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Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading the ....Quantum correlations in ultra-cold Fermi gases. The field of ultra-cold Fermi gases provides a unique opportunity to develop and test theoretical methods for novel experimental environments of exceptional purity and simplicity. This improved understanding will have potential applications in many fields, ranging from the astrophysics of neutron stars to condensed matter systems such as superconductors or nanostructures. Just as importantly, the project will develop linkages with world leading theoretical groups, which will greatly aid research student education. There are direct applications to experiments on molecule formation with ultra-cold fermions in the ARC Centre of Excellence for Quantum-Atom Optics.Read moreRead less
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
Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscal ....Effective and accurate model dynamics, deterministic and stochastic, across multiple space and time scales. A persistent feature of complex systems in engineering and science is the emergence of macroscopic, coarse grained, coherent behaviour from the interactions of microscopic agents (molecules, cells, grains) and with their environment. In current modeling, ranging from ecology to materials science, the underlying microscopic mechanisms are often known, but the closures to translate microscale knowledge to a system level macroscopic description are rarely available in closed form. Our novel methodology will explore this stumbling block, and promises to radically change the modeling, exploration and understanding of multiscale complex system behaviour.Read moreRead less
Quantum Integrable Systems and Applications: From Condensed Matter to Quantum Information. Quantum integrable systems have produced exciting results and techniques vital in the efforts to achieve the ultimate goal of understanding quantum science beyond perturbation. The proposal gathers four world experts from Australia, Japan and Russia to work on highly interdisciplinary projects designed to resolve fundamental problems in the field, which will underpin the development of emerging technologie ....Quantum Integrable Systems and Applications: From Condensed Matter to Quantum Information. Quantum integrable systems have produced exciting results and techniques vital in the efforts to achieve the ultimate goal of understanding quantum science beyond perturbation. The proposal gathers four world experts from Australia, Japan and Russia to work on highly interdisciplinary projects designed to resolve fundamental problems in the field, which will underpin the development of emerging technologies. As a result, Australian science will be seen to be at the forefront internationally, and the leading status of Australia in the field will be greatly strengthened. Early career researchers and PhD students will be trained as part of the project, important in enhancing Australia's capability to develop and retain scientific talent. Read moreRead less
ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions i ....ARC Complex Open Systems Research Network. Complexity is the common frontier in the physical, biological and social sciences. This Network will link specialists in all three sciences through five generic conceptual and mathematical theme activities. It will promote research into how subsystems self-organise into new emergent structures when assembled into an open, non-equilibrium system. Outcomes will include new technologies and software tools and deeper understanding of fundamental questions in science. An essential function of the network will be introducing researchers end users to new tools and broadening the horizons of graduate students.Read moreRead less
Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also ....Fluctuations in the properties of nonequilibrium fluids and the influence of thermostatting mechanisms. The behaviour of nonequilibrium fluids will be studied by combining ideas from liquid state theory, statistical mechanics and dynamical systems theory. This work will result in development and testing of mathematical expressions (Fluctuation Theorems) that are consistent with the Second Law of Thermodynamics, which determines the direction of any change in any macroscopic system, but are also applicable to microscopic systems. The expressions will determine the probability that finite sized systems will violate the Second Law for small periods of time and will therefore contribute to development of a fundamental understanding of microscopic systems and the development of nanotechnology.
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Special Research Initiatives - Grant ID: SR0354741
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of t ....Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of the quantum realm will lead to breakthrough science of vital importance to the development of frontier technologies in Australia. This Network will also place a strong emphasis on research training, the mentoring of early career researchers and establishing collaborations with leading international research groups and networks.
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Modelling of Adsorption Dynamics in Microporous Adsorbents Using Fractional Order Diffusion Equations. This project investigates the use of fractional order diffusion equations in modelling adsorption dynamics in microporous carbons. The long tail behaviour of adsorption processes cannot be readily explained by the classical second order Fickian model, and makes adsorption a candidate for the use of fractional order diffusion equations that have the potential to model such features. In the pre ....Modelling of Adsorption Dynamics in Microporous Adsorbents Using Fractional Order Diffusion Equations. This project investigates the use of fractional order diffusion equations in modelling adsorption dynamics in microporous carbons. The long tail behaviour of adsorption processes cannot be readily explained by the classical second order Fickian model, and makes adsorption a candidate for the use of fractional order diffusion equations that have the potential to model such features. In the present project we shall develop suitable numerical techniques for solving the fractional order diffusion model, and apply these to the interpretation of experimental kinetic data. The outcome will be an improved model of adsorption dynamics considering the fractal nature of the solid.Read moreRead less
Fluid properties and chaotic dynamics in equilibrium and nonequilibrium states. Over the last decade a revolution has been taking place in nonequilibrium statistical mechanics [Physics Today, Sept, 2002]. This revolution is characterized by adapting the mathematical theory of chaos to nonequilibrium statistical mechanics. Fundamental new theorems and algorithms for computing transport coefficients have been derived. The CIs have played a key role in this revolution. We seek to broaden these dev ....Fluid properties and chaotic dynamics in equilibrium and nonequilibrium states. Over the last decade a revolution has been taking place in nonequilibrium statistical mechanics [Physics Today, Sept, 2002]. This revolution is characterized by adapting the mathematical theory of chaos to nonequilibrium statistical mechanics. Fundamental new theorems and algorithms for computing transport coefficients have been derived. The CIs have played a key role in this revolution. We seek to broaden these developments by: generalizing a theorem which relates transport coefficients to chaoticity; detailed studies of the influence of thermostatting mechanisms on nonequilibrium chaoticity and fluctuations, and by understanding the range of applicability of a nonequilibrium fluctuation theorem for non-isoenergetic systems.Read moreRead less
Integrable quantum systems: mathematical foundations for developing quantum science. Quantum science is an exciting and challenging area, one which will underpin the development of the next generation of computers and novel devices such as atom lasers. New mathematical techniques are being pursued, to formulate the frameworks that will provide deep insights into the complex nature of the physical principles governing this field, in order to fully realise the potential applications. This project ....Integrable quantum systems: mathematical foundations for developing quantum science. Quantum science is an exciting and challenging area, one which will underpin the development of the next generation of computers and novel devices such as atom lasers. New mathematical techniques are being pursued, to formulate the frameworks that will provide deep insights into the complex nature of the physical principles governing this field, in order to fully realise the potential applications. This project will enhance the scale of an established and internationally competitive program in mathematics research, producing new approaches to meet these demands. It will also provide opportunities for research training, important in ensuring that Australia is well equipped to play a leading role in future quantum science developments.
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