Physics staff and students with visiting academics
from London institutions, the Imperial College and
Brunel University.

A mini workshop on the topic of Quantum Dynamics and non-Hermitian Hamiltonians was held on UKZN’s Pietermaritzburg campus.

Hosted by Dr Alessandro Sergi of the Physics Cluster in the School of Chemistry and Physics, the workshop featured guests from London’s Brunel University and the Imperial College as well as UKZN delegates who held seminars and gave input on the topic and the challenges it presents to scientists.

The workshop aimed to join the expertise of researchers at the Imperial College London and in the Physics Cluster of the University of KwaZulu-Natal, with especial focus on the discussion of problems currently faced by scientists in the computer simulation of quantum dynamics (in the presence of disorder) and in the use of non-Hermitian Hamiltonians.

According to Sergi, quantum theory is the key for understanding the microcosm: high-energy particle physics, chemical bonds and phase of condensed matter.

‘All these phenomena can, in general, be understood by means of such a theory,’ said Sergi. ‘Historically, quantum mechanics was created in order to describe systems in isolation from sources of disorder (thermal and otherwise), which almost inevitably lead to dissipative effects. For such isolated systems, the energy values obtained from quantum theory are represented by real numbers. However, since the dawn of quantum mechanics, the famous Russian Physicist Lev Landau, one of the last polymaths, proposed the use of complex energy values (which, in the mathematical theory, arise from so called non-Hermitian Hamiltonians) in order to describe disintegration processes. From these shy beginnings, nowadays, non-Hermitian Hamiltonians are becoming one of the most efficient theoretical tools to investigate dissipative processes in condensed matter.’

During the three-day workshop, particular attention was given to the cross-fertilisation between the fields of computer simulation and quantum dynamics described by non-Hermitian Hamiltonians. The workshop format allowed the group of lecturers, professors and postdoctoral researchers to engage in intensive discussion and activities on the subject and included brain-storming sessions and practical work after the oral presentations.

Speakers at the workshop included Dr Eva-Maria Graefe of the Imperial College; Professor Dorje Brody, Chair in Mathematics in the Department of Mathematical Sciences at Brunel University, and Dr Daniel Uken of the UKZN Physics Cluster in Pietermaritzburg.

Graefe, who is working on the development of a semi-classical framework for non-Hermitian quantum theories, has a research background in theoretical quantum dynamics in the context of atomic physics, and in the description of ultracold atoms and Bose-Einstein condensates. In this context, she has been working on non-Hermitian and PT-symmetric quantum theories, semi-classical methods and quantum chaos.

Brody’s research covers a broad range of topics in applied mathematics, from quantum gravity to financial mathematics. He is on the advisory panel for the Journal of Physics and the editorial board for the International Journal of Theoretical and Applied Finance.

Uken is an expert in the methods of simulation of nonadiabatic effects. Currently, he holds an NRF postdoctoral bursary in the research group led by Sergi. This group comprises an NRF C3 postdoctoral researcher, Dr Zloshchastiev; PhD students, Mr Nkosinathi Dlamini, Mr Emmanuel Obaga and Mr Sashwin Sewran, and MSc student, Derrick Beckedahl, all of whom are performing advanced research on numerical methods for the computer simulation of quantum dynamics.

The group had the opportunity to interact with Graefe and Brody during the workshop in order to establish a scientific collaboration on the topics discussed.

Sergi, who extended an invitation to the workshop to all members of UKZN’s School of Chemistry and Physics, hopes that the event can become a regular, fully-fledge workshop in future.