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.
Properties of nonequilibrium steady states. A nonequilibrium steady state (NESS) occurs when work is performed on a system and the heat so generated is absorbed by a thermostatting mechanism. The system settles into steady state and its properties no longer change. Almost all experimental systems of interest are in a nonequilibrium state, so understanding NESSs is highly significant. Unlike time stationary equilibrium states, the distribution of microstates in a NESS cannot be described by simpl ....Properties of nonequilibrium steady states. A nonequilibrium steady state (NESS) occurs when work is performed on a system and the heat so generated is absorbed by a thermostatting mechanism. The system settles into steady state and its properties no longer change. Almost all experimental systems of interest are in a nonequilibrium state, so understanding NESSs is highly significant. Unlike time stationary equilibrium states, the distribution of microstates in a NESS cannot be described by simple closed form distributions. This project will determine properties, symmetries and extrema of NESS using concepts and theorems developed for studying transient nonequilibrium states, and will also determine if approximate, physically relevant forms of the phase space distributions can be developed.Read moreRead less
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
Ionic Dispersion Forces in Physical Chemistry: Implications for pH, Electrochemistry, Nanoparticle Formation and Organic Synthesis. Our current understanding of charged systems in solution is deeply flawed . Existing theories are not predictive, mainly because they concentrate entirely on electrostatics. This proposal aims to partially rectify this by including the effects of previously neglected dispersion forces in a number of problems. These forces are responsible for much of the behaviou ....Ionic Dispersion Forces in Physical Chemistry: Implications for pH, Electrochemistry, Nanoparticle Formation and Organic Synthesis. Our current understanding of charged systems in solution is deeply flawed . Existing theories are not predictive, mainly because they concentrate entirely on electrostatics. This proposal aims to partially rectify this by including the effects of previously neglected dispersion forces in a number of problems. These forces are responsible for much of the behaviour seen in the following systems: the theory of electrolytes; electrochemistry pH and buffers; self energy effects in organic chemistry; and zeolite and nano-particle synthesis. The main outcome will be accurate and predictive theories for these systems.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.
ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this ....ARC Centre of Excellence for Mathematical and Statistical Frontiers of Big Data, Big Models, New Insights. In today's world, massive amounts of data in a variety of forms are collected daily from a multitude of sources. Many of the resulting data sets have the potential to make vital contributions to society, business and government, as well as impact on international developments, but are so large or complex that they are difficult to process and analyse using traditional tools. The aim of this Centre is to create innovative mathematical and statistical models that can uncover the knowledge concealed within the size and complexity of these big data sets, with a focus on using the models to deliver insight into problems vital to the Centre's Collaborative Domains: Healthy People, Sustainable Environments and Prosperous Societies.Read moreRead less
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
Quantum symmetries: mathematical models for topological matter. This project aims to investigate quantum symmetries, new mathematical objects which allow an algebraic description of topological phases of matter. The project expects to bridge the current gap between our mathematical and physical understandings of these topological phases of matter. The project will develop innovative tools for analysing and constructing new exotic symmetries, and provide an extensive survey of examples. It is exp ....Quantum symmetries: mathematical models for topological matter. This project aims to investigate quantum symmetries, new mathematical objects which allow an algebraic description of topological phases of matter. The project expects to bridge the current gap between our mathematical and physical understandings of these topological phases of matter. The project will develop innovative tools for analysing and constructing new exotic symmetries, and provide an extensive survey of examples. It is expected to build national research capacity in an emerging field and put Australia at the forefront of the mathematics of topological matter.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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