The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. ....The mathematics and physics of interacting systems. Much of the world around us involves the networked interaction between a large number of components. For example, such complex networks may be physical, biological, social or technical in nature and represent connections between magnetic spins, species, people or computers. This Project will provide a firm theoretical foundation for such complex interacting systems through an investigation of the fascinating mathematics and physics behind them. This perspective from mathematical physics, in particular using the tools of statistical mechanics, will lead to a better understanding of many real-world complex systems.Read moreRead less
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
Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the re ....Solvable models on regular and random lattices in statistical mechanics and field theory. There are only a few solvable models in statistical mechanics and field theory, but those that are known give deep insights into the cooperative behaviour that characterizes a critical point, as well as
leading to fascinating mathematics. The two chief investigators have been at the forefront of this field for many years. Currently there are many notable exciting challenges they wish to address:
the relationship between Tutte's work on dichromatic polynomials and matrix models, the outstanding problem of calculating the order parameters of the chiral Potts model, and the eigenvalue spectra of the transfer matrices that occur in integrable models.
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Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level ....Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level of expertise in mathematical physics across Australia to focus on exciting new developments in the theory of these algebraic structures and their application to physics, thus ensuring Australia plays a leading role in this rapidly expanding field.Read moreRead less
Fundamental Implantation, Epitaxy and Defect studies in Silicon to support ultra-shallow junction formation. If successful this project will provide key data and understanding that are fundamentally important for semiconductor science and technologically essential for the global semiconductor industry. Hence successful outcomes will benefit the Nation by raising the international profile of Australian science in these areas. More direct benefit will be derived from the two Australian ventures ....Fundamental Implantation, Epitaxy and Defect studies in Silicon to support ultra-shallow junction formation. If successful this project will provide key data and understanding that are fundamentally important for semiconductor science and technologically essential for the global semiconductor industry. Hence successful outcomes will benefit the Nation by raising the international profile of Australian science in these areas. More direct benefit will be derived from the two Australian ventures that require successful implementation of ultra-shallow junction formation. One is the new silicon phase-change memory company, WRiota, that requires ultra-shallow silicon layers. The second is the quantum computing initiatives in silicon, where understanding of defect-mediated processes in shallow implanted layers is essential to the technology.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.
Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an i ....Statistical Mechanics of Classical Glasses. Glasses and ceramics can possess a combination of properties not available in other materials and thus they are of technological importance with rapidly developing applications. However a fundamental theoretical basis for describing these systems has been missing. The reason for this is that glasses are not in thermodynamic equilibrium, so the standard tools of equilibrium statistical mechanics cannot be rigorously applied . This project will make an important contribution towards building a strong local knowledge base by addressing the problem of understanding the glassy state. The knowledge base can then serve as a springboard for possible high tech applications in materials science and engineering.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
Left-handed metamaterials and negative refraction. This project will establish and support the first team in Australia working in the field of left-handed metamaterials, artificial materials in which waves behave in a unique and counter-intuitive way. The project will promote this new field, enhance its rapid development, and facilitate emerging novel technologies in Australia. It will also lead to close international collaborations with active theoretical and experimental groups, and bring impo ....Left-handed metamaterials and negative refraction. This project will establish and support the first team in Australia working in the field of left-handed metamaterials, artificial materials in which waves behave in a unique and counter-intuitive way. The project will promote this new field, enhance its rapid development, and facilitate emerging novel technologies in Australia. It will also lead to close international collaborations with active theoretical and experimental groups, and bring important expertise to Australia. We believe our initial efforts of purely fundamental nature and extensive collaboration with the overseas groups will have a significant impact on the development of this field and related novel technologies in Australia, attracting strong interest from industry.Read moreRead less
Engineering and control of metamaterials with negative refraction. This project will extend significantly the research activity on metamaterials in Australia, promoting this new field and aiming to solve high priority problems and paving the way to creation of practical sub-wavelength devices. This project is therefore of national benefit for its advances in critical fundamental research and for potential applications in a large number of engineering tasks in microwave and optical devices. The p ....Engineering and control of metamaterials with negative refraction. This project will extend significantly the research activity on metamaterials in Australia, promoting this new field and aiming to solve high priority problems and paving the way to creation of practical sub-wavelength devices. This project is therefore of national benefit for its advances in critical fundamental research and for potential applications in a large number of engineering tasks in microwave and optical devices. The project will initialize collaboration with world leading experts in the area, bringing important expertise to Australia. It will provide a greater acceptance of Australia as a major world player in fundamental research.Read moreRead less