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We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size $N$ and the facilitation of operator delocalization by specific graph structures. A novel graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes., Comment: 9 pages, 4 figures

We present numerical results for the Rosenzweig Porter model for all symmetry classes of the Dyson threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the spectral properties as measures to explore the transition from Poisson to Wigner Dyson WD statistics. Furthermore, we performed thorough studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback Leibler KL divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

We present a detailed study of an asymmetrically driven quantum Otto engine with a time-dependent harmonic oscillator as its working medium. We obtain analytic expressions for the upper bounds on the efficiency of the engine for two different driving schemes having asymmetry in the expansion and compression work strokes. We show that the Otto cycle under consideration cannot operate as a heat engine in the low-temperature regime. Then, we show that the friction in the expansion stroke is significantly more detrimental to the performance of the engine as compared to the friction in the compression stroke. Further, by comparing the performance of the engine with sudden expansion, sudden compression, and both sudden strokes, we uncover a pattern of connections between the operational points, and we indicate the optimal operation regime for each case. Finally, we analytically characterize the complete phase diagram of the Otto cycle for both driving schemes and highlight the different operational modes of the cycle as a heat engine, refrigerator, accelerator, and heater.

We introduce a quantum charging distance as the minimal time that it takes to reach one state (charged state) from another state (depleted state) via a unitary evolution, assuming limits on the resources invested into the driving Hamiltonian. For pure states it is equal to the Bures angle, while for mixed states, its computation leads to an optimization problem. Thus, we also derive easily computable bounds on this quantity. The charging distance tightens the known bound on the mean charging power of a quantum battery, it quantifies the quantum charging advantage, and it leads to an always achievable quantum speed limit. In contrast with other similar quantities, the charging distance does not depend on the eigenvalues of the density matrix, it depends only on the corresponding eigenspaces. This research formalizes and interprets quantum charging in a geometric way, and provides a measurable quantity that one can optimize for to maximize the speed of charging of future quantum batteries., Comment: 15 pages, 4 figures, v2: added Table I: main results, extended discussion on the quantum speed limit

We demonstrate that an image recognition algorithm based on a convolutional neural network provides a powerful procedure to differentiate between ergodic, non-ergodic extended (fractal) and localized phases in various systems: single-particle models, including random-matrix and random-graph models, and many-body quantum systems. The network can be successfully trained on a small data set of only 500 wave functions (images) per class for a single model. The trained network can then be used to classify phases in the other models and is thus very efficient. We discuss the strengths and limitations of the approach., Comment: 9 pages, 10 figures + 2 pages, 4 figures, 1 table in appendices

The generation of a large amount of entanglement is a necessary condition for a quantum computer to achieve quantum advantage. In this paper, we propose a method to efficiently generate pseudo-random quantum states, for which the degree of multipartite entanglement is nearly maximal. We argue that the method is optimal, and use it to benchmark actual superconducting (IBM's ibm_lagos) and ion trap (IonQ's Harmony) quantum processors. Despite the fact that ibm_lagos has lower single-qubit and two-qubit error rates, the overall performance of Harmony is better thanks to low error rate in state preparation and measurement and to the all-to-all connectivity of qubits. Our result highlights the relevance of the qubits network architecture to generate highly entangled state., Comment: 14 pages, 8 figures

Understanding the mechanisms underlying many-body quantum chaos is one of the big challenges in theoretical physics. We tackle this problem by considering a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows to disambiguate between operator growth and \emph{delocalization}, showing that the latter is the dominant process in the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians, in this case up to dimension $2^{19}\times 2^{19}$. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective., Comment: 5 + 1 pages, 4 + 1 figures

We present a method to estimate the probabilities of outcomes of a quantum observable, its mean value, and higher moments by measuring any other observable. This method is general and can be applied to any quantum system. In the case of estimating the mean energy of an isolated system, the estimate can be further improved by measuring the other observable at different times. Intuitively, this method uses interplay and correlations between the measured observable, the estimated observable, and the state of the system. We provide two bounds: one that is looser but analytically computable and one that is tighter but requires solving a non-convex optimization problem. The method can be used to estimate expectation values and related quantities such as temperature and work in setups where performing measurements in a highly entangled basis is difficult, finding use in state-of-the-art quantum simulators. As a demonstration, we show that in Heisenberg and Ising models of ten sites in the localized phase, performing two-qubit measurements excludes 97.5% and 96.7% of the possible range of energies, respectively, when estimating the ground state energy., Comment: 7+9 pages, 6 figures, 3 tables. v2: significantly reworked structure and made it easier to read. Proofs simplified and moved to the main text. v3: title changed, cosmetic changes. Questions and comments are welcome

We propose a general computational framework for optimizing model-dependent parameters in quantum batteries (QB). We apply this method to two different charging scenarios in the micromaser QB and we discover a new charging protocol for stabilizing the battery in upper-laying Hilbert space chambers in a controlled and automatic way. This protocol is found to be stable and robust, and it leads to an improved charging efficiency in micromaser QBs. Moreover, our optimization framework is highly versatile and efficient, holding great promise for the advancement of QB technologies at all scales., Comment: 15 pages, 7 figures

We consider a micromaser model of a quantum battery, where the battery is a single mode of the electromagnetic field in a cavity, charged via repeated interactions with a stream of qubits, all prepared in the same non-equilibrium state, either incoherent or coherent, with the matter-field interaction modeled by the Jaynes-Cummings model. We show that the coherent protocol is superior to the incoherent one, in that an effective pure steady state is achieved for generic values of the model parameters. Finally, we supplement the above collision model with cavity losses, described by a Lindblad master equation. We show that battery performances, in terms of stored energy, charging power, and steady-state purity, are slightly degraded up to moderated dissipation rate. Our results show that micromasers are robust and reliable quantum batteries, thus making them a promising model for experimental implementations., Comment: 15 pages, 7 figures

We study the dynamical generation of entanglement for a two-body interacting system, starting from a separable coherent state. We show analytically that in the quasiclassical regime the entanglement growth rate can be simply computed by means of the underlying classical dynamics. Furthermore, this rate is given by the Kolmogorov-Sinai entropy, which characterizes dynamical complexity of classical motion. Our results, illustrated by numerical simulations on a model of coupled rotators, establish in the quasiclassical regime a link between the generation of entanglement, a purely quantum phenomenon, and classical complexity., Comment: 10 pages. 3 figures

We investigate the thermodynamic uncertainty relation (TUR), \textit{i.e.} a trade-off between entropy production rate and relative power fluctuations, for nondegenerate three-level and degenerate four-level maser heat engines. In the nondegenerate case, we consider two slightly different configurations of three-level maser heat engine and contrast their degree of violation of standard TUR. In the high-temperature limit, standard TUR relation is always violated for both configurations. We also uncover an invariance of TUR under simultaneous rescaling of the matter-field coupling constant and system-bath coupling constants. For the degenerate four level engine, we study the effects of noise-induced coherence on TUR. We show that depending on the parametric regime of operation, noise-induced coherence can either suppress or enhance the relative power fluctuations., Comment: 12 pages, 5 figures

Energy extraction is a central task in thermodynamics. In quantum physics, ergotropy measures the amount of work extractable under cyclic Hamiltonian control. As its full extraction requires perfect knowledge of the initial state, however, it does not characterize the work value of unknown or untrusted quantum sources. Fully characterizing such sources would require quantum tomography, which is prohibitively costly in experiments due to the exponential growth of required measurements and operational limitations. Here, we therefore derive a new notion of ergotropy applicable when nothing is known about the quantum states produced by the source, apart from what can be learned by performing only a single type of coarse-grained measurement. We find that in this case the extracted work is defined by the Boltzmann and observational entropy, in cases where the measurement outcomes are, or are not, used in the work extraction, respectively. This notion of ergotropy represents a realistic measure of extractable work, which can be used as the relevant figure of merit to characterize a quantum battery., Comment: 5+1(Appendix)+7(Supplemental) pages, 4 figures. Comments and questions welcome. v2: changed the interpretation of the coarse-grained extraction operations (former eq (6), now eq (7)). Appendix with examples added. Results unchanged. v3: technical details moved into a short appendix. Added explanatory figure for the extraction operations. Added extra proof in the Supplemental Material

We study the thermalizing properties of the mass-deformed SYK model, in a regime of parameters where the eigenstates are ergodically extended over just portions of the full Fock space, as an all-to-all toy model of many-body localization. Our numerical results strongly support the hypothesis that, although considerably delayed, thermalization is still present in this regime. Our results add to recent studies indicating that many-body localization should be interpreted as a strict Fock-space localization., Comment: 9 pages, 6 figures

We show that a micromaser is an excellent model of quantum battery. A highly excited, pure, and effectively steady state of the cavity mode, charged by coherent qubits, can be achieved, also in the ultrastrong coupling regime of field-matter interaction. Stability of these appealing features against loss of coherence of the qubits and the effect of counter-rotating terms in the interaction Hamiltonian are also discussed., Comment: 6 pages, 1 figure

Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a $PT$-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: the elliptic Ginibre ensemble of random matrices and a non-Hermitian Sachdev-Ye-Kitaev (SYK) model. The free energy of the Ginibre model is temperature-independent in the low-temperature phase. The SYK model has a similar behavior for sufficiently low temperature, then it experiences a possible continuous phase transition to a phase with a temperature-dependent free energy before the first-order transition takes place at a higher temperature. We identify the order parameter of the first-order phase transition and obtain analytical expressions for the critical temperature. The mechanism behind the transition is the existence of replica symmetry breaking configurations coupling Left and Right replicas that control the low-temperature limit of the partition function. We speculate that quantum chaos may be necessary for the observed dominance of off-diagonal replica symmetry breaking configurations in the low-temperature limit., Comment: 44+20 pages. Some of the results of this paper were announced in arxiv:2102:06630 (Phys.Rev.Lett. 128 (2022) 8, 081601)

We analyze a two-body nonhermitian two-site Sachdev-Ye-Kitaev model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of phase transitions which is a consequence of the partition function factorizing into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways, first in terms of the single-particle energies, and second by solving the Schwinger-Dyson equations. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases is determined by the spectral density. The four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. However the low-temperature free energy of the two-body SYK model is not flat, in fact it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive, which most likely is a consequence of the nonhermiticity., Comment: To be submitted to the Dyson memorial volume of the Journal of Mathematical Physics

We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the universal structure of random matrix models in high-depth circuit states. We construct different layer unitaries corresponding to the GOE and GUE distributions and quantify their VQA performance. Our study also highlights a potential tension between the OTOC and BGS-type diagnostics of quantum chaos., Comment: 12 pages, 10 figures