Berlin 2015 – scientific programme

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SYME: Symposium Frontiers of Electronic Structure Theory: Many-body Effects on the Nano-Scale

SYME 2: Frontiers of Electronic Structure Theory: Many-Body Effects on the Nano-Scale I

SYME 2.1: Invited Talk

Tuesday, March 17, 2015, 10:30–11:00, MA 004

Electronic structure in the vicinity of strong non-adiabatic couplings — •Eberhard K.U. Gross — Max Planck Institute of Microstructure Physics, Halle (Saale), Germany

The Born-Oppenheimer (BO) approximation is among the most fundamental ingredients of modern Condensed-Matter Theroy. Yet, some of the most fascinating phenomena such as the process of vision or phonon-driven superconductivity occur in the regime where the BO approximation breaks down. To tackle such situations one has to face the Hamiltonian of the complete system of interacting electrons and nuclei. We deduce an exact factorization [1] of the full electron-nuclear wavefunction into a purely nuclear part and a many-electron wavefunction which parametrically depends on the nuclear configuration. The resulting equations of motion for the nuclear and electronic wavefunctions lead to a unique definition of exact potential energy surfaces as well as exact geometric phases. We show an example [2] where the geometric phase associated with the conical intersection of BO surfaces has no counterpart in the true electron-nuclear wavefunction. In the time-domain, whenever there is a splitting of the nuclear wavepacket in the vicinity of an avoided crossing, the exact time-dependent surface shows a nearly discontinuous step [3], reminiscent of Tully surface hopping algorithms. Based on this observation we propose novel mixed-quantum-classical algorithms.

[1] Abedi, Maitra, Gross, PRL 105, 123002 (2010).

[2] Min, Abedi, Kim, Gross, PRL 113, 263004 (2014).

[3] Abedi, Agostini,Suzuki, Gross, PRL 110, 263001 (2013).