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
From superintegrability to quasi-exact solvability: theory and application. This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models ....From superintegrability to quasi-exact solvability: theory and application. This project aims to develop mathematical techniques to resolve longstanding problems in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to construct sophisticated mathematical tools to settle key questions across a variety of models such as superintegrable systems, quantum spin chains, and spin-boson models. Anticipated applications of the proposed research include the accurate prediction of physical phenomena, from energy spectra to quantum correlations. Such advances should have significant ramifications, and provide benefits, well beyond the mathematical discipline itself.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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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
Dissipation and relaxation in statistical mechanics. This project studies the mathematical conditions for relaxation either to equilibrium or to steady states, which is important in predicting behaviour in diverse fields including climate modelling, materials science, nanotechnology and biology. Early career researchers will be involved in the project, gaining valuable skills in theory and simulation.
Soft modes in glasses: chemical control of relaxation and mechanical response. The unusual dynamical and mechanical properties of viscous liquids and glasses underpins many existing and emerging technologies, from lubrication to the strength and fragility of bulk metallic glasses. An improved understanding of how macroscopic properties such as viscous flow, ductility and fracture emerge from the microscopic interactions between atoms and molecules will provide the enabling scientific knowledge f ....Soft modes in glasses: chemical control of relaxation and mechanical response. The unusual dynamical and mechanical properties of viscous liquids and glasses underpins many existing and emerging technologies, from lubrication to the strength and fragility of bulk metallic glasses. An improved understanding of how macroscopic properties such as viscous flow, ductility and fracture emerge from the microscopic interactions between atoms and molecules will provide the enabling scientific knowledge for exploiting the properties of such materials on the nanoscale. National expertise in this area will help establish and strengthen international collaboration with leading research institutes in the field.Read moreRead less
Advanced numerical and analytical techniques for exact studies in combinatorics and statistical mechanics. Exactly solved models are of immense importance in all areas of the theoretical sciences and play important roles in our understanding of complex natural and social phenomena. This project aims to develop powerful new methods that will enable mathematicians and physicists to greatly expand the types of models for which we can find a solution.
Relative free energies from nonequilibrium simulations: algorithms for determination of binding affinities, conformational states and phase transitions. Leading edge research will enable state of the art techniques in statistical mechanics to be applied to practical problems. All processes in biological, chemical and physical systems are governed by their free energy landscape, often only accessible computationally. This project will lead to an advanced tool for free energy calculation. Advanc ....Relative free energies from nonequilibrium simulations: algorithms for determination of binding affinities, conformational states and phase transitions. Leading edge research will enable state of the art techniques in statistical mechanics to be applied to practical problems. All processes in biological, chemical and physical systems are governed by their free energy landscape, often only accessible computationally. This project will lead to an advanced tool for free energy calculation. Advancement of emerging technologies in nanoscience, porous materials, membrane transport and drug design will benefit from this capability. The project therefore addresses the Priority Goal 'Breakthrough science'. A PhD student and an Early Career Research will be trained in research, gaining a range of valuable skills in theory and simulation. Read moreRead less
Foundations of quantum cryptography for distribution of secret keys. Quantum cryptographic systems have the advantage of mathematically provable security and privacy, addressing security threats to communications as information and communications technologies proliferate. This project aims to quantify a quantum channel's capability for secure communications. This quantity provides the ultimate limit to benchmark practical quantum key distribution protocols for their performance. This will signif ....Foundations of quantum cryptography for distribution of secret keys. Quantum cryptographic systems have the advantage of mathematically provable security and privacy, addressing security threats to communications as information and communications technologies proliferate. This project aims to quantify a quantum channel's capability for secure communications. This quantity provides the ultimate limit to benchmark practical quantum key distribution protocols for their performance. This will significantly advance the theory of quantum cryptography and knowledge of the fundamental resource of secret keys. It is expected to have immediate application for the classical security of existing (non-quantum) communication devices, and benefit security, military, government, industry, individuals, and the community.Read moreRead less
Quantum effects in zero-error communication. This project will establish a systematic quantum zero-error information theory to build highly reliable quantum communications networks. This innovative, breakthrough technology will advance research into the physical realisation of quantum communication. It has global implications and will promote Australia's position in this new research field.