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.
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 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.
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.
The competition between evolution time, interaction strength, and temperature challenges our understanding of many-body quantum systems out-of-equilibrium. Here, we consider a benchmark system, the Hubbard dimer, which allows us to explore all the relevant regimes and calculate exactly the related average quantum work. At difference with previous studies, we focus on the effect of increasing temperature, and show how this can turn the competition between many-body interactions and driving field into synergy. We then turn to use recently proposed protocols inspired by density functional theory to explore if these effects could be reproduced by using simple approximations. We find that, up to and including intermediate temperatures, a method which borrows from ground-state adiabatic local density approximation improves dramatically the estimate for the average quantum work, including, in the adiabatic regime, when correlations are strong. However at high temperature and at least when based on the pseudo-LDA, this method fails to capture the counterintuitive qualitative dependence of the quantum work with interaction strength, albeit getting the quantitative estimates relatively close to the exact results.
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 functional renormalization group provides a nonperturbative and systematically improvable route to constructing density functionals for quantum many-body systems from microscopic Hamiltonians. Here we advance this program by benchmarking functional-renormalization-group density functional theory (FRG-DFT) against the exact thermodynamics of the single-site Bose-Hubbard model. This model provides an ideal testing ground because it is analytically solvable, yet remains subtle in the imaginary-time coherent-state path integral, where a naive continuum treatment generates a spurious self-interaction. We show that a careful Hubbard-Stratonovich derivation identifies the self-interaction correction term that must be included in the FRG-DFT flow to recover the exact thermodynamics. We then systematically compare several closures of the resulting hierarchy of flow equations for the free energy, chemical potential, and connected density correlators over broad ranges of density, temperature, and interaction strength. The benchmark shows that the free energy is comparatively robust, whereas the chemical potential and fluctuation observables provide much sharper diagnostics of the hierarchy closure. A maximum-entropy closure gives the most accurate overall description and reproduces even the low-temperature oscillatory structure of the connected two-density correlator. These results identify two general requirements for functional approaches to quantum thermodynamics: the renormalization group flow equation must retain the equal-time contact subtraction to avoid spurious self-interactions, and any closure of the hierarchy must preserve the statistical consistency of density correlators. This work provides a controlled foundation for deriving ab initio density functionals for quantum many-body systems across condensed-matter, ultracold-atom, and nuclear physics, as well as quantum chemistry.