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Berry Phases and Potential Energy Surfaces beyond the Born-Oppenheimer Approximation

Date: 2017-10-24
Time: 14:00
Venue: 物理研究所M楼236会议室
Speaker: Prof. E.K.U. Gross

Max Planck Institute of Microstructure Physics

报告摘要
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. 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]. This is demonstrated for the laser-induced ring opening of the oxirane molecule [5]. We present a multi-component density functional theory [6] 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 [7].
 
[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]  S.K. Min, F. Agostini, I. Tavernelli, E.K.U. Gross, J. Phys. Chem. Lett. 8, 3048 (2017).
[6]  R. Requist, E.K.U. Gross, Phys. Rev. Lett. 117, 193001 (2016).
[7]  A. Schild, E.K.U. Gross, Phys. Rev. Lett. 118, 163202 (2017).

报告人简介
Prof. Dr. E. K. U. Gross is a director of Max Planck Institute of Microstructure Physics, Halle, Germany. Prof. Gross is the founder of the Time-Dependent Density Functional Theory (TDDFT) and a pioneer in ab initio theory for superconductivity. He received his Dr. phil. nat. from J.W. Goethe University Frankfurt Physics Department in 1980, then became a postdoctoral physicist at University of California, Santa Barbara (with Walter Kohn). In 1990 he joined University of Würzburg as Fiebiger Professor. During 2001-2009 he was Professor of Theoretical Physics at the Free University Berlin. Since 2009 he become director at the Max Planck Institute of Microstructure Physics.

邀请人及联系人:孟  胜 研究员(电话:82649396)