Imperial College London
Alternate

ProfessorDarrylHolm

Faculty of Natural Sciences, Department of Mathematics

Chair in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8531d.holm Website

 
 
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Location

 

6M27Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Foskett:2019:10.1007/s10440-019-00257-1,
author = {Foskett, MS and Holm, DD and Tronci, C},
doi = {10.1007/s10440-019-00257-1},
journal = {Acta Applicandae Mathematicae},
pages = {63--103},
title = {Geometry of nonadiabatic quantum hydrodynamics},
url = {http://dx.doi.org/10.1007/s10440-019-00257-1},
volume = {162},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The Hamiltonian action of a Lie group on a symplectic manifold induces a momentum map generalizing Noether’s conserved quantity occurring in the case of a symmetry group. Then, when a Hamiltonian function can be written in terms of this momentum map, the Hamiltonian is called ‘collective’. Here, we derive collective Hamiltonians for a series of models in quantum molecular dynamics for which the Lie group is the composition of smooth invertible maps and unitary transformations. In this process, different fluid descriptions emerge from different factorization schemes for either the wavefunction or the density operator. After deriving this series of quantum fluid models, we regularize their Hamiltonians for finite  by introducing local spatial smoothing. In the case of standard quantum hydrodynamics, the ≠0 dynamics of the Lagrangian path can be derived as a finite-dimensional canonical Hamiltonian system for the evolution of singular solutions called ‘Bohmions’, which follow Bohmian trajectories in configuration space. For molecular dynamics models, application of the smoothing process to a new factorization of the density operator leads to a finite-dimensional Hamiltonian system for the interaction of multiple (nuclear) Bohmions and a sequence of electronic quantum states.
AU  - Foskett,MS
AU  - Holm,DD
AU  - Tronci,C
DO  - 10.1007/s10440-019-00257-1
EP  - 103
PY  - 2019///
SN  - 0167-8019
SP  - 63
TI  - Geometry of nonadiabatic quantum hydrodynamics
T2  - Acta Applicandae Mathematicae
UR  - http://dx.doi.org/10.1007/s10440-019-00257-1
UR  - http://hdl.handle.net/10044/1/73988
VL  - 162
ER  -
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