A 1-day workshop, entitled “Recent Developments and Possible Extensions to the World of the Exact Factorization and Bohmian Dynamics” was held at the University of Bristol on Monday 22 April 2019. The workshop comprised a forum of eight 40-minute seminars with four breaks for discussion with world experts in the two related subjects of Bohmian Dynamics (BD) and Exact Factorization. This 1-day scientific encounter was intended to engage the CHAMPS team’s postdocs in these two topics, disseminate the recent work in these two areas performed by members of the CHAMPS team to the visiting world experts and inform all of the participants of the latest advances in these topics in the chemistry community.

To define the topics, Bohmian trajectories are meant to represent classical particle paths corresponding to quantum solutions when the quantum coupling constant h-bar has been set equal to zero in the 1927 Born-Oppenheimer (BO) approximation. J von Neumann’s 1931 approach (described in his textbook) is now called the “Exact Factorization” (EXF). The EXF approach generalised the formulation of the quantum-classical problem which has recently seen an active revival and development in numerical simulations of molecular chemistry.

Sophya Garashchuk discussed finite-dimensional representations of Bohmian trajectories and numerical difficulties in the implementation of Bohmian dynamics.

Salvador Miret-Artes discussed stochastic Bohmian particle trajectories as a possible representation of solutions of the Schrödinger-Langevin equation. In one of the discussion sessions which followed this lecture, the idea of stochasticity as a means of quantifying uncertainty in numerical simulations of the dynamics of molecular chemistry was a prominent topic.

Werner Koch discussed Bohmian trajectories whose space and time parameters and complex. This intriguing concept led to considerable discussion.

Cesare Tronci discussed a new mathematical formulation of EXF in terms of density matrices. In this new formulation, an analogue of the Bohmian trajectories arises as the Lagrangian paths of quantum complex-fluid parcels. The talk was based on a paper co-authored with a CHAMPS co-PI (Holm), which is to appear in Acta Mathematica Applicandae.

Eberhard Gross surveyed the modern development of the EXF approach and many of its successful applications in computational simulations of molecular chemistry processes during the past few years.

Ivano Tavernelli surveyed a series of standard applications of Bohmian trajectories in the BO framework, obtained upon setting the quantum coupling constant h-bar equal to zero.

Basile Curchod surveyed recent applications of the more modern EXF which involved the effects of h-bar at linear order. He also discussed many successful applications of EXF in computational simulations of molecular chemistry and explained the strategy of design of modern computational algorithms for these applications. Also

Mike Robb discussed recent applications of the BO approximation to computational simulations of atto-second processes in quantum molecular chemistry.

The many computational results displayed during the workshop raised the question of quantifying the uncertainty in these solutions. The discussions of these questions among the participants raised issues about how to model the combination of theoretical and computational errors in the quantum-classical interaction problem at the foundations of molecular chemistry which has an intrinsic uncertainty. We hope that the workshop will stimulate our efforts in improving the understanding of mathematical features of Bohmian Dynamics and Exact Factorization and creating new computational simulation techniques for use in chemistry.

*Abstracts and slides for the lectures can be found here soon…*