EPSRC-SFI: Non-Equilibrium Steady-States of Quantum many-body systems: uncovering universality and thermodynamics (QuamNESS)

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QuamNESS will develop novel mathematical tools and powerful simulations to understand the fundamental principles governing the performance of the smallest possible engines. Miniaturised to only handfuls of atoms, these machines hold the promise of offering highly efficient ways of generating power, managing heat flows and recovering wasted energy in wide-ranging technologies, from microprocessors to chemical reactions. In contrast to conventional engines, the pistons and gears of nanoscale machines are instead the flow of individual particles, such as electrons. By being so small, even a single electron hopping through the engine represents a remarkably disruptive stochastic event. Therefore, the operation of such machines is subject to violent random fluctuations, not dissimilar to a wildly spluttering engine. Moreover, these microscopic constituents of the engine do not behave like everyday objects, but instead obey the laws of quantum mechanics. Both these features make it extremely problematic to define familiar concepts, like heat and temperature, central to the formalism of thermodynamics that so successfully describes conventional engines. Yet such apparently unhelpful complications should rather be seen as unique features of such small machines, presenting a multitude of opportunities to be harnessed. Developing a new framework to unravel these quantum enhancements is of paramount importance and is a core objective of this project.Quantum systems are well known to possess counterintuitive properties. This includes coherence, namely the idea that a particle can be in many places at once as a superposition. When there are many particles interacting, we can also have entanglement - a superposition of different multi-particle configurations - giving rise to novel correlations and spooky action-at-a-distance. Under the right conditions, these strange quantum effects can compete with and radically alter the usual random jittery thermal motion occurring in a system. This project will sharpen our view of this interplay and how it can be harnessed by reassessing the fundamental concepts of irreversibility and fluctuations. Useful engines produce a finite power output. This means they are never as efficient as an ideal infinitely slow engine because they inevitably waste energy as friction during a rapid cycle. The trade-off between power output and efficiency relies on quantifying this waste as irreversible entropy production. Our work will reformulate entropy production in new ways best suited to reveal the contributions of quantum coherence and correlations prevalent at the nanoscale. Further to this, for classical machines entropy production is known to bound the fluctuations in time of the power output. Specifically, to make an engine splutter less at a given power output necessitates increasing entropy production. We will determine the highly non-trivial generalization of this relation to the quantum domain. Simultaneous to this, we will develop sophisticated numerical methods for simulating complex quantum machines composed of many interacting constituents, allowing these crucial properties to be predicted.Our theoretical framework will be high beneficial to current experimental efforts aimed at engineering quantum technologies with super-efficient thermal management. The most pressing applications in this direction will be explored within the scope of this project, including an assessment of novel mechanisms for enhancing quantum thermal machines, the ability to control quantum systems via periodic driving and proposals for experimentally verifying these findings. The bold ambition of this project leverages the synergistic talents of the research team, with PI Clark's expertise in numerical methods complementing the analytical skills of Co-Is Paternostro and Goold.