Abstract:
The Born-Oppenheimer approximation is among the most fundamental ingredients of modern Theoretical Chemistry and Condensed-Matter Physics. This approximation not only makes calculations feasible, it also provides us with an intuitive picture of chemical reactions. Yet it is an approximation, and some of the most fascinating phenomena occur in the regime where the Born-Oppenheimer approximation breaks down. Prime examples are the process of vision, photovoltaic processes as well as phonon-driven superconductivity. To tackle such situations where strong non-adiabatic couplings dominate the scene, one has to face the full Hamiltonian of the complete system of electrons and nuclei. We deduce an exact factorization of the complete electron-nuclear wavefunction into a purely nuclear part and a many-electron wavefunction which parametrically depends on the nuclear configuration and which has the meaning of a conditional probability amplitude. From this we derive equations of motion for the nuclear and electronic wavefunctions which lead to a unique definition of exact potential energy surfaces as well as exact geometric phases [1]. We discuss a case where the exact Berry phase vanishes although there is a non-trivial Berry phase for the same system in Born-Oppenheimer approximation, implying that in this particular case the Born-Oppenheimer Berry phase is an artifact which has no counterpart in the true electron-nuclear wave function. [2] Furthermore, whenever there is a splitting of the exact 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 [4].
[1] A. Abedi, N.T. Maitra, E.K.U. Gross, Phys. Rev. Lett. 105, 123002 (2010).
[2] S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, Phys. Rev. Lett. 113, 263004 (2014).
[3] A. Abedi, F. Agostini,Y. Suzuki, E.K.U. Gross, Phys. Rev. Lett. 110, 263001 (2013).
[4] S.K. Min, F. Agostini, E.K.U. Gross, Phys. Rev. Lett. 115, 073001 (2015).
Brief Bio:
Eberhard Gross completed his doctorate in physics at J. W. Goethe University Frankfurt in 1980. After postdoctoral fellowships at J. W. Goethe University and UC Santa Barbara, he joined the University of Würzburg as a Fiebiger Professor in 1990. He became an elected Max Planck Fellow and Professor of Theoretical Physics at the Free University Berlin in 2001. Since 2009, he has been a Director at the Max Planck Institute of Microstructure Physics in Halle. The research interests of Eberhard Gross span superconductivity, magnetism, quantum transport as well as how these phenomena evolve in real time under the influence of external fields. He layed the foundation of time-dependent density functional theory with a statement now known as Runge-Gross theorem. This theorem demonstrates that the intricate dynamics of an interacting many-electron system can be described and understood by knowledge of the time-dependent density alone. In recent years his research interests included the coupled motion of electrons and nuclei beyond the Born-Oppenheimer approximation. He has published over 240 articles and book chapters which have been cited more than 23000 times.