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J. Burgdörfer:
"Time-dependent second-order density matrix theory: first results";
Vortrag: 19th Conference on Recent Progress in Many-Body Theories, Pohang, Südkorea (eingeladen); 26.06.2017 - 30.06.2017.

Time-dependent second-order density matrix theory: first results
Joachim Burgdorfer
Institute for Theoretical Physics, Vienna University of Technology,
Wiedner Hauptstrasse 8-10, A1040 Vienna, Austria, EU

Abstract
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. The ab-initio simulation of dynamical correlations, for example particle-particle correlations in the break-up of many-body systems, requires approaches beyond mean-field descriptions. The full solution of the full N-body Schrödinger equation is still prohibitive for large systems due to the unfavourable exponential (or factorial) scaling with the number of degrees of freedom. The present approach aims at bridging the gap between descriptions based on the reduced
one particle density ρ(r;t) such as TDDFT and mean-field models on one end and the full wavefunction based N-particle description on the other. Our working variable is the timedependent two-particle reduced density matrix (2RDM), D(r1r2;r´1r´2;t). As a hybrid between
the one-body density and the full wavefunction, the 2RDM contains the complete information on two-particle correlations but still scales polynomially with particle number. We have developed a time-dependent two-particle reduced density matrix (TD-2RDM) theory that is based on a contraction consistent reconstruction of the 3RDM, as required for the proper closure of the equations of motion for the TD-2RDM. Contraction consistency and enforcing N-representability constraints are key to achieve accurate and stable propagation of non-equilibrium dynamics. We benchmark our approach for N-fermion systems.

Work in collaboration with Fabian Lackner, Iva Brezinova, Takeshi Sato, Kenichi Ishikawa.