Regensburg 2019 – wissenschaftliches Programm

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O: Fachverband Oberflächenphysik

O 58: Focus Session: Electron-Phonon Interactions II

O 58.1: Hauptvortrag

Mittwoch, 3. April 2019, 15:00–15:30, H15

Towards a systematic way of treating non-adiabatic effects — •E.K.U. Gross — Max Planck Institut of Microstructure Physics, 06120 Halle, Germany

Some of the most fascinating quantum phenomena, such as the process of vision or phonon-driven superconductivity are examples of non-adiabatic effects. To treat such phenomena in a genuine first-principles way, one has to start from the full Hamiltonian of the complete system of electrons and nuclei. We employ the exact factorization [Abedi, Maitra, Gross, PRL 105, 123002 (2010)] of the full electron-nuclear wavefunction into a purely nuclear part and a many-electron wavefunction which parametrically depends on the nuclear configuration and carries the meaning of a conditional probability amplitude. The equations of motion of these wavefunctions uniquely define ``exact phonons" beyond the Born-Oppenheimer approximation and the electron-phonon interaction (to all orders) in a very compact way. In addition to the exact potential energy surface there appears a Berry-type vector potential in the ionic equation of motion which gives rise to a geometric phase beyond the Born-Oppenheimer limit. We discuss how this exact geometric phase differs from the Born-Oppenheimer Berry phase, and how this difference can potentially be measured [Requist, Proetto, Gross, PRA 96, (6), 062503, (2017)]. In the time-domain, we deduce, from the exact equations of motion, a novel mixed-quantum-classical algorithm [Min, Agostini, Tavernelli, Gross, JPCL 8, 3048 (2017)] which provides a much improved (over surface hopping) description of decoherence.