Potential Energy Surfaces and Berry Phases beyond the Born-Oppenheimer Approximation (Prof. E. Gross)
- Datum: 02.05.2017
- Uhrzeit: 14:30 - 15:30
- Vortragende(r): Prof. Dr. Eberhard K. U. Gross
- Max-Planck-Institut für Mikrostrukturphysik
- Raum: Herbert Walther Lecture Hall
- Gastgeber: MPQ
Yet 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 [1] 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 [2], 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 [3]. 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 [4]. We present a multi-component density functional theory [5] 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 [6].
References:
[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).
[5] R. Requist, E.K.U.
Gross, Phys. Rev. Lett. 117, 193001 (2016).
[6]
A. Schild, E.K.U. Gross, Phys. Rev.
Lett. (2017, in press).