Multisymplectic Koopman dynamics of correlated molecular systems

The statistical correlations realized in several molecular experiments require large computational resources that challenge current numerical methods. Typical situations involve strong light-matter correlations arising from the molecular motion in optical cavities. In several cases, light may be well described as a macroscopic classical eld, while the molecular motion requires a microscopic description. Despite their computational advantages, such reduced approaches currently fail to capture correlations with satisfactory accuracy, or do not even retain fundamental consistency criteria. A new level of mathematical multiscale models is required.

We propose to tackle this challenge by exploiting our successful progress on the symplectic geometry of Koopman wavefunctions, which has recently opened an entirely new direction in the simulation of correlated molecular systems. Arising as a Hilbert-space formulation of classical dynamics, Koopman wavefunctions undergo Hamiltonian dynamics associated to crucial structures in symplectic geometry. These symplectic structures provide Koopman wavefunctions with exceptional properties, and ultimately allow capturing correlations with unprecedented accuracy for such reduced models. However, classical elds currently lie beyond this description since their geometry is more complex and involves the jet bundle construction for Taylor polynomials. Also, the resulting Hamiltonian dynamics hinges on multi-symplectic structures, whose role in Koopman dynamics is yet unknown.

This project aims at exploiting the exibility of the variational framework to blend Koopman dynamics and multisymplectic geometry. With this substantial mathematical step, this project will ultimately lead to new reduced models for correlated light-matter systems in molecular sciences that both tackle computational complexity and provide satisfactory accuracy, while retaining mathematical consistency.

Open to both UK and international candidates.

Up to 30% of our UKRI-funded studentships can be awarded to candidates paying international rate fees. Find out more about eligibility.

You will need to meet the minimum entry requirements for our Mathematics PhD programme.