Potential Energy Surfaces and Berry Phases beyond the Born-Oppenheimer Approximation (Prof. E. Gross)
14:30 - 15:30
Prof. Dr. Eberhard K. U. Gross
Max-Planck-Institut für Mikrostrukturphysik
Herbert Walther Lecture Hall
The starting point of essentially all modern electronic-structure techniques is the Born-Oppenheimer approximation. It not only makes calculations feasible, it also provides us with an intuitive picture of chemical reactions.
it is an approximation, and some of the most fascinating phenomena, such as
photovoltaic dynamics, the process of vision, as well as phonon-driven
superconductivity occur in the regime where the Born-Oppenheimer approximation
breaks down. To tackle such situations one has to face the full Hamiltonian of
the complete system of electrons and nuclei. We deduce an exact factorization 
of the full 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.
The equations of motion for these wavefunctions lead to a unique definition of exact potential energy surfaces as well
as exact geometric phases, both in
the time-dependent and in the static case. 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. 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 . This makes the classical force on the nuclei jump from one to another
adiabatic surface, reminiscent of Tully surface hopping algorithms. Based on this
observation, we propose novel mixed-quantum-classical algorithms which provide
a rather accurate, much improved (over surface hopping) description of
decoherence . We present a multi-component density functional theory 
that provides an avenue to make the fully coupled electron-nuclear system
tractable in practice. Finally, we apply the concept of exact factorization to
a purely electronic wave function, thereby separating, in a formally exact way,
fast degrees of freedom (the core electrons) from slow degrees of freedom
(electrons that ionize or produce harmonics). This allows us to deduce, in a
controlled way, the so-called single-active-electron approximation and systematic
improvements thereof .
 A. Abedi, N.T. Maitra, E.K.U. Gross, Phys.
Rev. Lett. 105, 123002 (2010).
 S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross,
Phys. Rev. Lett. 113, 263004 (2014).
 A. Abedi, F. Agostini, Y. Suzuki, E.K.U.
Gross, Phys. Rev. Lett. 110, 263001 (2013).
 S.K. Min, F. Agostini, E.K.U. Gross, Phys. Rev.
Lett. 115, 073001 (2015).
 R. Requist, E.K.U.
Gross, Phys. Rev. Lett. 117, 193001 (2016).
A. Schild, E.K.U. Gross, Phys. Rev.
Lett. (2017, in press).