Floquet driven long-range interactions induce super-extensive scaling in quantum batteries

Aditi Sen De; Leela Ganesh Chandra Lakkaraju; Stavya Puri; Tanoy Kanti Konar

REVIEW 5 major objections 6 minor 6 cited by

Floquet driven long-range interactions induce super-extensive scaling in quantum batteries

T0 review · 5 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A single periodic drive and long-range spin couplings can make quantum battery power scale superlinearly with system size.

desk verdict A solid, honest QB paper with a real O(N^2) bound and an analytic solvable model, but the super-extensive scaling claim rests on per-N frequency optimization and short fits; the abstract oversells it as 'genuine quantum advantage'. read the letter →

arxiv 2412.00921 v2 pith:5TH7V5BS submitted 2024-12-01 quant-ph cond-mat.mes-hallcond-mat.quant-gas

Stavya Puri , Tanoy Kanti Konar , Leela Ganesh Chandra Lakkaraju , Aditi Sen De This is my paper · ORCID

classification quant-phcond-mat.mes-hallcond-mat.quant-gas

keywords quantumbatteryFloquetdrivinglong-rangeinteractionssuper-extensivescalingLipkin-Meshkov-Glickmodelpower-lawadvantageFloquet-Magnusexpansion

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that periodic, square-wave driving of a long-range interacting charger gives a quantum battery a genuine scaling advantage: the charging power grows faster than the number of battery units ($N$), rather than merely linearly. The authors prove analytically that the stroboscopic instantaneous power of a non-interacting spin battery charged by a Kac-normalized long-range XY Hamiltonian is bounded by $O(N^2)$ for moderate $N$ (Theorem 1). They then show numerically that the maximum average power, optimized over the drive frequency, scales as $aN^\eta+b$ with $\eta>1$, reaching about $1.68$ for low fall-off rate, high coordination number, and interaction-dominated parameters. If the claim is right, a charger that collectively couples distant spins and is modulated periodically can outperform short-range or nearest-neighbour chargers in energy delivery speed.

What carries the argument

The mechanism is a two-step square-wave Floquet drive $J(t) = \pm J$ alternating every half period $T/2$, acting through a long-range XY Hamiltonian with coordination number $Z$ and power-law fall-off $\alpha$, Kac-normalized by $\mathcal{N} = \sum_{r=1}^{Z} r^{-\alpha}$. The Floquet unitary is $U_F = e^{-i(H_B - H_{\mathrm{int}})T/2} e^{-i(H_B + H_{\mathrm{int}})T/2}$, and the paper bounds instantaneous power through $|P_{\mathrm{ins}}(nT)| \le \|[H_F, H_B]\|$. The load-bearing structural fact comes from the Floquet-Magnus expansion: the $k$-th order term is a sum of nested commutators producing at most $(k+1)$-body interactions, and once $k \ge N$ the interactions saturate at $N$-body, generating the $N^2$ contribution in the bound. For the extended XY model, the Jordan-Wigner transformation yields an exact mode-by-mode work formula $W(nT) = \sum_k 2 h_z (1 - (n^z_k)^2) \sin^2(n \cos^{-1} u^0_k)$, which lets the authors test the scaling at larger $N$ than direct evolution allows.

What would settle it

Fix a single drive frequency (for example the optimal frequency for $N=8$) and compute $\langle P\rangle^\omega_{\max}$ for $N=4$ to $N=10^4$ using the exactly solvable extended XY model. If the fitted exponent drops to 1 as $N$ grows, or if the exponent found by re-optimizing $\omega$ for each $N$ differs significantly from the exponent at fixed $\omega$, then the claimed super-extensive scaling is a finite-size or re-optimization effect rather than a genuine asymptotic advantage.

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Extended reading notes

Core claim

The central claim is Theorem 1: for a battery Hamiltonian $H_B = h_z \sum_j \sigma^z_j$ initialized in its product ground state, and a charging Hamiltonian $H_{\mathrm{ch}}(t) = H_B + H_{\mathrm{int}}(t)$ with long-range two-body interactions $H_{\mathrm{int}}(t) = \sum_{i<j, |i-j|\le Z} \frac{J(t)}{\mathcal{N}|i-j|^\alpha}(\sigma^x_i\sigma^x_j + \gamma \sigma^y_i\sigma^y_j)$ under square-wave modulation, the stroboscopic instantaneous power obeys $|P_{\mathrm{ins}}(nT)| \le a N^\eta + bN + c$ with $\eta \le 2$. The proof bounds $|P_{\mathrm{ins}}|$ by $\|[H_F, H_B]\|$, expands the Floquet Hamiltonian $H_F$ in the Floquet-Magnus series, and isolates an $N^2$ contribution that appears once nested commutators generate $N$-body terms. The paper also reports numerical evidence that the frequency-optimized maximum average power $\langle P\rangle^\omega_{\max}$ follows $\langle P\rangle^\omega_{\max} \sim aN^\eta + b$ with $\eta > 1$ (up to about $1.68$ for $\alpha = 0.5$, $\gamma=-1$, $h_z/J \ll 1$), while exponents fall to roughly $1$ for short-range ($\alpha > 2$) or low-coordination ($Z=2$) chargers.

Load-bearing premise

The load-bearing premise is that fitting $\langle P\rangle^\omega_{\max}$ to $aN^\eta + b$ over small to moderate system sizes, with the drive frequency optimized separately for each $N$, correctly identifies a true super-linear trend; the analytic theorem only proves an $O(N^2)$ upper bound and does not by itself establish $\eta > 1$.

Editorial extensions

If this is right

A quantum battery can achieve super-extensive power scaling without any explicit many-body term in the battery Hamiltonian; the needed resource sits entirely in the long-range two-body charger under periodic driving.
The regime that matters is the paramagnetic phase with $h_z/J \ll 1$, low fall-off rate ($\alpha \le 2$), and coordination number close to $N-1$; outside this regime the scaling falls back to linear.
Frequency optimization is essential: maximum average power vanishes in both the adiabatic limit $\omega \to 0$ and the high-frequency limit $\omega \to \infty$, so the advantage lives at intermediate Floquet frequencies.
The quadratic upper bound is not tight for asymptotically large systems: factorial denominators in the Floquet-Magnus expansion suppress the $N^2$ term as $N$ grows, so the super-linear advantage is a finite-size effect at moderate, experimentally accessible sizes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The evidence for $\eta > 1$ is numerical power-law fitting over small-to-moderate $N$ with the frequency re-optimized at each size; a rigorous lower bound on $\langle P\rangle^\omega_{\max}$ would be needed to certify that the exponent is not a finite-size artifact.
A clean test is to fix one drive frequency (say the optimum for $N=8$) and repeat the scaling analysis: if the fitted exponent drops toward 1, the per-$N$ frequency optimization is doing much of the work.
Real chargers start from thermal rather than pure states; checking whether $\eta$ survives at finite temperature would test whether the advantage is robust outside the zero-temperature polarized initial state.
The authors connect the advantage to entanglement distribution; a direct test would be to compute a bipartite entanglement or mutual information measure during charging and check whether its growth rate tracks the power exponent.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Mike,

Quick read on arXiv:2412.00921. The genuinely new thing here is the pairing of Floquet square-wave driving with long-range interactions for quantum battery charging, and the paper does more than most in this subfield: Theorem 1 gives an O(N^2) bound on instantaneous power via the Floquet-Magnus expansion, and the extended XY model is solved analytically (Appendix D), allowing clean numerics up to N=100. The NN/NNN control in Appendix C correctly shows no super-linear scaling without long-range interactions, which is a useful sanity check. I believe the central mechanism is real: long-range interactions generate higher-body effective interactions under Floquet driving, and that can push power above linear scaling at moderate sizes.

The soft spots are exactly where you'd expect. The analytic theorem bounds instantaneous power, not the maximum average power that actually shows eta > 1. The scaling exponents come from fits of aN^eta + b to short ranges (N=4-12 in Fig. 2) with no error bars and no sliding-window analysis. The most serious issue is the per-N frequency optimization: the maximum is taken over omega separately for each N, so the reported exponent describes a family of drives tuned to each system size, not a single physical drive. The paper's own Note after Eq. (8) concedes the advantage washes away in the thermodynamic limit, so the abstract's 'genuine quantum advantage' overstates what is a finite-size effect.

That said, the extended XY results (Fig. 3) give some support that the trend persists to larger N, and the analytic solution means the numerics are not a black box. I would not call this a fatal flaw; I'd call it a claim that needs better quantified evidence. The fix is straightforward: show error bars, do a sliding-window exponent analysis, and ideally test a fixed frequency (e.g., the optimal omega for the largest N) to see whether the super-linear trend survives without per-N tuning. If it does, the paper is a solid contribution; if not, it is still an interesting finite-size effect but the abstract needs to say so.

Who is this for? People working on quantum batteries, especially those interested in Floquet charging and long-range spin models. It deserves a serious referee -- the math is real, the control is good, and the question is meaningful. I'd send it out, with a referee asked to focus on the scaling evidence and the abstract's wording.

Best,

Referee Report

5 major / 6 minor

Summary. The manuscript proposes that long-range interacting spin chains under square-wave Floquet driving can charge a non-interacting spin battery with super-extensive scaling of power. Section II states Theorem 1, an upper bound on the stroboscopic instantaneous power, |P_ins(nT)| ≤ aN^η + bN + c with η ≤ 2, obtained via a Floquet-Magnus expansion (Eq. (8)). The main numerical evidence is the quantity ⟨P⟩^ω_max = max_{n,ω} W(nT)/(nT) (Eq. (A6)), which is fitted to aN^η + b for N up to 12 (Fig. 2), 100 (Fig. 3), or 200 (Fig. 1), yielding exponents up to about 1.68 in the paramagnetic phase for low α and high coordination number Z. The paper also solves the extended XY model analytically and notes, after Eq. (8), that the super-extensive advantage washes away for very large N.

Significance. If the claimed super-extensive scaling were established for a fixed driving protocol, the work would be a useful contribution to the quantum battery literature, showing that Floquet engineering combined with long-range interactions can overcome the absence of super-extensive scaling reported for periodic charging in Ref. [65]. The manuscript deserves credit for the analytic Floquet-Magnus bound, the analytic treatment of the extended XY model, and the explicit admission that the advantage is finite-size. However, the central claim is not proven by Theorem 1 and currently rests on small-N fits combined with per-system-size frequency optimization; these weaknesses prevent the paper from supporting its strongest conclusions as written.

major comments (5)

[Sec. II, Theorem 1 and Eq. (8)] Theorem 1 only provides an upper bound on instantaneous power; it does not establish that the instantaneous power or the maximum average power actually grows super-linearly. The abstract's statement that the upper bound scales quadratically is accurate, but the claim that the maximum average power 'can achieve the super-extensive scaling' is inferred solely from the numerical fits of ⟨P⟩^ω_max. Since |⟨P(nT)⟩| ≤ max_n |P_ins(nT)|, the upper bound cannot rule out η = 1. A rigorous lower bound, or an analytic derivation of the fitted exponent, is needed to support the central claim.
[Sec. II A and Eq. (A6)] The definition of ⟨P⟩^ω_max maximizes over the driving frequency separately for each N. This means the scaling comparison is made across a family of optimized Floquet drives, not a single physical driving scheme. If the optimal frequency ω_opt(N) shifts systematically with N, the reported exponent may reflect resonance tuning with system size rather than an intrinsic many-body charging enhancement. Please report ω_opt(N) as a function of N for the main parameter sets and demonstrate that a fixed, N-independent frequency (for example, one in the high-frequency regime) still yields η > 1 over the same N range.
[Fig. 2 and Fig. 4] The most dramatic exponent, η ≈ 1.68 for α = 0.5 in Fig. 2, is extracted from a small number of points in the range N = 4 to 12 using the three-parameter fit aN^η + b, with no error bars, confidence intervals, or residual analysis. Over such a short interval, the fit cannot distinguish a genuine power law from a smooth finite-size crossover, especially because the paper's own Note after Eq. (8) states that the advantage washes away for large N. Please provide bootstrap or least-squares uncertainties, the effective local exponent d ln⟨P⟩^ω_max / d ln N, and the largest N at which η > 1 remains distinguishable from η = 1.
[Appendix D and Fig. 3] The analytic solution of the extended XY model gives a closed expression for W(nT), but the scaling conclusion in Fig. 3 still rests on fitting ⟨P⟩^ω_max after per-N frequency optimization. Since the exact formula is available, it should be used to test the scaling more directly: compute the exponent over a wider N range without the offset b, and check whether the super-linear behavior persists when the frequency is fixed to a common value rather than optimized separately for each N.
[Eq. (8) and the Note after Eq. (8)] The proof of Theorem 1 contains an unquantified assertion that 'the factor inside the third bracket does not scale with N-1 (especially when N is moderate).' That bracket is an infinite sum involving binomial coefficients and factorial denominators; without a controlled estimate of its N-dependence, the conclusion that the right-hand side scales as N^2 is not rigorously established. Moreover, the Note concedes that the advantage diminishes with increasing N, so the observed behavior is explicitly finite-size. The abstract and conclusions should state this finite-size crossover clearly rather than presenting super-extensive scaling as an asymptotic property.

minor comments (6)

[Abstract] The phrase 'the maximum average power which is a lower bound of the instantaneous power' is imprecise; the average power is bounded above by the maximum instantaneous power, so it would be clearer to say that the average power cannot exceed the maximum instantaneous power.
[Sec. II A and Eq. (A6)] The quantity ⟨P⟩^ω_max is used in the main text from Sec. II A onward but is defined only in Appendix A; it should be defined when first introduced in the main text.
[Figs. 1 and 3] The fitted curves are indicated only by annotations such as '∼ N^1.28' without displaying the fitted function, the data points with error bars, or the residuals; including fit parameters, uncertainties, and goodness-of-fit measures in the captions or text would make the evidence more transparent.
[Sec. III A] The heading contains a typo: 'inetraction' should be 'interaction'.
[Eq. (B4)] In Eq. (B4), an inequality is written for operators or commutators without taking norms; the inequality is only meaningful for scalar quantities such as operator norms, and this should be corrected.
[Introduction and Ref. [65]] The discussion of Ref. [65] states that periodic charging does not lead to super-extensive scaling; since the present protocol differs by including long-range interactions and, crucially, by optimizing over the frequency in Eq. (A6), the text should clarify which ingredient is responsible for the difference.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the analytical upper bound is derived in-paper and the super-extensive scaling is presented as an explicit empirical fit, not as a prediction forced by construction.

full rationale

The central analytic result (Theorem 1 and Eq. (8)) is self-contained: starting from the stated battery Hamiltonian H_B = h_z Σ σ^z_j and the long-range XY charging Hamiltonian with square-wave Floquet driving, the paper uses the Floquet-Magnus expansion and triangle inequalities to bound nested commutators, obtaining |P_ins(nT)| ≤ N[...] + N²[...]. That is a derivation from the stated Hamiltonian, not an input restated as an output. The super-extensive claim is then supported by least-squares fits of ⟨P⟩^ω_max = aN^η + b to numerically computed values (Figs. 1–4); fitting a scaling exponent to data is empirical characterization, and the fitted η is reported as the observed scaling rather than as an independent prediction, so no fitted parameter is renamed as a new result. The per-system-size maximization over ω defining ⟨P⟩^ω_max is introduced explicitly in Appendix A, Eq. (A6), and is a legitimate performance quantifier; optimizing over a control parameter before studying its N-dependence is not equivalent to assuming the scaling. The self-citations in the paper (e.g., Refs. [24–26,73,89]) are contextual and non-load-bearing; the main external inputs—the power bound from Ref. [9], the Floquet-Magnus expansion [81], and the Kac normalization [77]—are independent. The manuscript's Note after Eq. (8) explicitly concedes that the advantage washes away in the thermodynamic limit; this undercuts the abstract's 'genuine quantum advantage' wording and is an inference-strength limitation, but it is not a circular step. No specific equation-to-equation reduction or fitted-input-called-prediction step can be exhibited from the text.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claims rest on standard many-body models, Floquet theory, and numerical fitting of scaling exponents.

free parameters (3)

scaling exponent eta = 1.0 to 1.68 depending on model and parameters
Obtained by least-square fitting of <P>^omega_max vs N (Figs. 1-4); the central claim of super-extensive scaling rests on these fitted exponents.
fit offset b = -2.24 (Fig. 1 example)
Fitted constant in aN^eta + b; the value and sign of b affect the inferred scaling at small N.
optimal driving frequency omega_opt(N) = N-dependent (not reported in detail)
<P>^omega_max is defined by maximizing average power over omega for each N; the scaling of the envelope depends on how the optimum shifts with N.

assumptions (4)

domain assumption Convergence of Floquet-Magnus expansion for the square-wave drive
The analytical bound in Theorem 1 uses an all-orders FME (Eq. 8) without proving convergence or truncation error; the series may diverge for low frequencies.
standard math Bound on instantaneous power from Ref. [9]: |P(t)| <= sum_k k||H_ch|| ||Hs - Es_min||
Used in Eq. (B2) to relate power to norms of the Floquet Hamiltonian; this is an external theorem.
domain assumption The Kac-normalized LR Hamiltonian with open or periodic boundary conditions is an appropriate charger model and the ground state of HB is the initial state
The physical relevance of the results depends on this model being realizable; the fully polarized initial state is a standard choice.
ad hoc to paper Maximization over driving frequency is a valid definition of charging power
The paper introduces optimization over omega in <P>^omega_max, acknowledging it was not considered in earlier Floquet charging work; the scaling results depend on this definition.

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Pith. "Pith review of Floquet driven long-range interactions induce super-extensive scaling in quantum batteries." pith.science (2026). https://pith.science/paper/5TH7V5BS

@misc{pith2026241200921,
  author       = {Pith},
  title        = {Pith review of: Floquet driven long-range interactions induce super-extensive scaling in quantum batteries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5TH7V5BS}},
  note         = {Machine review of arXiv:2412.00921}
}

read the original abstract

Achieving quantum advantage in energy storage and power extraction is a primary objective in the design of quantum-based batteries. We explore how long-range (LR) interactions in conjunction with Floquet driving can improve the performance of quantum batteries, particularly when the battery is initialized in a fully polarized state. In particular, we analytically prove that the upper bound of the instantaneous power obtained through this system-charger duo scales quadratically with moderate system-size. By optimizing the driving frequency, we demonstrate that the maximum average power which is a lower bound of the instantaneous power can achieve the super-extensive scaling with system-size, thereby providing genuine quantum advantage. Further, we illustrate that the inclusion of either two-body or many-body interaction terms in the LR charging Hamiltonian leads to a scaling benefit. We also discover that a super-linear scaling in power results from increasing the strength of interaction compared to the transverse magnetic field and the range of interaction with low fall-off rate, highlighting the advantageous role of long-range interactions in optimizing quantum battery charging.

Figures

Figures reproduced from arXiv: 2412.00921 by the authors.

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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**Figure 5.** Figure 5: FIG. 5. Behavior of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

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Forward citations

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Fast charging of a quantum battery assisted by noise,

Srijon Ghosh, Titas Chanda, Shiladitya Mal, and Aditi Sen(De), “Fast charging of a quantum battery assisted by noise,” Phys. Rev. A 104, 032207 (2021)

2021
[24]

Dimensional enhancements in a quantum battery with imperfections,

Srijon Ghosh and Aditi Sen(De), “Dimensional enhancements in a quantum battery with imperfections,” Phys. Rev. A 105, 022628 (2022)

2022
[25]

Local passivity and entangle- ment in shared quantum batteries,

Kornikar Sen and Ujjwal Sen, “Local passivity and entangle- ment in shared quantum batteries,” Phys. Rev. A 104, L030402 (2021)

2021
[26]

Ultrafast charging in a two-photon dicke quantum bat- tery,

Alba Crescente, Matteo Carrega, Maura Sassetti, and Dario Fer- raro, “Ultrafast charging in a two-photon dicke quantum bat- tery,” Phys. Rev. B102, 245407 (2020)

2020
[27]

Enhancing coherent energy transfer between quantum de- vices via a mediator,

Alba Crescente, Dario Ferraro, Matteo Carrega, and Maura Sas- setti, “Enhancing coherent energy transfer between quantum de- vices via a mediator,” Phys. Rev. Res.4, 033216 (2022)

2022
[28]

Quantum battery with ultracold atoms: Bosons versus fermions,

Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, Srijon Ghosh, and Aditi Sen(De), “Quantum battery with ultracold atoms: Bosons versus fermions,” Phys. Rev. A 106, 022618 (2022)

2022
[29]

Multimode advantage in continuous-variable quantum batteries,

Tanoy Kanti Konar, Ayan Patra, Rivu Gupta, Srijon Ghosh, and Aditi Sen(De), “Multimode advantage in continuous-variable quantum batteries,” Phys. Rev. A110, 022226 (2024)

2024
[30]

Quantum battery with non-hermitian charging,

Tanoy Kanti Konar, Leela Ganesh Chandra Lakkaraju, and Aditi Sen (De), “Quantum battery with non-hermitian charging,” Phys. Rev. A 109, 042207 (2024)

2024
[31]

Positive and non-positive measurements in en- ergy extraction from quantum batteries,

Paranjoy Chaki, Aparajita Bhattacharyya, Kornikar Sen, and Ujjwal Sen, “Positive and non-positive measurements in en- ergy extraction from quantum batteries,” arXiv (2024), 10.48550/arXiv.2404.18745, 2404.18745

2024 doi arXiv
[32]

Performance of quantum batteries with correlated and uncorrelated chargers,

Mohammad B. Arjmandi, Abbas Shokri, Esfandyar Faizi, and Hamidreza Mohammadi, “Performance of quantum batteries with correlated and uncorrelated chargers,” Phys. Rev. A 106, 13 062609 (2022)

2022
[33]

Vacuum-enhanced charging of a quantum battery,

Tiago F. F. Santos, Yohan Vianna de Almeida, and Marcelo F. Santos, “Vacuum-enhanced charging of a quantum battery,” Phys. Rev. A 107, 032203 (2023)

2023
[34]

Auxiliary-assisted stochastic en- ergy extraction from quantum batteries,

Paranjoy Chaki, Aparajita Bhattacharyya, Kornikar Sen, and Ujjwal Sen, “Auxiliary-assisted stochastic en- ergy extraction from quantum batteries,” arXiv (2023), 10.48550/arXiv.2307.16856, 2307.16856

2023 doi
[35]

Universal and complete extraction for energy-invariant catal- ysis in quantum batteries versus no uncorrelated state- invariant catalysis,

Paranjoy Chaki, Aparajita Bhattacharyya, and Ujjwal Sen, “Universal and complete extraction for energy-invariant catal- ysis in quantum batteries versus no uncorrelated state- invariant catalysis,” arXiv (2024), 10.48550/arXiv.2409.14153, 2409.14153

2024 doi arXiv
[36]

Artificial intelli- gence discovery of a charging protocol in a micromaser quantum battery,

Carla Rodr ´ıguez, Dario Rosa, and Jan Olle, “Artificial intelli- gence discovery of a charging protocol in a micromaser quantum battery,” Phys. Rev. A108, 042618 (2023)

2023
[37]

Sunburst quantum ising battery,

Akash Mitra and Shashi C. L. Srivastava, “Sunburst quantum ising battery,” Phys. Rev. A110, 012227 (2024)

2024
[38]

Charging by quantum measure- ment,

Jia-shun Yan and Jun Jing, “Charging by quantum measure- ment,” Phys. Rev. Appl.19, 064069 (2023)

2023
[39]

Remote charging and degradation suppression for the quantum battery,

Wan-Lu Song, Hai-Bin Liu, Bin Zhou, Wan-Li Yang, and Jun- Hong An, “Remote charging and degradation suppression for the quantum battery,” Phys. Rev. Lett.132, 090401 (2024)

2024
[40]

Topological quantum batteries,

Zhi-Guang Lu, Guoqing Tian, Xin-You L ¨u, and Cheng Shang, “Topological quantum batteries,” (2024), arXiv:2405.03675 [quant-ph]

2024 arXiv
[41]

Experimental investigation of coherent ergotropy in a sin- gle spin system,

Zhibo Niu, Yang Wu, Yunhan Wang, Xing Rong, and Jiangfeng Du, “Experimental investigation of coherent ergotropy in a sin- gle spin system,” Phys. Rev. Lett.133, 180401 (2024)

2024
[42]

Ergotropy, bound en- ergy and entanglement in 1d long range kitaev model,

Akash Mitra and Shashi C. L. Srivastava, “Ergotropy, bound en- ergy and entanglement in 1d long range kitaev model,” (2024), arXiv:2408.05063 [cond-mat.str-el]

2024 arXiv
[43]

Extractable energy from quantum superposition of cur- rent states,

Francesco Perciavalle, Davide Rossini, Juan Polo, and Luigi Amico, “Extractable energy from quantum superposition of cur- rent states,” Quantum Sci. Technol.10, 025046 (2025)

2025
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Charging quantum batteries via indefinite causal order: Theory and experiment,

Gaoyan Zhu, Yuanbo Chen, Yoshihiko Hasegawa, and Peng Xue, “Charging quantum batteries via indefinite causal order: Theory and experiment,” Phys. Rev. Lett.131, 240401 (2023)

2023
[45]

Many-body localized quantum batteries,

Davide Rossini, Gian Marcello Andolina, and Marco Polini, “Many-body localized quantum batteries,” Phys. Rev. B 100, 115142 (2019)

2019
[46]

Localiza- tion effects in disordered quantum batteries,

Mohammad B. Arjmandi, Hamidreza Mohammadi, Andreia Saguia, Marcelo S. Sarandy, and Alan C. Santos, “Localiza- tion effects in disordered quantum batteries,” Phys. Rev. E 108, 064106 (2023)

2023
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Beneficial and detrimental entanglement for quantum battery charging,

Ju-Yeon Gyhm and Uwe R. Fischer, “Beneficial and detrimental entanglement for quantum battery charging,” A VS Quantum Sci. 6, 012001 (2024)

2024
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Exper- imental analysis of energy transfers between a quantum emitter and light fields,

I. Maillette de Buy Wenniger, S. E. Thomas, M. Maffei, S. C. Wein, M. Pont, N. Belabas, S. Prasad, A. Harouri, A. Lemaˆıtre, I. Sagnes, N. Somaschi, A. Auff `eves, and P. Senellart, “Exper- imental analysis of energy transfers between a quantum emitter and light fields,” (2023...

2023 arXiv
[49]

Superconducting transmon qubit-resonator quantum battery,

Fu-Quan Dou and Fang-Mei Yang, “Superconducting transmon qubit-resonator quantum battery,” Phys. Rev. A 107, 023725 (2023)

2023
[50]

Optimal charging of a superconducting quantum battery,

Chang-Kang Hu, Jiawei Qiu, Paulo J P Souza, Jiahao Yuan, Yuxuan Zhou, Libo Zhang, Ji Chu, Xianchuang Pan, Ling Hu, Jian Li, Yuan Xu, Youpeng Zhong, Song Liu, Fei Yan, Dian Tan, R Bachelard, C J Villas-Boas, Alan C Santos, and Dapeng Yu, “Optimal charging of a superconducting q...

2022
[51]

Ibm quantum platforms: A quantum bat- tery perspective,

Giulia Gemme, Michele Grossi, Dario Ferraro, Sofia Vallecorsa, and Maura Sassetti, “Ibm quantum platforms: A quantum bat- tery perspective,” Batteries8 (2022), 10.3390/batteries8050043

2022 doi
[52]

Superab- sorption in an organic microcavity: Toward a quantum battery,

James Q. Quach, Kirsty E. McGhee, Lucia Ganzer, Dominic M. Rouse, Brendon W. Lovett, Erik M. Gauger, Jonathan Keeling, Giulio Cerullo, David G. Lidzey, and Tersilla Virgili, “Superab- sorption in an organic microcavity: Toward a quantum battery,” Sci. Adv. 8 (2022), 10.1126/sc...

2022 doi
[53]

Experimental investigation of a quantum battery using star-topology nmr spin systems,

Jitendra Joshi and T. S. Mahesh, “Experimental investigation of a quantum battery using star-topology nmr spin systems,” Phys. Rev. A 106, 042601 (2022)

2022
[54]

Uni- versal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering,

Marin Bukov, Luca D’Alessio, and Anatoli Polkovnikov, “Uni- versal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering,” Adv. Phys. (2015)

2015
[55]

High-frequency ap- proximation for periodically driven quantum systems from a Floquet-space perspective,

Andr ´e Eckardt and Egidijus Anisimovas, “High-frequency ap- proximation for periodically driven quantum systems from a Floquet-space perspective,” New J. Phys.17, 093039 (2015)

2015
[56]

Floquet States in Open Quantum Systems,

Takashi Mori, “Floquet States in Open Quantum Systems,” Annu. Rev. Condens. Matter Phys. , 35–56 (2023)

2023
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Floquet topological phase transitions in a periodically quenched dimer,

Milad Jangjan, Luis E. F. Foa Torres, and Mir Vahid Hos- seini, “Floquet topological phase transitions in a periodically quenched dimer,” Phys. Rev. B106, 224306 (2022)

2022
[58]

Prethermalization in periodically driven nonre- ciprocal many-body spin systems,

Adam J. McRoberts, Hongzheng Zhao, Roderich Moessner, and Marin Bukov, “Prethermalization in periodically driven nonre- ciprocal many-body spin systems,” Phys. Rev. Res. 5, 043008 (2023)

2023
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From quantum chaos to quantum thermalization,

Luca D’Alessio, Yonatan Kafri, Anatoli Polkovnikov, and Mar- cos Rigol, “From quantum chaos to quantum thermalization,” in AIP Conference Proceedings (AIP Publishing, 2016)

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Many- body physics with ultracold gases,

Immanuel Bloch, Jean Dalibard, and Wilhelm Zwerger, “Many- body physics with ultracold gases,” Rev. Mod. Phys. 80, 885– 964 (2008)

2008
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Realization of the hofstadter hamiltonian with ul- tracold atoms in optical lattices,

M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, “Realization of the hofstadter hamiltonian with ul- tracold atoms in optical lattices,” Phys. Rev. Lett. 111, 185301 (2013)

2013
[62]

Colloquium: Atomic quantum gases in peri- odically driven optical lattices,

Andr ´e Eckardt, “Colloquium: Atomic quantum gases in peri- odically driven optical lattices,” Rev. Mod. Phys. 89, 011004 (2017)

2017
[63]

Unified light-matter floquet theory and its application to quan- tum communication,

Georg Engelhardt, Sayan Choudhury, and W. Vincent Liu, “Unified light-matter floquet theory and its application to quan- tum communication,” Phys. Rev. Res.6, 013116 (2024)

2024
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Quantum computing Floquet energy spectra,

Benedikt Fauseweh and Jian-Xin Zhu, “Quantum computing Floquet energy spectra,” Quantum 7, 1063 (2023)

2023
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Floquet quantum thermal transistor,

Nikhil Gupt, Srijan Bhattacharyya, Bikash Das, Subhadeep Datta, Victor Mukherjee, and Arnab Ghosh, “Floquet quantum thermal transistor,” Phys. Rev. E106, 024110 (2022)

2022
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Performance limits of multilevel and multipartite quantum heat machines,

Wolfgang Niedenzu, David Gelbwaser-Klimovsky, and Ger- shon Kurizki, “Performance limits of multilevel and multipartite quantum heat machines,” Phys. Rev. E92, 042123 (2015)

2015
[68]

Cooperative many- body enhancement of quantum thermal machine power,

Wolfgang Niedenzu and Gershon Kurizki, “Cooperative many- body enhancement of quantum thermal machine power,” New J. Phys. 20, 113038 (2018)

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[69]

Periodically driven many-body quantum battery,

Saikat Mondal and Sourav Bhattacharjee, “Periodically driven many-body quantum battery,” Phys. Rev. E105, 044125 (2022)

2022
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Validity of many- body approximation methods for a solvable model: (i). exact solutions and perturbation theory,

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Single-qubit quantum memory exceeding ten-minute coher- 14 ence time,

Ye Wang, Mark Um, Junhua Zhang, Shuoming An, Ming Lyu, Jing-Ning Zhang, L.-M. Duan, Dahyun Yum, and Kihwan Kim, “Single-qubit quantum memory exceeding ten-minute coher- 14 ence time,” Nat. Photonics 11, 646–650 (2017)

2017
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Manipulation and detection of a trapped yb+ hyperfine qubit,

S. Olmschenk, K. C. Younge, D. L. Moehring, D. N. Matsuke- vich, P. Maunz, and C. Monroe, “Manipulation and detection of a trapped yb+ hyperfine qubit,” Phys. Rev. A76, 052314 (2007)

2007
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Riemann zeros from Floquet engineering a trapped-ion qubit,

Ran He, Ming-Zhong Ai, Jin-Ming Cui, Yun-Feng Huang, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo, G. Sierra, and C. E. Creffield, “Riemann zeros from Floquet engineering a trapped-ion qubit,” npj Quantum Inf. 7, 1–6 (2021)

2021
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Entan- glement entropy for the long-range ising chain in a transverse field,

Thomas Koffel, M. Lewenstein, and Luca Tagliacozzo, “Entan- glement entropy for the long-range ising chain in a transverse field,” Phys. Rev. Lett.109, 267203 (2012)

2012
[75]

Kitaev chains with long-range pair- ing,

Davide V odola, Luca Lepori, Elisa Ercolessi, Alexey V . Gor- shkov, and Guido Pupillo, “Kitaev chains with long-range pair- ing,” Phys. Rev. Lett.113, 156402 (2014)

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[76]

Nonclassical correlations in subsystems of globally entangled quantum states,

Chandan Mahto, Vijay Pathak, Ardra K. S., and Anil Shaji, “Nonclassical correlations in subsystems of globally entangled quantum states,” Phys. Rev. A106, 012427 (2022)

2022
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Better sensing with variable-range interactions,

Monika, Leela Ganesh Chandra Lakkaraju, Srijon Ghosh, and Aditi Sen De, “Better sensing with variable-range interactions,” (2023), arXiv:2307.06901 [quant-ph]

2023 arXiv
[78]

Entanglement of weighted graphs uncovering transitions in variable-range interacting models,

Debkanta Ghosh, Keshav Das Agarwal, Pritam Halder, and Aditi Sen(De), “Entanglement of weighted graphs uncovering transitions in variable-range interacting models,” Phys. Rev. A 110, 022431 (2024)

2024
[79]

Control- lable floquet topological phases in the magnetic ladder system,

Xu-Jin Wang, Lu Zhang, Liang Yan, and Jie-Yun Yan, “Control- lable floquet topological phases in the magnetic ladder system,” New Journal of Physics 26, 033016 (2024)

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Quasienergy band engineering and broadband dy- namic localization in photonic lattices with long-range interac- tion,

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En- tanglement dynamics in the lipkin-meshkov-glick model,

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Mimicking quantum correlation of a long-range hamiltonian by finite-range interactions,

Leela Ganesh Chandra Lakkaraju, Srijon Ghosh, Debasis Sad- hukhan, and Aditi Sen(De), “Mimicking quantum correlation of a long-range hamiltonian by finite-range interactions,” Phys. Rev. A 106, 052425 (2022)

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

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Floquet analysis of a superradiant many-qutrit refrigerator,

Dmytro Kolisnyk, Friedemann Queißer, Gernot Schaller, and Ralf Sch¨utzhold, “Floquet analysis of a superradiant many-qutrit refrigerator,” Phys. Rev. Appl.21, 044050 (2024)

work page 2024

[2] [1]

N N −2X i=0 (i + 2) k − 1 i ! + N 2 k−1X i=N −1 k − 1 i !# = N

Detailed proof of Theorem 1 Let us consider the aforementioned battery Hamiltonian HB charged using the Hch = HB + H LR int (Eq. (A1)). Following the results in ref. [9] |P (t)| ≤ NX k=1 k||Hch|| ||Hs − Esmin ||, |P (nT )| ≤ NX k=1 k||H F ch|| ||Hs − Esmin ||, (B2) 7 where H F ch is the time-independent Floquet Hamiltonian. In our case, ||Hs − Es) min|| i...

[3] [2]

We use two parameters to vary the range of interactions in order to analyze the characteristic response of power calculated for a normal- ized work

Response of power with variable range interactions For physical systems like ion traps [58, 67–69], the variable- range interactions appear naturally in the system. We use two parameters to vary the range of interactions in order to analyze the characteristic response of power calculated for a normal- ized work. (A) Power-law fall-off rate coefficient, α....

[4] [3]

Gain in power with NNN interacting charger We establish here that although short-range interaction can be beneficial to enhance the power of the QB, super- extensive scaling can only be attained with LR interactions. More precisely, we focus here on the trade-off relation be- tween nearest-neighbor and next-nearest neighbor interaction strengths present i...

[5] [4]

J1 X j (σy j σx j+1 + σx j σy j+1) + J2 X j (σy j σx j+2 + σx j σy j+2) # H F2 = − T 2 3 (1 − γ)hz

No benefit in scaling with NNN interactions To perform the scaling analysis analytically, we will derive the time-independent Floquet Hamiltonian for the charging by using Floquet-Magnus expansion (FME) [50, 81, 95]. Since the charging Hamiltonian is periodic in time, i.e., Hch(t) = Hch(t + T ), we invoke Floquet theory to study the dynam- ics of the quan...

[6] [5]

Entanglement boost for ex- tractable work from ensembles of quantum batteries,

Robert Alicki and Mark Fannes, “Entanglement boost for ex- tractable work from ensembles of quantum batteries,” Phys. Rev. E 87, 042123 (2013)

2013

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Quantum batteries,

Francesco Campaioli, Felix A. Pollock, and Sai Vinjanampa- thy, “Quantum batteries,” in Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions , edited by Felix Binder, Luis A. Correa, Christian Gogolin, Janet Anders, and Gerardo Adesso (Springer International Publishing, Cham,

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Colloquium: Quantum batteries,

Francesco Campaioli, Stefano Gherardini, James Q. Quach, Marco Polini, and Gian Marcello Andolina, “Colloquium: Quantum batteries,” Rev. Mod. Phys.96, 031001 (2024)

2024