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arXiv:2502.11313 · Physical Review A

Tracking adiabaticity in nonequilibrium many-body systems using x-ray photoemission from metals as a stringent test

Gustavo Diniz, Felipe D. Picoli, L. Nunes de Oliveira, Irene D’Amico

Published Jan 9, 2026• 1 citation
arXivHTMLPDF

Abstract

The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion to check and track it remains an open question, especially for complex many-body systems. Here we test techniques based on metrics which have been recently proposed to quantitatively characterize and track adiabaticity. We investigate the time evolution of x-ray photoemission in metals, which displays a strongly out-of-equilibrium character, continuum energy spectrum, and experiences the Anderson orthogonality catastrophe: a nightmarish scenario for this type of test. Our results show that the metrics-based methods remains valid. In particular, we demonstrate that the natural local density distance is able not only to track adiabaticity, but also to provide information not captured by the corresponding Bures' or trace distances about the system's dynamics. In the process, we establish an explicit upper limit for this local density distance in terms of the trace distance, and derive a simple analytical solution that accurately describes the time evolution of a Fermi gas with a localized scattering potential for a large range of parameters. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much simpler to compute than the corresponding quantum state and it is experimentally measurable: this makes the method tested extremely appealing.

DOI
10.1103/m17z-4g58

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The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion to check and track it remains an open question, especially for complex many-body systems. Here we test techniques based on metrics which have been recently proposed to quantitatively characterize and track adiabaticity. We investigate the time evolution of x-ray photoemission in metals, which displays a strongly out-of-equilibrium character, continuum energy spectrum, and experiences the Anderson orthogonality catastrophe: a nightmarish scenario for this type of test. Our results show that the metrics-based methods remains valid. In particular, we demonstrate that the natural local density distance is able not only to track adiabaticity, but also to provide information not captured by the corresponding Bures' or trace distances about the system's dynamics. In the process, we establish an explicit upper limit for this local density distance in terms of the trace distance, and derive a simple analytical solution that accurately describes the time evolution of a Fermi gas with a localized scattering potential for a large range of parameters. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much simpler to compute than the corresponding quantum state and it is experimentally measurable: this makes the method tested extremely appealing.
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.
Abstract 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.
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 adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.
We evaluate the density matrix of an arbitrary quantum mechanical system in terms of the quantities pertinent to the solution of the time-dependent density functional theory (TDDFT) problem. Our theory utilizes the adiabatic connection perturbation method of G\"orling and Levy, from which the expansion of the many-body density matrix in powers of the coupling constant $\ensuremath{\lambda}$ naturally arises. We then find the reduced density matrix ${\ensuremath{\rho}}_{\ensuremath{\lambda}}(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}},t)$, which, by construction, has the $\ensuremath{\lambda}$ independent diagonal elements ${\ensuremath{\rho}}_{\ensuremath{\lambda}}(\mathbf{r},\mathbf{r},t)=n(\mathbf{r},t)$, n(r,t)n(\mathbf{r},t)n(r,t) being the particle density. The off-diagonal elements of ${\ensuremath{\rho}}_{\ensuremath{\lambda}}(\mathbf{r},{\mathbf{r}}^{\ensuremath{'}},t)$ contribute importantly to the processes unaccessible via the density, directly or by the use of the known TDDFT functionals. Of those, we consider the momentum-resolved photoemission, doing this to the first order in $\ensuremath{\lambda}$, i.e., on the level of the exact exchange theory. In illustrative calculations of photoemission from the quasi-2D electron gas and isolated atoms, we find quantitatively strong and conceptually far-reaching differences with the independent-particle Fermi's golden rule formula.
The fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed matter systems, the time scale for such "ultrafast" processes is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we observed nonequilibrium dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the nonperturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasi-particles and the quantum interference between attractive and repulsive states throughout the full depth of the Fermi sea. Ultrafast time-domain methods applied to strongly interacting quantum gases enable the study of the dynamics of quantum matter under extreme nonequilibrium conditions.