In his career as a theoretical physicist, Prof Hendrik Geyer has always put up his hand for the big problems in physics – from developing a mathematical framework in the 1990s that has become fundamental to the building of quantum mechanical systems today, to building the field of physics in South Africa.
The South African Institute of Physics (SAIP) has recently awarded him with the Institute's De Beers Gold Medal, the greatest distinction that is conferred in South Africa for achievements in physics. During a special ceremony at the Stellenbosch Institute for Advanced Study (STIAS) on 13 September 2022, SAIP president Prof Makaiko Chithambo said the award recognises Prof Geyer's fundamental and novel contributions to the field of non-Hermitian quantum mechanics, his leadership in building the field of theoretical physics in South Africa, and his significant contributions to education and training of students.
“Most importantly, we want to recognise his competent leadership in the establishment of important structures such as the SAIP, the National Institute for Theoretical Physics (NITheP) and the Stellenbosch Institute for Advanced Study," he added.
Just before handing over the medal in person, the praise singer Mandlenkosi Sixolo also praised Prof Geyer for his contributions in true African style.
In his acceptance speech, Prof Geyer lifted out three take-home lessons from his own career.
Firstly, never underestimate the value of dedicated teachers
His formative years were spent at Templeton High School in Bedford, a small settler town 200km from Gqeberha (then Port Elizabeth). The first principal of the school in 1865 was the Scot, Reverend Templeton, who had been recruited from Lovedale College, a forerunner of the current Fort Hare University. Due to this Scottish legacy, the school maintained an ethos of dedicated teachers who knew how to teach the basics, he recalled.
He later matriculated from Afrikaanse Hoër Seunskool in Pretoria where a subject such as mechanics took the learners beyond the standard physics curriculum, focussing on Newton's Laws of Motion: a lasting impression about the implications of the third law resulted from the teacher asking questions such as: “Boys, can I pull myself up tugging on my own shoelaces", answering with an emphatic “No"."
This exposure to Newtonian physics awakened in him an interest in nuclear physics. With a bursary of R360 a year from the Atomic Energy Corporation, he studied physics at Stellenbosch University. During holiday work at the AEC, he rubbed shoulders with senior theoretical physicists such as Dr Chris Engelbrecht and Dr Fritz Hahne. They later became his study leaders, mentors, and lifelong friends.
At the time a new (and successful) collective model of nuclear excitations of the atomic nucleus drew on previous phenomenological descriptions, while adding a microscopic element by treating pairs of nucleons (in themselves fermions) as bosons. Since the fundamental classes of quantum particles, viz, fermions and bosons, have widely different properties, this seeming contradiction called for a systematic approach requiring a mathematical framework which allows pairs of fermions to be described in a bosonic language. This was the focus of his doctoral research for which he enrolled at SU under the leadership of Prof Engelbrecht (then at SU) and Dr Hahne. The mathematical framework resulting from the so-called boson mappings which were introduced in the thesis successfully captured the essence of introducing boson degrees of freedom to describe a quantum system comprised of fermions. It also provided a solid framework for understanding the phenomenology of the so-called interacting boson model of the nucleus.
After completion of his PhD in 1981, he took up a postdoctoral fellowship in the nuclear theory research group at the State University of New York in Stony Brook.
In the 1980s the theoretical physics group at the AEC was moved to Stellenbosch University, as part of a country-wide program to situate the fundamental sciences at universities, and the applied sciences at bodies such as the AEC and the CSIR.
This is his second take-home lesson: Opportunities seldom arrive on a golden platter, so when something worthwhile comes along, grab it and do what you can with what you have
For the next decade, the nuclear physics research group continued with their basic research in a house at 7 Joubert Street – currently home to the Africa Open Institute for Music, Research and Innovation at SU – just opposite the street from the Department of Physics in the Merensky Building.
“We achieved something during that time in Joubert Street. Apart from lecturing honours courses and supervising postgraduate students, we didn't bother anybody, and nobody bothered us," he recalls.
Prof Geyer continued working on quantum systems with another AEC-bursary holder, Prof Frikkie Scholtz, who joined the Pelindaba group in 1983.
By taking the non-Hermitian structures which result from a boson mapping at face value, they realised that it is often more advantageous to use variables that do not comply to the standard Hermitian point of departure. Prof Scholtz explains: “We realised that these variables still represent a consistent quantum mechanical system even if they do not comply with the standard Hermitian matrix. We then got the idea to use this as our point of departure for the construction of a quantum system".
Traditionally an observer decides which dynamical variables in a specific quantum mechanical framework are measurable (such as position and momentum) and then proceeds accordingly to introduce the Hamiltonian (or energy) from which to calculate properties of the system described in terms of these variables. The Stellenbosch group realised that by starting from the system description (or Hamiltonian, now non-Hermitian) one could systematically identify the dynamical variables in a consistent way, and thereby provide a fully self-consistent framework of quantum mechanics bases on a non-Hermitian Hamiltonian.
“People did not really know what they were doing when using a so-called variational approach to calculate the properties of a quantum system when confronted with a non-Hermitian Hamiltonian" explains Prof Geyer. “We mainly wanted to correct this at the time, but in doing so actually developed the full mathematical framework for dealing with non-Hermitian variables."
After three decades, the 1992-paper in which they published the results of this framework still receives up to two citations per week, with more than 700 citations in total.
In the world of academic publishing, this type of paper is called a “sleeping beauty", explains Prof Scholtz. In other words, nearly three decades after the publication of this fundamental work, it has literally “woken up" to find new applications, now also in the field of parity-time symmetry (PT symmetry). This includes PT symmetric optical sensors, lasers, antenna receivers and transmitters, and even invisibility cloaks.
According to Prof Mark Tame, a physicist specialising in quantum information science in SU's Department of Physics, all these physics applications are based on the novel way in which loss and gain in a physical system can be engineered to obtain a distinct advantage over conventional approaches: “Prof Geyer and his colleagues' work on PT symmetry has helped lay the mathematical foundation for these applications," he explains.
Prof Geyer also played a pivotal role in setting up long-running programmes such as the Chris Engelbrecht Summer School, which for the past 40 years have brought together physicists from all over the world and Africa. Another major initiative was the establishment of the National Institute for Theoretical Physics (NITheP) which was established in 2008, and which has recently been renamed the National Institute for Theoretical and Computational Sciences (NITheCS). Due to his ongoing involvement with STIAS, Prof Geyer is now also part of the organising committee for the first Nobel in Africa Symposium.
“We will host a series of Nobel symposia over the next seven years, the first and only place outside Sweden to host such an event," he adds.
The last life-lesson he dedicated to his wife, Jane, whom he met 50 years ago in the first-year chemistry class at SU, saying that what he achieved had all to do with her support, encouragement and love over all those years.
Several of Prof Geyer's former colleagues and students also congratulated him on this achievement, including Prof Rudolf Erasmus (SAIP council member), Prof Erich Rohwer (SU Department of Physics), Dr Hannes Kriel (former student), Prof Louise Warnich (Dean: Faculty of Science) and Dr Christine Steenkamp (SU Department of Physics).
On the photo above, from left to right, Prof Makaiko Chithambo, president of SAIP, Prof Hendrik Geyer, and the praise singer Mandlenkosi Sixolo. Photo: Wiida Fourie-Basson