Mathematical structure of the quantum Rabi model. This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the ....Mathematical structure of the quantum Rabi model. This project aims to find the mathematical structure behind the quantum Rabi model, the simplest model describing the interaction between quantum light and matter. The Rabi model is the connecting link in the essential interplay between mathematics, physics, and technological applications. Solving the mathematical structure behind it is expected to form the basis for solving related and equally important models. Such models describe a qubit, the building block of quantum information technologies, and so could realise quantum algorithms and quantum computations.Read moreRead less
Canonical quantisation for classical integrable equations. This project is in the area of fundamental, enabling science. Integrable systems, both classical and quantum, arise as certain classes of dynamical universality in various problems of pure and applied mathematics and in physics. The project will significantly deepen our understanding of cross-relations between geometry and integrable systems.
Algebraic and computational approaches for classical and quantum systems. This project aims to use a combination of algebraic, analytic and numerical techniques to develop computational algorithms to address a range of notoriously challenging problems in the mathematical sciences. These problems involve predicting the large-scale behaviour of strongly interacting classical and quantum spin systems originating in condensed matter physics, including models of relevance to proposals for topological ....Algebraic and computational approaches for classical and quantum systems. This project aims to use a combination of algebraic, analytic and numerical techniques to develop computational algorithms to address a range of notoriously challenging problems in the mathematical sciences. These problems involve predicting the large-scale behaviour of strongly interacting classical and quantum spin systems originating in condensed matter physics, including models of relevance to proposals for topological quantum computation and the latest progress using field theory. The project outcomes will involve advances in understanding these systems from new exact results and high precision numerical estimates.Read moreRead less
The connection between discrete holomorphicity and Yang-Baxter integrability. This project will develop and apply the mathematical theory underlying the rigorous study of phase transitions and critical phenomena, which defines what we know about 'everyday' matter and its transformations. The project will also contribute to training in an area for which Australia has an outstanding international reputation.