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HL: Fachverband Halbleiterphysik
HL 84: Joint Focussed Session: Theory and Computation of Electronic Structure: New Frontiers VII
HL 84.1: Topical Talk
Thursday, March 17, 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.