The world of quantum mechanics is characterised by its discrete nature, where particles can only have energies in step-like amounts, known as quantum energy levels. They cannot continuously change their momenta. Werner Heisenberg received the Nobel Prize in Physics 1932 for his discovery of quantum mechanics.
In more modern times, it was discovered that even the Hall effect, or electrical conductivity in topological insulators, has to be discrete. When an electric field impinges on insulating systems, the electrons are instead “pumped” in a perpendicular direction via special quantum channels that are not easily destroyed, and hence respond in a quantized manner. Such behaviour tied theoretical condensed matter physics with the deep mathematical field of topology, and is behind the Nobel Prize in Physics 2016 awarded to Duncan Haldane.
Recently, our research team led by Asst Prof Lee Ching Hua and Prof Gong Jiangbin made the surprising discovery that quantized response behaviour is not only restricted to quantum systems. The team devised a way to observe quantized response behaviour in generic systems, be they classical or quantum, such as electrical circuits, metamaterials and even deterministic games.
Their inspiration stems from the complex nature of energy values in non-equilibrium systems, where the total energy or number of particles is not fixed. As complex paths can assume topologically distinct loops in complex planes, akin to how a rope tied around a pole must be unwound a distinctive number of times before it is freed, there is always a notion of quantized topology whenever such complex paths can be defined and measured.
This work was published in Nature Communications (September 2021).