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arXiv:2508.01444 · Physical Review A

Impact of quantum coherence on the dynamics and thermodynamics of quenched free fermions coupled to a localized defect

Beatrice Donelli, Gabriele De Chiara, Francesco Scazza, Stefano Gherardini

Published Dec 2, 2025• 2 citations
arXivHTMLPDF

Abstract

We investigate the non-equilibrium quantum dynamics and thermodynamics of free fermions suddenly coupled to a localized defect in a one-dimensional harmonic trap. This setup realizes a quantum quench transformation that gives rise to the orthogonalization of the system's wave-function as an effect of the localized perturbation. Using the Loschmidt echo and the Kirkwood-Dirac quasiprobability (KDQ) distribution of the work done by the defect, we quantify the extent and rate of the orthogonalization dynamics. In particular, we show that initializing the system in a coherent superpositions of energy eigenstates leads to non-classical features, such as Wigner function's negativity and non-positivity of the work KDQ distribution. Starting from simple single-particle superpositions and then progressing with coherent and cat states of few-body fermionic systems, we uncover how quantum coherence and few-body correlations shape the out-of-equilibrium response due to the presence of the defect.

DOI
10.1103/5kt1-5m83

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We investigate the non-equilibrium quantum dynamics and thermodynamics of free fermions suddenly coupled to a localized defect in a one-dimensional harmonic trap. This setup realizes a quantum quench transformation that gives rise to the orthogonalization of the system's wave-function as an effect of the localized perturbation. Using the Loschmidt echo and the Kirkwood-Dirac quasiprobability (KDQ) distribution of the work done by the defect, we quantify the extent and rate of the orthogonalization dynamics. In particular, we show that initializing the system in a coherent superpositions of energy eigenstates leads to non-classical features, such as Wigner function's negativity and non-positivity of the work KDQ distribution. Starting from simple single-particle superpositions and then progressing with coherent and cat states of few-body fermionic systems, we uncover how quantum coherence and few-body correlations shape the out-of-equilibrium response due to the presence of the defect.
We introduce a nonequilibrium phenomenon, reminiscent of Anderson’s orthogonality catastrophe, that arises in the transient dynamics following an interaction quench between a quantum system and a localized defect. Even if the system comprises only a single particle, the overlap between the asymptotic and initial superposition states vanishes according to a power-law scaling with the number of energy eigenstates entering the initial state and an exponent that depends on the interaction strength. The presence of quantum coherence in the initial state is reflected onto the discrete counterpart of an infinite discontinuity in the quasiprobability distribution of work due to the quench transformation, and onto the subsequent power-law decay of the work distribution. The positivity loss of the work distribution is directly linked with a reduction of the minimal time imposed by quantum mechanics for the state to orthogonalize, thus leading to a quantum coherence-enhanced state-orthogonalization. We propose an experimental test of coherence-enhanced orthogonalization dynamics based on Ramsey interferometry of a trapped cold-atom system.
We investigate the non-equilibrium work statistics originating from a sudden quench in a bosonic Josephson junction. In particular, by employing the Holstein-Primakoff approximation, the work statistics are analytically characterized in the weak-interaction regime, where the dynamics map onto a time-dependent quantum harmonic oscillator. For a junction initialized in the ground state of the pre-quench Hamiltonian, we demonstrate that the work statistics are governed by a negative binomial distribution, as occurs in fully-connected models driven across a critical point. Furthermore, we also consider initial superposition states containing quantum coherences in the energy basis. To characterize the corresponding work distributions, we employ Kirkwood-Dirac quasiprobabilities (KDQ). Even in the simplest case, when the junction is initialized in a superposition of the ground and second excited states, the KDQ distribution of work exhibits negative or complex values, reflecting non-classical features. Moreover, the coherence content of the initial state can be optimized to enhance the extractable work extracted from the quench, beyond classical bounds. Finally, we propose an experimental interferometric protocol to directly measure the characteristic function of the work distribution in experimentally accessible settings.
We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the establishment of entanglement. We extend our analysis to multipartite systems by examining the case of three trapped atoms. We show the initial (pre-quench) interactions play a vital role in determining the dynamical features, while the qualitative features of the two particle case appear to remain valid. Finally, we propose the use of the atomic density profile as a readily accessible indicator of the non-equilibrium properties of the systems in question.
We study the out-of-equilibrium dynamics of two interacting atoms in a one-dimensional harmonic trap after a quench by a tightly pinned impurity atom. We make use of an approximate variational calculation called the Lagrange-mesh method to solve the Schr\"odinger equation as a function of interparticle interaction and impurity quench strength. We investigate the out-of-equilibrium dynamics by calculating the Loschmidt echo which quantifies the irreversibility of the system following the quench, while its probability distribution after long times can be used to identify distinct dynamical regimes. These quantities are related to the spectral function which describes the full dynamical spectrum, and we show through a thorough examination of the parameter space the existence of distinct scattering states and collective oscillations. This work demonstrates how these dynamics are strongly dependent on the interaction strength between the atoms and may be tuned to observe the establishment of the orthogonality catastrophe in few-body systems.
The non-equilibrium quantum thermodynamics of many-body open systems is notoriously rich, especially in the strong-coupling regime where strong system-bath correlations develop and interactions produce non-perturbative effects. Such systems can be described by `quantum impurity models' where the system and bath are treated on an equal footing as a single composite. Paradigmatic examples are the spin-boson and Anderson impurity models, in which system degrees of freedom interact with either bosonic or fermionic gapless baths. Here we study the quantum work distribution function (WDF) of such systems following a quench. Capturing the full continuum of many-body excitations in the WDF requires a non-perturbative solution of the underlying non-equilibrium quantum impurity problem. For this purpose, we extend the time-dependent numerical renormalization group (TDNRG) approach to the calculation of the WDF, which applies directly in the thermodynamic limit, can be used for arbitrary quench amplitudes at zero or finite temperature, and provides exponentially fine low-energy resolution. Our numerically-exact solution reveals power-law threshold behavior due to the Anderson orthogonality catastrophe when the work approaches its minimum value, with universal scaling collapse of the distribution below an emergent low-energy scale induced by system-bath correlations.
I investigated the quench dynamics of inhomogeneous quantum spin chains. Here quench means the sudden change of an external parameter. The system is initially in its ground state. After the change of the parameter the ground state is not an eigenstate of the new Hamiltonian and a non-trivial dynamics starts. The dynamics is investigated with free fermion techniques. Various types of inhomogeneities were considered, homogeneous system with local defect, quasi-periodic systems and a disordered model. The results are qualitatively described by a special quasi-classical theory.