New methods in spectral geometry. This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are ....New methods in spectral geometry. This project aims to use methods from mathematical scattering theory to resolve problems in the spectral analysis and index theory of differential operators. Both areas underpin the theoretical understanding of physical materials at micro length scales where quantum phenomena dominate. The project will develop new mathematical results in spectral analysis and geometry, and apply its results to theoretical models of quantum phenomena whose spectral properties are at the limit of the range of mathematical techniques. Solving these problems is expected to influence non-commutative analysis.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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Physico-chemical effects on long-time fluid transport for CO2 geostorage. This project aims to develop an efficient multi-scale laboratory-based modelling framework for the analysis of nonequilibrium transport and reaction processes occurring in CO2 storage scenarios. In a significant technological advance two non-destructive analysis techniques, Xray computed tomography and nuclear magnetic resonance, are combined with pore-scale simulations to address uncertainties in dynamic wettability alter ....Physico-chemical effects on long-time fluid transport for CO2 geostorage. This project aims to develop an efficient multi-scale laboratory-based modelling framework for the analysis of nonequilibrium transport and reaction processes occurring in CO2 storage scenarios. In a significant technological advance two non-destructive analysis techniques, Xray computed tomography and nuclear magnetic resonance, are combined with pore-scale simulations to address uncertainties in dynamic wettability alteration occurring during gravity driven convection. Expected outcomes are the in-situ characterisation of solid-surface interactions and predictions of multi-phase fluid flow. The project benefits the Australian resources sector by improving injectivity, storage efficiency and security of supercritical CO2 storage projects.Read moreRead less
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
Discovery Early Career Researcher Award - Grant ID: DE230100054
Funder
Australian Research Council
Funding Amount
$432,000.00
Summary
Spectral estimates in the presence of a magnetic field. Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnet ....Spectral estimates in the presence of a magnetic field. Estimates on eigenvalues of integral operators are at the core of numerous results in the study of quantum phenomena and in associated mathematical fields. This project aims to establish detailed spectral properties of the integral operators arising in quantum models incorporating magnetic fields. An anticipated goal is the generation of new and significant theoretical results in analysis that will open novel approaches to the use of magnetic differential operators. This is expected to benefit Australian science by invigorating collaboration between mathematics and theoretical physics, by providing research training relevant to emerging quantum science based technology and strengthening research collaborations with world leading scientists.Read moreRead less
Topological stability from spectral analysis. The aim is to use mathematical scattering theory to find and study new topological features of the spectra of linear transformations on Hilbert space. The significance derives from mathematical models of low temperature conducting quantum materials. These have revealed `topological phases of matter' that are stable with respect to a range of variations in the parameters that determine the system. The stability is desired for applications to quantum ....Topological stability from spectral analysis. The aim is to use mathematical scattering theory to find and study new topological features of the spectra of linear transformations on Hilbert space. The significance derives from mathematical models of low temperature conducting quantum materials. These have revealed `topological phases of matter' that are stable with respect to a range of variations in the parameters that determine the system. The stability is desired for applications to quantum devices. Our results will give topological stability from the scattering spectrum, a feature not previously seen. The benefits stem from new results in mathematical scattering theory with a primary novelty being the analysis of ``zero energy resonances'' in mathematical models of graphene.Read moreRead less
A new energy absorption system for brain injury mitigation. This research aims to propose and investigate a next generation high-energy absorbing helmet pad that will protect the Australian Defence Force soldiers against both ballistic and blast threats. New fundamental knowledge in the area of high-energy absorbing metamaterials will be obtained by using numerical modelling and experimental studies. The expected outcomes of the project include the development of a new wearable energy absorbing ....A new energy absorption system for brain injury mitigation. This research aims to propose and investigate a next generation high-energy absorbing helmet pad that will protect the Australian Defence Force soldiers against both ballistic and blast threats. New fundamental knowledge in the area of high-energy absorbing metamaterials will be obtained by using numerical modelling and experimental studies. The expected outcomes of the project include the development of a new wearable energy absorbing pad which can be used as the next generation combat helmet liners and accessories. The novel high-performance energy absorption system will have a wide range of direct applications in future personal armour, as well as sports gears and elderly healthcare products.Read moreRead less
Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, ....Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, statistics and different ways of aggregating information. By building a more complete theoretical map it is expected that new machine learning methods will be developed, but more importantly that machine learning will be able to be better integrated into larger socio-technical systems.Read moreRead less
Quantum non-locality with mass-entangled metastable helium atoms atoms. The aim of this project is to use ultracold helium atoms to test aspects of quantum entanglement. The unique properties of metastable helium will provide significant new knowledge of this fundamental quantum property. Expected outcomes include measuring a Bell test between mass entangled atoms and testing the weak equivalence principle (the universality of free fall) using a quantum entangled state as the test masses. This s ....Quantum non-locality with mass-entangled metastable helium atoms atoms. The aim of this project is to use ultracold helium atoms to test aspects of quantum entanglement. The unique properties of metastable helium will provide significant new knowledge of this fundamental quantum property. Expected outcomes include measuring a Bell test between mass entangled atoms and testing the weak equivalence principle (the universality of free fall) using a quantum entangled state as the test masses. This should provide benefits including input into new theories that attempt to unify quantum mechanics with general relativity and will be relevant for emerging quantum technologies such as more powerful quantum computing or quantum simulation of complex systems.Read moreRead less
Quantum entanglement with atoms: from individual pairs to many-body systems. The aim of this project is to use ultracold helium atoms to test aspects of quantum entanglement. The unique properties of metastable helium will provide significant new knowledge of this fundamental quantum property. Expected outcomes include measuring a Bell test between momentum entangled atoms and showing how many-body entanglement builds up following a quantum quench. This should provide benefits including new theo ....Quantum entanglement with atoms: from individual pairs to many-body systems. The aim of this project is to use ultracold helium atoms to test aspects of quantum entanglement. The unique properties of metastable helium will provide significant new knowledge of this fundamental quantum property. Expected outcomes include measuring a Bell test between momentum entangled atoms and showing how many-body entanglement builds up following a quantum quench. This should provide benefits including new theories that attempt to unify quantum mechanics with general relativity and will be relevant for emerging quantum technologies such as more powerful quantum computing or quantum simulation of complex systems. Read moreRead less