# Advances in the study of large quantum systems

22 November 2019

Scientists at Oxford University’s Physics Department have developed a new way to simulate quantum systems of many particles to allow for the investigation of the dynamic properties of quantum systems. It is based on a long-known alternative formulation of quantum mechanics which now has been empowered to allow the study of large quantum systems.

The astonishing world of subatomic particles is governed by quantum mechanics which gives rise to a large number of phenomena unknown in our daily experience: fractional occupancy of several states at the same time, spooky instantaneous interaction over large distances or the inability of electrons to be in the same state are just a few examples.

**Understanding large quantum systems**

Most of these phenomena have been studies of single or just a few interacting particles as large complex quantum systems overpower our theoretical and computational capabilities to make predictions. Nevertheless, many-body quantum systems are at the core of many scientific problems ranging from the complex biochemistry in our bodies to the behaviour of matter inside of large planets or even technological challenges like high-temperature superconductivity. In recent decades, huge progress has been made to simulate such quantum systems but a decoupling of the electron and ions dynamics is usually at the core of these methods and prohibits the investigation of the full dynamics of the system.

To consider the full dynamics of quantum many-body systems, the research group at Oxford University led by Professor Gianluca Gregori along with PhD student Brett Larder, revived an old alternative formulation of quantum mechanics developed by David Bohm. It follows a main trajectory of quantum particles like in classical mechanics and has a separate, but coupled, equation for the phase information. As it is fully equivalent to the standard description, the numerical effort is also prohibitive in its pure form. However, the present work shows that a suit of approximations can be found that leave the results almost unchanged but increases the computational speed by several orders of magnitude. With this huge increase of numerical efficiency, it is now possible to follow the full dynamics of fully interacting electron-ion systems. This new approach thus opens new classes of problems for efficient solutions – in particular, where either the system is evolving or quantum dynamics of the electrons has a significant effect on the heavier ions or the entire system.

**Reformulating quantum mechanics**

Professor Gregori commented: ‘Bohm quantum mechanics has often been tainted by scepticism and controversy. In its original formulation, however, this is just a different reformulation of quantum mechanics. The advantage of doing this is that different approximations become simpler to implement and this can increases the speed and accuracy of simulations involving many-body systems.’

Dr Gericke from the University of Warwick, who helped to design the new computer code, added: ‘This new numerical tool will be a great asset when designing and interpreting experiments on warm dense matter. From its results, and especially when combined with designated experiments, we can learn much about matter in the large planets and for laser fusion research. However, I believe its true strength lies in its universality and possible applications in quantum chemistry or strongly driven solids.’

‘Fast nonadiabatic dynamics of many-body quantum systems’ by B Larder et al, *Science Advances*

*Image caption: Static ion-ion sturcture factors for aluminum*