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Asymptotics and quantum variational principles


   Department of Mathematics

  Dr Cesare Tronci  Friday, July 22, 2022  Competition Funded PhD Project (UK Students Only)

About the Project

This is a project for highly motivated students with a background in Lagrangian/Hamiltonian mechanics and ideally looking to pursue a research career. The adiabatic theory of molecular motion of Born and Oppenheimer is ordinarily derived by applying suitable asymptotic/WKB methods to Schrödinger's quantum evolution equation. This project aims at studying how these methods can be instead applied to the variational principle underlying the wavefunction dynamics. More specifically, recent variational approaches to molecular motion will serve as the starting point for a new departure in Born-Oppenheimer asymptotics, which will be combined with the geometric structures appearing in the variational principles of quantum mechanics. Eventually, we want to investigate the possible formulation of new molecular dynamics models that can avoid the presence of the well-known topological singularities appearing in the standard approach.

Supervisor: Dr Cesare Tronci

This is a minimum 3 year project. We are able to offer this opportunity starting in October 2022.

Entry requirements

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

English language requirements: IELTS Academic 6.5 or above (or equivalent) with 6.0 in each individual category.

How to apply

Applications should be submitted via the Mathematics PhD programme page on the "Apply" tab.

Please state clearly the studentship project at you would like to apply for.


Funding Notes

Full UK tuition fees and a tax-free stipend. This project is on offer in competition with a number of other projects for funding. This opportunity may be available with partial funding for overseas fees for exceptional applicants. However, funding for overseas students is limited and applicants are encouraged to find suitable funding themselves. Funded by the University of Surrey.

References

Holm D D, Schmah T and Stoica C 2009 Geometric Mechanics and Symmetry: From Finite to Infinite Dimensions (OUP)
Foskett M.S., Holm D.D. & Tronci C. 2019 Geometry of nonadiabatic quantum hydrodynamics. Acta Appl. Math. 162 63–103

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