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 interpretations of discrete integrable equations. The important mathematical disciplines of discrete geometry on one hand, and structure in discrete non-linear dynamics known as integrability on the other, have an emerging and fruitful interrelation. This project will construct a new algebraic framework in order to better understand and exploit this point of intersection.
Discovery Early Career Researcher Award - Grant ID: DE160100958
Funder
Australian Research Council
Funding Amount
$307,536.00
Summary
Quantum integrability and symmetric functions. This project aims to develop new connections between quantum integrability and a central area of pure mathematics, symmetric function theory. Quantum integrability is one of the most important areas of mathematical physics, in view of its application to modern physical theories and its mathematical richness. The project intends to use advanced symmetric function techniques to calculate quantum mechanical quantities without any approximation, and to ....Quantum integrability and symmetric functions. This project aims to develop new connections between quantum integrability and a central area of pure mathematics, symmetric function theory. Quantum integrability is one of the most important areas of mathematical physics, in view of its application to modern physical theories and its mathematical richness. The project intends to use advanced symmetric function techniques to calculate quantum mechanical quantities without any approximation, and to use the framework of quantum integrability to provide new results in symmetric function theory. The intended outcomes of the project will be new asymptotic expressions for correlation functions and more efficient computer algorithms for the calculation of a variety of symmetric functions.Read moreRead less
Topological properties of exactly-solvable, two-dimensional quantum systems. Two-dimensional quantum systems have unique properties which are driving developments in the emerging generation of quantum-based technologies. This project will facilitate progress by elucidating the mathematics underlying these systems. The results will impact on downstream research and development in the area of superior information processing.
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.
Discovery Early Career Researcher Award - Grant ID: DE210101581
Funder
Australian Research Council
Funding Amount
$411,000.00
Summary
Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project includ ....Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems. Read moreRead less
Microwave Frequency Standards: Testing Fundamental Physics and Developing New Devices. Highly frequency stable oscillators may be used as frequency or timing standards (clocks) and have commercial application as well as application of testing fundamental physical principles. This project is to continue the development of novel frequency standards in collaboration with some of the best research institutes in France funded by the French Space Agency (CNES). With the advent of the International Spa ....Microwave Frequency Standards: Testing Fundamental Physics and Developing New Devices. Highly frequency stable oscillators may be used as frequency or timing standards (clocks) and have commercial application as well as application of testing fundamental physical principles. This project is to continue the development of novel frequency standards in collaboration with some of the best research institutes in France funded by the French Space Agency (CNES). With the advent of the International Space Station and new atomic clocks, the physics community is embarking on an experimental program that will make use of the microgravity environment of space. Combined with the new improved timing it will be possible to perform new experimental tests of general and special relativity, tests for drifts in the fine structure constant and tests for a preferred direction of the speed of light at unprecedented sensitivity.Read moreRead less
Discrete integrable systems. Discrete integrable systems are a fundamental generalisation of traditional integrable systems. This project, combining 5 world experts from 3 countries and 2 early career researchers, will expand and systematise this new interdisciplinary field, and will place Australia at the forefront of this intensive international activity.
Many-body problems. The discovery of new superheavy elements, chemical evolution of the Universe, nuclear reactions deep under the Coulomb barrier in nuclear reactors, in stars and during the Big Bang Nucleosynthesis, accuracy of precise atomic clocks, consistency of the Standard Model in strong fields are among the most vital problems of modern science. This project suggests several new ideas in these areas, which are based on knowledge accumulated in different research fields. The outcomes of ....Many-body problems. The discovery of new superheavy elements, chemical evolution of the Universe, nuclear reactions deep under the Coulomb barrier in nuclear reactors, in stars and during the Big Bang Nucleosynthesis, accuracy of precise atomic clocks, consistency of the Standard Model in strong fields are among the most vital problems of modern science. This project suggests several new ideas in these areas, which are based on knowledge accumulated in different research fields. The outcomes of the research will help Australia to build up a "critical mass" of scientific expertise, which is necessary to place and keep it among leaders in these frontier areas of physics, and to train the next generation of experts in these fields.Read moreRead less
Quantum and Geometric Aspects of Gauge Theories, Supergravity and String Theory. A central problem of modern high-energy physics is the unification of gravity with the other fundamental interactions that is consistent at the quantum level. Led by a team of internationally recognized experts, this project will yield breakthroughs in supergravity and string theory - crucial ingredients of current approaches to unification. As well as putting Australia at the forefront of this mainstream activity, ....Quantum and Geometric Aspects of Gauge Theories, Supergravity and String Theory. A central problem of modern high-energy physics is the unification of gravity with the other fundamental interactions that is consistent at the quantum level. Led by a team of internationally recognized experts, this project will yield breakthroughs in supergravity and string theory - crucial ingredients of current approaches to unification. As well as putting Australia at the forefront of this mainstream activity, a fertile environment will be provided for the training of graduate students. They will be ideally placed to lead Australia's involvement in the revolution sparked by the expected experimental confirmation of supersymmetry with the Large Hadron Collider. Read moreRead less