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Quantum thermodynamic properties in many-body systems out-of-equilibrium

Amy Skelt

Published Apr 1, 2020• 0 citations
OpenAlex

Abstract

Relatively small many-body quantum systems are often used as hardware for quantum devices. Most of these devices will operate below the thermal limit where thermodynamics must be treated differently to account for quantum behaviours. It is therefore imperative that the thermodynamic properties of these systems are well understood, especially as they can limit the technologies but also help the fabrication and running of efficient quantum devices. \n \nIn this thesis we study quantum work and entropy production in closed many-body quantum systems out-of-equilibrium. We find that, for the systems studied, the largest average quantum work can be extracted in adiabatic weakly correlated regimes. These regimes are also seen to minimise the entropy produced, making them efficient regimes in which to operate devices based on these systems. \n \nAdiabatic evolutions are important for many quantum devices, and so it is important that they can be accurately characterised. The validity of current methods has been questioned recently, so in this thesis we propose the use of metrics as a good quantitative measure to characterise adiabaticity. We found that the density distance (a more accessible quantity than the wavefunction and its distance measures) alone can determine adiabaticity in a range of quantum systems, even at finite temperature. \n \nHowever, when calculating properties of many-body systems, there are many challenges often resulting in the need to approximate. In this thesis we propose a new style of approximation for quantum thermodynamic properties, taking inspiration from density functional theory (DFT). This new style uses the exact initial state of the system but approximates the dynamics and is seen to be computationally cheap but largely accurate. We test this with non-interacting and DFT approximated dynamics, finding that, surprisingly, the non-interacting dynamics give the most accurate results in most regimes, with the cheapest cost.

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Relatively small many-body quantum systems are often used as hardware for quantum devices. Most of these devices will operate below the thermal limit where thermodynamics must be treated differently to account for quantum behaviours. It is therefore imperative that the thermodynamic properties of these systems are well understood, especially as they can limit the technologies but also help the fabrication and running of efficient quantum devices. \n \nIn this thesis we study quantum work and entropy production in closed many-body quantum systems out-of-equilibrium. We find that, for the systems studied, the largest average quantum work can be extracted in adiabatic weakly correlated regimes. These regimes are also seen to minimise the entropy produced, making them efficient regimes in which to operate devices based on these systems. \n \nAdiabatic evolutions are important for many quantum devices, and so it is important that they can be accurately characterised. The validity of current methods has been questioned recently, so in this thesis we propose the use of metrics as a good quantitative measure to characterise adiabaticity. We found that the density distance (a more accessible quantity than the wavefunction and its distance measures) alone can determine adiabaticity in a range of quantum systems, even at finite temperature. \n \nHowever, when calculating properties of many-body systems, there are many challenges often resulting in the need to approximate. In this thesis we propose a new style of approximation for quantum thermodynamic properties, taking inspiration from density functional theory (DFT). This new style uses the exact initial state of the system but approximates the dynamics and is seen to be computationally cheap but largely accurate. We test this with non-interacting and DFT approximated dynamics, finding that, surprisingly, the non-interacting dynamics give the most accurate results in most regimes, with the cheapest cost.
Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown.Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production.As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting.We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.
The fabrication, utilisation, and efficiency of quantum technology devices rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between particles make the complexity of related calculations grow exponentially with the system size. Here we explore and systematically compare 'simple' and 'hybrid' approximations to the average work and entropy variation built on static density functional theory concepts. These approximations are computationally cheap and could be applied to large systems. We exemplify them considering driven one-dimensional Hubbard chains and show that, for 'simple' approximations and low to medium temperatures, it pays to consider a good estimate of the Kohn-Sham Hamiltonian to approximate the driving Hamiltonian. Our results confirm that a 'hybrid' approach, requiring a very good approximation of the initial and, for the entropy, final states of the system, provides great improvements. This approach should be particularly efficient when many-body effects are not increased by the driving Hamiltonian.
Abstract Thermodynamics of quantum systems out-of-equilibrium is very important for the progress of quantum technologies, however, the effects of many-body interactions and their interplay with temperature, different drives and dynamical regimes is still largely unknown. Here we present a systematic study of these interplays in the case of driven Hubbard chains subject to a variety of interaction (from non-interacting to strongly correlated) and dynamical regimes (from sudden quench to quasi-adiabatic), and discuss which effects all these ingredients have on the work extraction and entropy production. As treatment of many-body interacting systems is highly challenging, we introduce a simple approximation which includes, for the average quantum work, many-body interactions only via the initial state, while the dynamics is fully non-interacting. We demonstrate that this simple approximation is surprisingly good for estimating both the average quantum work and the related entropy production, even when many-body correlations are significant.
In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems.The method is articulated in various approximation protocols which allow to achieve increasing levels of accuracy, it is relatively simple to implement even for medium and large number of interactive particles, and uses tools and concepts from density functional theory.We test the method on the driven Hubbard dimer at half filling, and compare exact and approximate results.We show that the proposed method reproduces the average quantum work to high accuracy: for a very large region of parameter space (which cuts across all dynamical regimes) estimates are within 10% of the exact results.
In the framework of quantum thermodynamics, we propose a method to quantitatively describe thermodynamic quantities for out-of-equilibrium interacting many-body systems. The method is articulated in various approximation protocols which allow to achieve increasing levels of accuracy, it is relatively simple to implement even for medium and large number of interactive particles, and uses tools and concepts from density functional theory. We test the method on the driven Hubbard dimer at half filling, and compare exact and approximate results. We show that the proposed method reproduces the average quantum work to high accuracy: for a very large region of parameter space (which cuts across all dynamical regimes) estimates are within 10% of the exact results.
The quantum adiabatic theorem is fundamental to time-dependent quantum systems, but being able to characterize quantitatively an adiabatic evolution in many-body systems can be a challenge. This work demonstrates that the use of appropriate state and particle-density metrics is a viable method to quantitatively determine the degree of adiabaticity in the dynamic of a quantum many-body system. The method applies also to systems at finite temperature, which is important for quantum technologies and quantum thermodynamics related protocols. The importance of accounting for memory effects is discussed via comparison to results obtained by extending the quantum adiabatic criterion to finite temperatures: it is shown that this may produce false readings being quasi-Markovian by construction. As the proposed method makes it possible to characterize the degree of adiabatic evolution by tracking only the system local particle densities, it is potentially applicable to both theoretical calculations of very large many-body systems and to experiments.