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.
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
New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact soluti ....New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact solutions to non-linear sigma-models which have important applications in many areas, including condensed matter physics, string and field theories and Riemannian geometry. The project expects to provide significant benefit to the advancement of knowledge in physics and mathematics.Read moreRead less
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.
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of th ....Free parafermions: a challenge for non-Hermitian physics. This project aims to calculate and understand the physical properties of free parafermions. Parafermions have attracted interest in topological schemes for quantum computation because they are computationally more powerful than Majorana fermions. The core of this project is a fundamental model of free parafermions, which has been shown to exhibit unexplained puzzling properties. The project outcomes include an in-depth understanding of this model by taking the non-Hermitian features into account, establishing a connection with open quantum systems. Non-Hermitian systems are also of increasing relevance in physics, especially in quantum optics. The project also aims to contribute to training researchers in the mathematical sciences.
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Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. ....Topological insulators and free fermions: from Hermitian to non-Hermitian. This project aims to develop and fully understand a class of mathematical models describing fundamental interacting systems of particles of central importance in the physics of topological insulators. This will include the extension of exact solutions to more complicated models and the development and application of topological data analysis for detecting topological phase transitions in these and more general materials. The project will also apply diagrammatic methods to address a long-standing challenge in solving a particular model. The project aims to contribute to training researchers in an area of the mathematical sciences of benefit to the future development of new concepts for next-generation electronic devices and smart materials.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL150100019
Funder
Australian Research Council
Funding Amount
$3,041,282.00
Summary
Precision laser levitation for quantum metrology and gravitational sensing. Precision laser levitation for quantum metrology and gravitational sensing: This fellowship project aims to levitate macroscopic objects using only laser beams, to provide a new tool to test physics theories. Strong laser beams can exert sufficient force to counteract gravity and make an object levitate. In contrast to other forms of levitation, laser levitation is scatter-free and can preserve system coherence. It has s ....Precision laser levitation for quantum metrology and gravitational sensing. Precision laser levitation for quantum metrology and gravitational sensing: This fellowship project aims to levitate macroscopic objects using only laser beams, to provide a new tool to test physics theories. Strong laser beams can exert sufficient force to counteract gravity and make an object levitate. In contrast to other forms of levitation, laser levitation is scatter-free and can preserve system coherence. It has superior optical and mechanical quality factors and complete information of the system dynamics is retained. This allows laser levitation to be turned into a highly controllable and ultra-sensitive device capable of detecting minute environmental changes. This research aims to probe the relationship between quantum and gravitational physics and develop laser levitation into a precision instrument for the sensing of gravity. Laser levitation has the potential to be developed into technology for mineral exploration and environmental sensing.Read moreRead less
Coherent Laser Levitation for Precision Sensing and Enabling Science. When light collides with matter, it may exert a force called radiation pressure. This project aims to use radiation pressure to levitate a small mirror. Using a tripod of laser beams, it is possible to levitate and trap the mirror in a stable position. Radiation pressure has been used before to levitate, but previous work has always involved scattering light from the levitating object. This project proposes the use of a high q ....Coherent Laser Levitation for Precision Sensing and Enabling Science. When light collides with matter, it may exert a force called radiation pressure. This project aims to use radiation pressure to levitate a small mirror. Using a tripod of laser beams, it is possible to levitate and trap the mirror in a stable position. Radiation pressure has been used before to levitate, but previous work has always involved scattering light from the levitating object. This project proposes the use of a high quality mirror, allowing the collection of the reflected light and the accurate measurement and control of the position of the mirror as it floats on the laser beams. Using the unique properties of the floating mirror, it will be possible to search for signatures of quantum gravity and develop tools for ultra-precision metrology.Read moreRead less