centro de Fisica de Materiales CSIC-UPV/EHU-MPC, Av. Tolosa 72, E-20018 San Sebastian, Spain

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. 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. The anti-adiabatic 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. I illustrate the formalism by applying it to the calculation of excitation energies in a few model systems.