Nonadiabatic Time Dependent Density Functional Theory and fast nonlinear dynamics of quantum many-body systems

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The project is aimed at a development and numerical implementation of new nonadiabatic approximations in Time Dependent Density Functional Theory (TDDFT). The description of nonadiabadic exchange-correlation (xc) effects is based on our recent advances in formulating the nonequilibrium many-body problem from the point of view of a co-moving observer in a local Lagrangian frame. This concept allows to account for the xc memory effects and thus to overcome a long standing problem of ultranon-locality in TDDFT. In this project TDDFT in a co-moving frame will be reformulated in the most general form, which operates with only one basic variable - the deformation tensor, and describes xc effects in terms of an effective vector potential. The main focus of the present proposal is a numerical implementation and applications of the Lagrangian (geometric) formulation of TDDFT to selected model systems. Numerical simulations of nonlinear many-electron dynamics beyond adiabatic approximation will be performed for quantum nanostructures, defects, and surfaces of semiconductors.