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
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.
Experimental Demonstrations of New Theorems of Nonequilibrium Thermodynamics. In the last decade, two theorems have been proposed to revolutionise the field of thermodynamics. These theorems lift the restriction of the thermodynamic limit, allowing thermodynamic concepts to be applied to small systems such as nanomachines, and characterise systems that may be far-from-equilibrium. These theorems are at odds with a traditional understanding of 19th century thermodynamics where equilibrium is cent ....Experimental Demonstrations of New Theorems of Nonequilibrium Thermodynamics. In the last decade, two theorems have been proposed to revolutionise the field of thermodynamics. These theorems lift the restriction of the thermodynamic limit, allowing thermodynamic concepts to be applied to small systems such as nanomachines, and characterise systems that may be far-from-equilibrium. These theorems are at odds with a traditional understanding of 19th century thermodynamics where equilibrium is central and the Second Law inviolate. However they are critical to the application of thermodynamic concepts to modern systems of the 21st century. Using Optical Tweezers, we will experimentally demonstrate these theorems, present irrefutable evidence of their validity, and demonstrate their application in modern systems.Read moreRead less
Experimental Demonstrations of Violations of the Second Law of Thermodynamics. Inventors and engineers strive to scale-down machines, devices and engines to nanometre sizes for a range of technological purposes and scientists investigate protein motors to understand their operation in hopes of modifying their biological behaviour. However, according to a new theorem in Non-equilibrium Statistical Mechanics, there is a fundamental limit to this scaling-down of engines: such nanomachines, includi ....Experimental Demonstrations of Violations of the Second Law of Thermodynamics. Inventors and engineers strive to scale-down machines, devices and engines to nanometre sizes for a range of technological purposes and scientists investigate protein motors to understand their operation in hopes of modifying their biological behaviour. However, according to a new theorem in Non-equilibrium Statistical Mechanics, there is a fundamental limit to this scaling-down of engines: such nanomachines, including protein motors, will run in "reverse" for appreciable amounts of time and in violation of the Second Law of Thermodynamics. We propose to demonstrate this inescapable, operational limit in nanotechnology with experiments using an Optical Tweezers apparatus.Read moreRead less
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.
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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