Quantum control designed from broken integrability. This Project aims to open new avenues in quantum device engineering design. This will be achieved through the use of advanced mathematical methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The expert team of Investigators will capitalise on their recent achievements in this field, which includes a first example of a quantum switch designed through broken integrability. The expected outco ....Quantum control designed from broken integrability. This Project aims to open new avenues in quantum device engineering design. This will be achieved through the use of advanced mathematical methodologies developed around the notion of quantum integrability, and the breaking of that integrability. The expert team of Investigators will capitalise on their recent achievements in this field, which includes a first example of a quantum switch designed through broken integrability. The expected outcomes will encompass novel applications of abstract mathematical physics towards the concrete control of quantum mechanical architectures. These outcomes will promote new opportunities for the construction of atomtronic devices, which are rising as a foundation for next-generation quantum technologies.
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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
Discovery Early Career Researcher Award - Grant ID: DE130101067
Funder
Australian Research Council
Funding Amount
$302,540.00
Summary
New constructions of superintegrable systems and the connection with Painlevé transcendents. The research of this project will lead to deep discoveries in the field of superintegrability and expand our knowledge of their related algebraic structures, supersymmetric quantum mechanics and Painlevé transcendents. The project will generate new techniques that will be utilised in future applications of mathematical and theoretical physics.
Unified theory of Richardson-Gaudin integrability. Richardson-Gaudin systems form a class of mathematical models of interacting particles that serve as a foundation to understand important phenomena in modern physics. Being integrable, these quantum systems enable deep insights. They are tractable so as to allow for exact analysis, while being elaborate enough to exhibit complex physical properties, notably phase transitions. The international team of researchers aims to merge various approaches ....Unified theory of Richardson-Gaudin integrability. Richardson-Gaudin systems form a class of mathematical models of interacting particles that serve as a foundation to understand important phenomena in modern physics. Being integrable, these quantum systems enable deep insights. They are tractable so as to allow for exact analysis, while being elaborate enough to exhibit complex physical properties, notably phase transitions. The international team of researchers aims to merge various approaches for analysing the integrability of such models. Successful outcomes are expected to produce inventive mathematical techniques, linking a diverse range of fields of current activity and growth. The resulting unified theory is expected to open the door to exciting and innovative pathways in mathematical physics research.Read moreRead less
Representation theory in exactly solvable systems. This project aims to develop the representation theory of Lie and generalised Lie algebras related to exactly solvable models. The project will exploit several innovative ideas on the structure of quadratic algebras, Casimir invariants, differential operator realisations, roots systems, characters and indecomposable representations. This will give fundamental mathematical insight and allow the construction of new, exactly solvable models. This w ....Representation theory in exactly solvable systems. This project aims to develop the representation theory of Lie and generalised Lie algebras related to exactly solvable models. The project will exploit several innovative ideas on the structure of quadratic algebras, Casimir invariants, differential operator realisations, roots systems, characters and indecomposable representations. This will give fundamental mathematical insight and allow the construction of new, exactly solvable models. This will have an impact on theoretical physics as exactly solvable models play a central role in our understanding of a plethora of physical phenomena.Read moreRead less
Quantum equilibration. This project will shed light on a fundamental problem in physics - how do fragile quantum systems, entirely isolated from the rest of the world, return to equilibrium when disturbed from their natural state? Our results will provide a theoretical underpinning for the development of quantum simulators that can be used for the design of advanced materials.
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
Representation theory of diagram algebras and logarithmic conformal field theory. Generalized models of polymers and percolation are notoriously difficult to handle mathematically, but can be described and solved using diagram algebras and logarithmic conformal field theory. Potential applications include polymer-like materials, filtering of drinking water, spatial spread of epidemics and bushfires, and tertiary recovery of oil.
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.
When quantum is not desirable: quantum noise vs. quantum technologies. One of the key remaining obstacles to the successful deployment of quantum computers & sensors in science, industry, and society is the existence of noise sources that are themselves quantum, and thus have an unmatched potential for disruption. This project will attack this problem by providing (i) a detailed understanding of the impact of quantum noise sources, and developing protocols to (ii) characterize and (iii) overcome ....When quantum is not desirable: quantum noise vs. quantum technologies. One of the key remaining obstacles to the successful deployment of quantum computers & sensors in science, industry, and society is the existence of noise sources that are themselves quantum, and thus have an unmatched potential for disruption. This project will attack this problem by providing (i) a detailed understanding of the impact of quantum noise sources, and developing protocols to (ii) characterize and (iii) overcome the negative effects such realistic noise entails. In taking this necessary step for the implementation of these breakthrough technologies, it will not only significantly advance knowledge but will have a direct impact in the development of a technology in which Australia and other leading nations are heavily invested.Read moreRead less