The Exact Factorization, a Universal Approach to Non-Adiabaticity

TH Department Seminar
Date: Dec 14, 2023
Time: 02:00 PM (Local Time Germany)
Speaker: Prof. Eberhard K. U. Gross
Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Israel
Location: https://zoom.us/j/97003916265?pwd=Qkg3Q0ZsSHA2YW1oaDB4MW5GOWQ2dz09
Room: Meeting ID: 970 0391 6265 | Passcode: 076169
Host: TH Department

The adiabatic approximation describes the molecular wave function as a single product of a Born-Oppenheimer state and a nuclear wave packet. This approximation is a corner stone of modern quantum chemistry and solid-state physics. It not only makes computations feasible, it also provides us with an intuitive picture of many chemical processes.

Yet, it is an approximation, and many fascinating phenomena appear in the non-adiabatic regime. Prominent examples are the microscopic processes underlying the physiology of vision, likewise laser-induced structural phase transitions in solids, phonon-mediated superconductivity and, very importantly, the phenomenon of electronic decoherence, i.e. the loss of “quantumness”, well-known for its capacity of preventing genuine scalable quantum computing to this day. In this lecture a unified approach to non-adiabaticity, known as the exact factorization, will be presented. Starting from the full many-body Hamiltonian of interacting electrons and nuclei, we deduce a formally exact factorization of the full electron-nuclear wave function into a purely nuclear part and a many-electron wave function which parametrically depends on the nuclear configuration and which has the meaning of a conditional probability amplitude [1]. This gives the exact molecular wave function an adiabatic-like appearance while the equations of motion for the two factors provide an ideal starting point to develop efficient algorithms for the study of non-adiabatic phenomena. The successful prediction of laser-induced isomerization processes [2], the ab-initio description of decoherence [3], calculations of the molecular Berry phase beyond the Born-Oppenheimer approximation [4] and accurate computations of vibrational dichroism will demonstrate the power of the approach. Moreover, the equations of motion give rise to the concept of exact forces (both quantum and classical) on the nuclei, a concept which holds even when the nuclear wave packet splits, and in the presence of topological (Berry-connection-type) vector potentials [5].

[1] A. Abedi, N.T. Maitra, E.K.U. Gross, PRL 105, 123002 (2010).

[2] F. Agostini, S.K. Min, I. Tavernelli, E.K.U. Gross, JPCL 8, 3048 (2017).

[3] S.K. Min, F. Agostini, E.K.U. Gross, PRL 115, 073001 (2015).

[4] S.K. Min, A. Abedi, K.S. Kim, E.K.U. Gross, PRL 113, 263004 (2014).

[5] Chen Li, R. Requist, E.K.U. Gross, PRL 128, 113001 (2022).