Madelung transform and variational asymptotics in Born-Oppenheimer
molecular dynamics
- URL: http://arxiv.org/abs/2305.18972v2
- Date: Tue, 18 Jul 2023 19:03:34 GMT
- Title: Madelung transform and variational asymptotics in Born-Oppenheimer
molecular dynamics
- Authors: Paul Bergold and Cesare Tronci
- Abstract summary: Born-Oppenheimer molecular dynamics (BOMD) has been widely studied by resorting to powerful methods in mathematical analysis.
This paper presents a geometric formulation in terms of Hamilton's variational principle and Euler-Poincar'e reduction by symmetry.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: While Born-Oppenheimer molecular dynamics (BOMD) has been widely studied by
resorting to powerful methods in mathematical analysis, this paper presents a
geometric formulation in terms of Hamilton's variational principle and
Euler-Poincar\'{e} reduction by symmetry. Upon resorting to the Lagrangian
hydrodynamic paths made available by the Madelung transform, we show how BOMD
arises by applying asymptotic methods to the variational principles underlying
different continuum models and their particle closure schemes. In particular,
after focusing on the hydrodynamic form of the fully quantum dynamics, we show
how the recently proposed bohmion scheme leads to an on-the-fly implementation
of BOMD. In addition, we extend our analysis to models of mixed
quantum-classical dynamics.
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