Article Outline
Glossary
Perturbation Theory, Introduction to
Introduction
The Framework
The Leading Order Born–Oppenheimer Approximation
Beyond the Leading Order
Future Directions
Bibliography
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Abbreviations
- Adiabatic decoupling :
-
In a complex system (either classical or quantum), the dynamical decoupling between the slow and the fast degrees of freedom.
- Adiabatic perturbation theory :
-
A mathematical algorithm which exploits the adiabatic decoupling of degrees of freedom in order to provide an approximated (but yet accurate) description of the slow part of the dynamics. In the framework of QMD, it is used to approximately describe the dynamics of nuclei, the perturbative parameter ε being related to the small electron/nucleus mass ratio.
- Electronic structure problem:
-
The problem consisting in computing, at fixed positions of thenuclei, the energies (eigenvalues) and eigenstates corresponding to the electrons. An approximate solution is usually obtained numerically.
- Molecular dynamics :
-
The dynamics of the nuclei in a molecule. While a first insight in the problem can be obtained by using classical mechanics (Classical Molecular Dynamics), a complete picture requires quantum mechanics (Quantum Molecular Dynamics) Perturbation Theory in Quantum Mechanics. This contribution focuses on the latter viewpoint.
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Books and Reviews
Bohm A, Mostafazadeh A, Koizumi A, Niu Q, Zwanziger J (2003) The geometric phase in quantum systems. Texts and monographs in physics. Springer, Heidelberg
Teufel S (2003) Adiabatic perturbation theory in quantum dynamics. Lecture notes in mathematics, vol 1821. Springer, Berlin
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Panati, G. (2012). Perturbation Theory and Molecular Dynamics. In: Meyers, R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1806-1_82
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