2pm - 4pm
Friday 14 February 2020

Launch event of the Quantum Foundations Centre

To mark the launch of the Centre, Dr Cesare Tronci from the Department of Mathematics will deliver a seminar on phase-space wave functions in mixed quantum-classical dynamics followed by an informal reception.


Seminar room, Alan Turing building (BB)
Floor 3, room 30
University of Surrey

There is no need to book onto this event, just show up on the day.


How does a classical particle interact with a quantum particle?

Since the early days in quantum mechanics, this question has represented one of the most outstanding problems in physics. After its emergence in measurement theory, quantum-classical coupling has been representing a long-standing question in ab-initio methods for molecular dynamics.

Conventional approaches beyond Born-Oppenheimer theory are often based on Born-Huang expansions invoking the existence of appropriate classical limits. While mean-field methods generally possess a solid mathematical ground, their applicability is rather limited and little consensus has yet been reached on models retaining classical-quantum correlations.

Recently, we have proposed a new perspective in which challenging aspects related to classical limits are overcome by regarding part of a hybrid system as entirely classical from the start. This picture requires an unprecedented approach combining Koopman’s theory of classical wavefunctions with modern methods in symplectic geometry. Koopman wavefunctions on phase-space have always been little known and Sudarshan's first suggestion in '76 of using them in quantum-classical coupling led to several issues.

We solved these issues through a geometric modification of Koopman’s original theory obtained from its underlying variational principle. Here, we shall show how a new type of quantum-classical wave equation is capable of reproducing essential features in hybrid dynamics, thereby leading to a new quantum-classical density operator and extending Bohmian trajectories to the hybrid setting.

Finally, we shall present exact solutions for the spin-boson model and show how differences with respect to the full quantum treatment may emerge depending on the value of the coupling constant.


Dr Tronci is a Reader in the Department of Mathematics at Surrey and works on the foundations of quantum mechanics.

Programme of events

Time Activity
2pm - 2:05pm Welcome and introduction from Jim Al-Khalili
2:05pm - 3pm Seminar with speaker Dr Cesare Tronci
3pm - 4pm Informal reception (tea, coffee, cakes and networking)
Visitor information

Find out how to get to the University, make your way around campus and see what you can do when you get here.