Adiabatic charging of open quantum battery

B. Mojaveri; M. A. Fasihi; R. Haji Mohammadzadeh; R. Jafarzadeh Bahrbeig

REVIEW 2 major objections 5 minor 78 references

Adiabatic charging of open quantum battery

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A three-level quantum battery, open to a thermal bath, can be fully charged by choosing one optimal total charging time.

desk verdict Legitimate technical kernel, but as written the central charging result contradicts the paper's own pulse schedule and initial state. read the letter →

arxiv 2411.17854 v1 pith:W5XSTVGI submitted 2024-11-26 quant-ph

M. A. Fasihi , R. Jafarzadeh Bahrbeig , B. Mojaveri , R. Haji Mohammadzadeh This is my paper · ORCID

classification quant-ph

keywords quantumbatteryadiabaticchargingdarkstateopensystemsmasterequationergotropyoptimaltimethree-levelsystem

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 claims that a three-level quantum battery, weakly coupled to an Ohmic thermal bath and driven through a dark state, can be fully charged by choosing a finite optimal total charging time $t_f$. At that time the stored energy and the extractable work (ergotropy) both reach their maximum, and the charging efficiency reaches one. Shorter times fail because the evolution is too non-adiabatic; longer times waste energy through thermal excitations that drive the system toward the Gibbs state. The result matters because it shows that in an open setting the fastest reliable charge is not as slow as possible, but a problem-dependent sweet spot that can be tuned by Hamiltonian parameters and by the system-bath coupling strength.

What carries the argument

The central object is the dark state $|\varepsilon_2(s)\rangle = -B(s)/\Delta(s)|\lambda_1\rangle + A(s)/\Delta(s)|\lambda_3\rangle$ of the driven three-level system, together with the time-dependent Lindblad operators of the adiabatic master equation. The dark state acts as a decoherence-free population channel connecting the bare states as the drive amplitudes $A(s)=\omega_A(1-s)$ and $B(s)=\omega_B s$ are swept; the adiabatic master equation supplies the rates at which relaxation and dephasing drain that channel, and the $M(s)$ terms describe the effect of the rotating eigenbasis. The optimal time is where the population transferred through the dark state is maximal before thermal excitation pulls it toward the Gibbs state.

What would settle it

Re-run the master equation in Eq. (30) with the stated initial condition $\rho_{22}(0)=1$ and schedules $A(s)=\omega_A(1-s)$, $B(s)=\omega_B s$, and compute $\Delta E = \mathrm{Tr}(\rho_B(t_f)H_B) - \mathrm{Tr}(\rho_B(0)H_B)$ at $t_f=9.93$ with $\lambda_1=0$, $\lambda_2=\omega$, $\lambda_3=1.95\omega$. If the result is negative rather than $+1.95$, the full-charge claim as described does not hold; a simpler check is to evaluate the dark state at $s=0$ and $s=1$, which goes from $|\lambda_3\rangle$ to $|\lambda_1\rangle$ as written.

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Extended reading notes

Core claim

The paper's central claim is that adiabatic charging of an open three-level quantum battery is governed by a competition between adiabaticity and thermal relaxation, and that this competition produces an optimal total evolution time $t_f^{\mathrm{opt}}$. Working within the adiabatic quantum master equation in the weak-coupling limit, the authors initialize the system in the instantaneous dark state $|\varepsilon_2(s)\rangle$ and sweep the two drive amplitudes linearly. They find that the dark-state population, stored energy, and ergotropy peak at $t_f^{\mathrm{opt}}$ (e.g., 9.93 for $\omega_A=\omega_B=1$), giving a fully charged battery with stored energy $\Delta E = 1.95$, ergotropy $W = 1.95$, and efficiency $\eta = 1$, whereas much shorter or much longer times yield much lower performance. They also find that the optimal time decreases when the system-bath coupling strengthens and that lower environmental temperature improves the charging, with the system at the optimal time still far from its Gibbs state.

Load-bearing premise

The entire charging result rests on the direction of the dark-state sweep: the schedule and initial-state choice must transfer population from the empty battery level to the full one (or the energy bookkeeping must be the reverse of what is written), because if the equations are taken literally, the initial dark state sits on the full level and the final one on the empty level, so the reported positive stored energy would not follow.

Editorial extensions

If this is right

For an open three-level battery, there exists a finite optimal charging time; running the protocol much longer than the heuristic adiabatic time lowers stored energy, ergotropy, and efficiency.
At low temperature and optimal time, the battery can reach full charge with unit efficiency, meaning all stored energy can be extracted as work.
Strengthening the system-bath coupling shortens the optimal charging time, so environment-induced decoherence is not purely harmful in this protocol.
Choosing unequal drive amplitudes $\omega_A$ and $\omega_B$ changes the optimal time and generally lowers the maximum dark-state population, so symmetric driving is preferable for full charge.

Reading between the lines

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

If the direction-of-transfer issue in the stated schedules is resolved by relabelling empty and full levels, the same optimal-time trade-off should appear in other driven multi-level batteries modeled with time-dependent Lindblad operators, since it follows from the competition between adiabatic following and thermalization rather than from the specific three-level structure.
The trace-norm distance from the Gibbs state at $t_f^{\mathrm{opt}}$ could serve as a practical figure of merit for how far a charging protocol is from thermal equilibrium; the paper plots it but does not propose it as a control objective.
A testable extension is to measure stored energy versus total charging time in a superconducting transmon qutrit; the predicted peak at finite $t_f$ would distinguish this adiabatic-master-equation description from a closed-system STIRAP picture that rewards arbitrarily slow driving.

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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

Short version: the paper has a legitimate technical kernel—explicit time-dependent Lindblad operators for the three-level STIRAP Hamiltonian derived from the Albash adiabatic master equation (Eqs. 28 and 30)—and the calculation is self-contained, with no fitted parameters. But the central charging claim, full charge at t_f=9.93 with ΔE=W=1.95, contradicts the paper's own equations. The stated schedules A(s)=ω_A(1−s), B(s)=ω_B s put the initial dark state at |λ3⟩ (the full level) and the final dark state at |λ1⟩ (empty). Starting with ρ22(0)=1 and following the dark state therefore discharges the battery; the energy defined in Eq. (19) should be about −1.95, not +1.95. This is not a sign convention. The entire figure 6 depends on it. The fix is likely straightforward—reverse the pulses, or swap λ1 and λ3—but as submitted the headline result is unsupported.

What the paper does well: it is a direct, honest application of a known formalism to a concrete model. The new element relative to Santos et al. is that the Lindblad operators are time-dependent, which changes the noise-induced dynamics and is worth checking. The adiabatic condition calculation in Eqs. (23)–(25) is standard and looks right. The self-citations to the group's earlier work do not bother me; they do not prop up the central claim.

Soft spots beyond the sign error: Fig. 5's caption is identical to Fig. 4's but the text says Fig. 5 shows bath-strength dependence—this is confusing, and no code or data are given. The ergotropy formula in Eq. (21) has a typo (the |r_j λ_k|^2 should be |⟨r_j|λ_k⟩|^2, presumably), and the paper never shows the lab-frame density matrix used to compute stored energy, so a referee cannot quickly verify which convention the numerics actually used. These are minor compared with the main contradiction.

Who this is for: someone working on STIRAP-based quantum batteries or adiabatic master equations. The paper is not a breakthrough, but if the sign error is repaired it could be a reasonable incremental contribution.

Recommendation: I would send it to a referee who knows the Albash formalism—this is not a desk-reject crank file. But the referee should be told to check the pulse direction explicitly; as written, the manuscript should not be accepted. I would not cite it in its current form.

Referee Report

2 major / 5 minor

Summary. The manuscript studies adiabatic charging of a three-level quantum battery coupled to an Ohmic thermal bath, using the adiabatic master equation framework of Albash et al. It initializes the system in the instantaneous dark state of the driven qutrit and evolves with the linear schedules A(s)=ω_A(1−s), B(s)=ω_B s over a total time t_f. The paper reports an optimal total time t_f^opt≈9.93 at which the stored energy, ergotropy, and efficiency reach ΔE=1.95, W=1.95, and η=1, with smaller values for shorter and longer evolution times. It also studies the dependence of these quantities on temperature and on the Hamiltonian parameters ω_A, ω_B, and compares the evolved state with the thermal Gibbs state via the trace-norm distance.

Significance. If the main result were correct, it would be a useful addition to the quantum-battery literature, showing that in an open-system adiabatic protocol there is a nontrivial optimal charging time balancing adiabaticity against thermal excitations. The manuscript is self-contained and does not fit parameters to the target result; the analytic expressions are explicit, and the central issue is not a missing derivation or a circular fitting step. However, the central charging claim as written is internally inconsistent with the paper's own definitions and equations, so the reported positive stored energy at t_f=9.93 is not supported by the stated protocol.

major comments (2)

[§3–§4, Eq. (18) and paragraph after Eq. (26)] Equation (18) defines the dark state as |ε2(s)⟩ = −B(s)/Δ(s)|λ1⟩ + A(s)/Δ(s)|λ3⟩. With the schedule A(s)=ω_A(1−s), B(s)=ω_B s stated in Section 4, one obtains |ε2(0)⟩=|λ3⟩ and |ε2(1)⟩=−|λ1⟩. Section 3 states that |λ3⟩ is the full charged state and |λ1⟩ the empty charged state, and the text sets λ1=0, λ3=1.95ℏω. Therefore the initial condition ρ22(0)=1 prepares the battery in the fully charged state, and the stated dynamics transfers population from the full to the empty state. According to Eq. (19), the stored energy in the fully adiabatic case would be negative, not ΔE=+1.95 as reported in Fig. 6. This is a load-bearing error, not a cosmetic sign convention: the positive-charging result, the optimal-time curve, and the interpretations of Figs. 2–7 all depend on reversing either the schedule or the initial state, and the numerical results must be recomputed accordingly.
[§4.2, Figs. 2 and 3] The paper treats the final dark-state population ρ22(t_f) as the success probability of the charging protocol. With the stated schedule, however, the instantaneous dark state at the final time is −|λ1⟩, an eigenstate of the empty level. Hence the maximum of ρ22(t_f) near t_f=9.93 is a maximum of population in the empty state and cannot by itself be evidence of successful charging. This reinforces the contradiction identified above: even the intermediate metric used to define the optimal time is tied to the wrong final level.

minor comments (5)

[Eq. (21)] The ergotropy formula contains the expression |r_jλ_k|^2, which is not a standard notation; it should presumably be the transition probability |⟨r_j|λ_k⟩|^2.
[Fig. 5] The caption of Fig. 5 appears to be a duplicate of the caption of Fig. 4, while the text describes Fig. 5 as showing the dependence of the optimal evolution time on the bath strength; the caption should be corrected.
[References] Reference [77] is a duplicate of reference [44] and should be removed or replaced.
[Numerics] The numerical integration of Eq. (30) is not described (method, tolerances, discretization), and no code is provided; a short description would improve reproducibility.
[Throughout] There are several typographical errors, including "protocils", "charing time", "Gibss", and "eingenvectors", which should be corrected in a revision.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the central results are numerical outputs of the stated adiabatic master equation, not fitted parameters or restatements of inputs; the paper's self-citations are contextual and not load-bearing.

full rationale

The charging protocol fixes the Hamiltonian schedules A(s)=ω_A(1−s), B(s)=ω_B s, the initial dark-state population ρ22(0)=1, and the bare energies λ1=0, λ2=ℏω, λ3=1.95ℏω. The optimal time tf=9.93 is obtained by numerically maximizing the dark-state population obtained from Eq. (30); it is not a fitted parameter, and the stored energy, ergotropy, and efficiency in Figs. 6–7 are evaluated from the same master-equation density matrix through Eqs. (19)–(22). No step in this derivation reduces an output to an input by construction. The cited prior work by the same group (Refs. [18], [20], [21]) is used only to motivate alternative charging protocols and is not invoked to justify the adiabatic-master-equation derivation or the numerical results. There is, however, a serious internal inconsistency in the manuscript: with the stated schedules, Eq. (18) gives |ε2(0)⟩=|λ3⟩ (full) and |ε2(1)⟩=−|λ1⟩ (empty), so starting from ρ22(0)=1 and following the dark state would discharge the battery, whereas the paper reports ΔE=+1.95 and η=1 at tf=9.93. This is a correctness or sign-error issue rather than circularity, because the reported ΔE is not obtained by equating it with λ3−λ1; it is presented as a numerical output that contradicts the paper's own definitions. The absence of simulation code or a lab-frame density matrix makes it impossible to resolve the discrepancy from the manuscript, but that omission is a reproducibility concern, not a circular one.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new physical entities; it uses standard dark-state STIRAP and standard spin-1 system-bath couplings. The free parameters are all chosen by hand for the numerical demonstration, and the main axioms are the validity of the adiabatic master equation, the Ohmic bath model, and the specific pulse schedule.

free parameters (5)

ω_A = ω_B = 1 (pulse amplitudes) = 1 (dimensionless)
Chosen by hand; sets the energy scale and the adiabatic threshold, and determines t_f^opt.
ηg^2 (system-bath coupling strength) = 10^{-4}
Chosen by hand; controls the thermalization rate and the value of t_f^opt, as discussed near Fig. 5.
β (inverse temperature) = 1/2.6 (in GHz^{-1})
Chosen to represent the low-temperature regime where the paper claims full charging.
λ3 (full-level energy) = 1.95ℏω
Chosen by hand; sets the maximum stored energy and ergotropy values reported in Fig. 6.
ω_c (Ohmic cutoff) = 8π GHz
Chosen to satisfy ω_c ≫ 1/β; affects the spectral density but not the qualitative conclusions.

assumptions (4)

domain assumption Albash et al. adiabatic master equation (Eqs. 9-15) is valid in the weak-coupling, Born-Markov, rotating-wave, and adiabatic approximations.
All results are obtained from this equation; the paper cites [42] but does not re-derive or validate the regime conditions at the specific parameter values used.
domain assumption The bath is Ohmic with spectral density γ(ω)=2πηg^2 ω e^{-|ω|/ω_c}/(1-e^{-βω}) and KMS detailed balance.
Used in Eq. (26) and throughout Section 4; it is assumed rather than derived.
domain assumption The drive is resonant and the rotating-frame Hamiltonian is H=A|1><2|+B|2><3|+h.c. with the dark state |ε2> given in Eq. (18).
This is the model setup; the dark state identity is central to the charging protocol.
ad hoc to paper The linear interpolation A(s)=ω_A(1-s), B(s)=ω_B s is the physical charging schedule.
This schedule is chosen without experimental justification, and it is the schedule that makes the initial dark state the full level rather than the empty level, creating the direction inconsistency.

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Cite this review

Pith. "Pith review of Adiabatic charging of open quantum battery." pith.science (2026). https://pith.science/paper/W5XSTVGI

@misc{pith2026241117854,
  author       = {Pith},
  title        = {Pith review of: Adiabatic charging of open quantum battery},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W5XSTVGI}},
  note         = {Machine review of arXiv:2411.17854}
}

abstract

We revisit the adiabatic charging of a three-level QBs, using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling regime with an Ohmic thermal bath and investigate the effects of relaxation and dephasing on the charging process. We analyze the dependence of the stored energy, ergotropy as well as efficiency of QB on the total time of evolution $t_f$. We demonstrate that for very short charging time ($t_f$), where the evolution is highly non-adiabatic, the stored energy and ergotropy are very small. However, with increasing $t_f$ we show that there is an optimal charging time, $t_f^{opt}$, for maximum energy charging such that at low temperatures we could fully charge the battery and effectively extract the whole amount of energy from it. Note that, the optimal charging time could be decreased by adjusting strength of the coupling between system and environment and also appropriate choice of the Hamiltonian parameters which in turn speed up the charging process. On the other hand, we show that for very long charing time $t_f$ the charging energy, ergotropy and efficiency decrease due to thermal excitations. Furthermore to get more insights about the problem we investigate the distance between density matrix of system at optimal charging time $t_f^{opt}$ and the corresponding thermal state using one-norm distance.

Figures

Figures reproduced from arXiv: 2411.17854 by the authors.

**Figure 2.** (Color online) Final dark state population, [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** (Color online) The effect of ωA(B) on the optimal value of the evolution time. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: (Color online) Trace-norm distance between the ev [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

**Figure 5.** Figure 5: (Color online) Trace-norm distance between the ev [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: (Color online) Dynamics of stored energy [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

**Figure 7.** Figure 7: (Color online) Dynamics of stored energy, ergotro [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

78 extracted references · 72 canonical work pages

[1]

Vinjanampathy and J

S. Vinjanampathy and J. Anders, CONTEMP PHYS 57, 545 (201 6)

work page
[2]

Alicki and R

R. Alicki and R. Kosloﬀ, Introduction to quantum thermod ynamics: History and prospects, in Thermodynamics in the Quantum Regime (Spring er, 2018)

work page 2018
[3]

Deﬀner and S

S. Deﬀner and S. Campbell, Quantum Thermodynamics: An in troduction to the ther- modynamics of quantum information (Morgan and Claypool Pub lishers, 2019)

work page 2019
[4]

Alicki and M

R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013)

2013
[5]

G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giov annetti, and M. Polini, Phys. Rev. B 98, 205423 (2018)

work page 2018
[6]

Farina, G

D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giova nnetti, Charger-mediated energy transfer for quantum batteries: An open-system appr oach, Phys. Rev. B 99, 035421 (2019)

work page 2019
[7]

A. C. Santos, A. Saguia, and M. S. Sarandy, Phys. Rev. E 101 , 062114 (2020)

work page 2020
[8]

T. P. Le, J. Levinsen, K. Modi, M. M. Parish, and F. A. Pollo ck, Phys. Rev. A 97, 022106 (2018)

work page 2018

Show all 78 references

[9]

Zhang, T.-R

Y.-Y. Zhang, T.-R. Yang, L. Fu, and X. Wang, Phys. Rev. E 99 , 052106 (2019)

2019
[10]

Rossini, G

D. Rossini, G. M. Andolina, and M. Polini, Phys. Rev. B 10 0, 115142 (2019)

2019
[11]

F. H. Kamin, F. T. Tabesh, S. Salimi, and A. C. Santos, Phy s. Rev. E 102, 052109 (2020)

2020
[12]

Crescente, M

A. Crescente, M. Carrega, M. Sassetti, and D. Ferraro, P hys. Rev. B 102, 245407 (2020)

2020
[13]

J. Q. Quach and W. J. Munro, Using dark states to charge an d stabilize open quantum batteries, Phys. Rev. Appl. 14, 024092 (2020)

2020
[14]

F. T. Tabesh, F. H. Kamin, and S. Salimi, Phys. Rev. A 102, 052223 (2020)

2020
[15]

M. L. Song, L. J. Li, X. K. Song, L. Ye, and D. Wang, Phys. Re v. E 106, 054107 (2022). 21

2022
[16]

Morrone1, M

D. Morrone1, M. A. C. Rossi, A. Smirne, and M. G. Genoni, Q uantum Sci. Technol. 8, 035007 (2023)

2023
[17]

K. Xu, H. G. Li, H. J. Zhu, and W. M. Liu, Phys. Rev. E 109, 05 4132 (2024)

2024
[18]

Mojaveri, R

B. Mojaveri, R. Jafarzadeh Bahrbeig, and M. A. Fasihi, E xtracting ergotropy from nonequilibrium steady states of an XXZ spin-chain quantum b attery, Phys. Rev. A 109, 042619 (2024)

2024
[19]

Ghosh, T

S. Ghosh, T. Chanda, S. Mal, and A. Sen, Phys. Rev. A 104, 0 32207 (2021)

2021
[20]

Mojaveri, R

B. Mojaveri, R. Jafarzadeh Bahrbeig, and M. A. Fasihi, C harging a Quantum Battery Mediated by Parity-Deformed Fields, https://doi.org/10. 48550/arXiv.2405.11356

doi arXiv
[21]

Mojaveri, R

B. Mojaveri, R. Jafarzadeh Bahrbeig, M. A. Fasihi, and S . Babanzadeh, Enhancing the direct charging performance of an open quantum battery by ad justing its velocity, Sci. Rep. 13, 19827 (2023)

2023
[22]

M. T. Mitchison, J. Goold, and J. Prior, Charging a quant um battery with linear feedback control, Quantum 5, 500 (2021)

2021
[23]

Yao and X

Y. Yao and X. Q. Shao, Optimal charging of open spin-chai n quantum batteries via homodyne-based feedback control, Phys. Rev. E 106, 014138 ( 2022)

2022
[24]

Koshihara and K

K. Koshihara and K. Yuasa, Quantum ergotropy and quantu m feedback control, Phys. Rev. E 107, 064109 (2023)

2023
[25]

De Pasquale, K

A. De Pasquale, K. Yuasa, and V. Giovannetti, Phys. Rev. A 96, 012316 (2017)

2017
[26]

Gherardini, A

S. Gherardini, A. Smirne, M. M. Muller, and F. Caruso, Pr oceedings 12, 11 (2019)

2019
[27]

Gherardini, F

S. Gherardini, F. Campaioli, F. Caruso, and F. C. Binder , Stabilizing open quantum batteries by sequential measurements Phys. Rev. Research 2 , 013095 (2020)

2020
[28]

A. C. Santos, B. Cakmak, S. Campbell, and N. T. Zinner, St able adiabatic quantum batteries, Phys. Rev. E 100, 032107 (2019)

2019
[29]

M. O. Scully, S.-Y. Zhu, and A. Gavrielides, Phys. Rev. L ett. 62, 2813 (1989)

1989
[30]

Mompart and R

J. Mompart and R. Corbalan, J. Opt. B: Quantum Semiclass ical Opt. 2, R7 (2000)

2000
[31]

Gaubatz, P

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, J . Chem. Phys. 92, 5363 (1990)

1990
[32]

N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergman n, Rev. Mod. Phys. 89, 015006 (2017)

2017
[33]

B. W. Shore, Picturing stimulated Raman adiabatic pass age: a STIRAP tutorial, Adv. Opt. Photon 9, 563 (2017). 22

2017
[34]

J. Liu, D. Segal, and G. Hanna, Loss-free excitonic quan tum battery, J. Phys. Chem. C 123, 18303 (2019)

2019
[35]

C.-K. Hu, J. Qiu, P. JP. Souza, J. Yuan, Y. Zhou, L. Zhang, J. Chu, X. Pan, L. Hu, J. Li, Y. Xu, Y. Zhong, S. Liu, F. Yan, D. Tan, R. Bachelard, C. J . Villas-Boas, A. C. Santos, and D. Yu, Quantum Sci. Technol. 7, 045018, (2022)

2022
[36]

Zheng, W

R.-H. Zheng, W. Ning, Z.-B. Yang, Y. Xia, and S.-B. Zheng , New J. Phys. 24, 063031 (2022)

2022
[37]

Y. Y. Ge, X. M. Yu, W. Xin, Z. M. Wang, Y. Zhang, W. Zheng, S. X. Li, D. Lan, and Y. Yu, Appl. Phys. Lett. 123, 154002 (2023)

2023
[38]

Gemme, M

G. Gemme, M. Grossi, S. Vallecorsa, M. Sassetti, and D. F erraro, Phys. Rev. Research 6, 023091 (2024)

2024
[39]

Dou Phys

F.-M Yang and F.-Q. Dou Phys. Rev. A 109, 062432, (2024)

2024
[40]

F. Q. Dou, Y. J. Wang, and J. A. Sun, EPL (Europhysics Lett ers) 131, 43001 (2020)

2020
[41]

F. Q. Dou, Y. J. Wang, and J. A. Sun, Frontiers of Physics 1 7, 31503 (2022)

2022
[42]

Albash, S

T. Albash, S. Boixo, D. A. Lidar, and P. Zanardi, New J. of Phys. 14, 123016 (2012)

2012
[43]

T. Kato, J. Phys. Soc. Japan. 5, 435 (1950)

1950
[45]

M. H. S. Amin, Consistency of the adiabatic theorem, Phy s. Rev. Lett. 102, 220401 (2009)

2009
[46]

Steﬀen, W

M. Steﬀen, W. V. Dam, T. Hogg, G. Breyta, and I. Chuang, Ex perimental implemen- tation of an adiabatic quantum optimization algorithm, Phy s. Rev. Lett. 90, 067903 (2003)

2003
[47]

M. S. Sarandy and D. A. Lidar, Adiabatic quantum computa tion in open systems, Phys. Rev. Lett. 95, 250503 (2005)

2005
[48]

M. S. Sarandy and D. A. Lidar, Adiabatic approximation i n open quantum systems, Phys. Rev. A 71, 012331 (2005)

2005
[49]

Albash and D

T. Albash and D. A. Lidar, Decoherence in adiabatic quan tum computation, Phys. Rev. A 91, 062320 (2015)

2015
[50]

Born and V

M. Born and V. Fock, Z. Phys. 51, 165 (1928)

1928
[51]

Farhi, J

E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgre n, and D. Preda, Science 292, 472 (2001). 23

2001
[52]

M. W. Johnson et al, Nature. 473, 194 (2011)

2011
[53]

A. M. Childs, E. Farhi and J. Preskill, Phys. Rev. A 65, 01 2322 (2001)

2001
[54]

Teufel, Adiabatic Perturbation Theory in Quantum Dy namics, (Berlin: Springer, 2003)

S. Teufel, Adiabatic Perturbation Theory in Quantum Dy namics, (Berlin: Springer, 2003)

2003
[55]

M. S. Sarandy, and D. A. Lidar, Phys. Rev. A 71, 012331 (20 05)
[56]

Alicki, D

R. Alicki, D. A. Lidar and P. Zanardi, Phys. Rev. A 73, 052 311 (2006)

2006
[57]

Joye, Commun

A. Joye, Commun. Math. Phys. 275, 139, (2007)

2007
[58]

X. L. Huang, X. X. Yi, C. Wu, X. L. Feng, S. X. Yu, and C. H. Oh , Phys. Rev. A 78, 062114 (2008)

2008
[59]

M. H. S. Amin, C. J. S. Truncik, and D. V. A verin, Phys. Rev . A 80, 022303 (2009)

2009
[60]

Oreshkov, and J

O. Oreshkov, and J. Calsamiglia, Phys. Rev. Lett. 105, 0 50503 (2010)

2010
[61]

Salmilehto J, P

J. Salmilehto J, P. Solinas, J. Ankerhold and M. Mttonen , Phys. Rev. A 82, 06211 (2010)

2010
[62]

J. P. Marangos, J. Mod. Opt. 45, 471 (1998)

1998
[63]

Bergmann, H

K. Bergmann, H. Theuer, and B.W. Shore, Rev. Mod. Phys. 7 0, 1003 (1998)

1998
[64]

Demirplak and S

M. Demirplak and S. A. Rice, J. Phys. Chem. A 107, 9937-99 45 (2003)

2003
[65]

Fleischhauer, A

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. M od. Phys. 77, 633 (2005)

2005
[66]

Lindblad, Commun

G. Lindblad, Commun. Math. Phys. 48, 119 (1976)

1976
[67]

J. M. Martinis, S. Nam, J. Aumentado, K. M. Lang, and C. Ur bina, Phys. Rev. B 67, 094510 (2003)

2003
[68]

J. Li, G. S. Paraoanu, K. Cicak, F. Altomare, J. I. Park, R . W. Simmonds, M. A. Sillanpaar, and P. J. Hakonen, Phys. Rev. B 84, 104527 (2011)

2011
[69]

J. Li, M. A. Sillanpaar, G. S. Paraoanu, and P. J. Hakonen , J. Phys.: Conf. Ser. 400, 042039 (2012)

2012
[70]

A. E. Allahverdyan, R. Balian and T. M. Nieuwenhuizen, M aximal work extraction from ﬁnite quantum systems. Eur. Phys. Lett 67, 565 (2004)

2004
[71]

M. H. Devoret and R. J. Schoelkopf, Science 339, 1169 (20 13)
[72]

Wendin, Rep

G. Wendin, Rep. Prog. Phys. 80, 106001 (2017)

2017
[73]

X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, Phys. Rep. 718719, 1 (2017). 24

2017
[74]

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster , J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. A 76 , 042319 (2007)

2007
[75]

J. Q. You, X. Hu, S. Ashhab, and F. Nori, Phys. Rev. B 75, 14 0515(R) (2007)

2007
[76]

Barends, J

R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeﬀrey, Y. C hen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. OMalley, P. Roushan, J. Wenner, T. C. Whit e, A. N. Cleland, and J. M. Martinis, Phys. Rev. Lett. 111, 080502 (2013)

2013
[77]

D. A. Lidar, A. T. Rezakhani, and A. Hamma, Adiabatic app roximation with expo- nential accuracy for manybody systems and quantum computat ion, J. Math. Phys. 50, 102106 (2009)

2009
[78]

Bhatia, Graduate Texts in Mathematics vol 169 Matrix Analysis, (New York: Springer) (1997)

R. Bhatia, Graduate Texts in Mathematics vol 169 Matrix Analysis, (New York: Springer) (1997)

1997
[79]

A Lidar, P

D. A Lidar, P. Zanardi, and K. Khodjasteh, Phys. Rev. A 78 012308 (2008). 25

2008

Pith tools

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

[1] [1]

Vinjanampathy and J

S. Vinjanampathy and J. Anders, CONTEMP PHYS 57, 545 (201 6)

work page

[2] [2]

Alicki and R

R. Alicki and R. Kosloﬀ, Introduction to quantum thermod ynamics: History and prospects, in Thermodynamics in the Quantum Regime (Spring er, 2018)

work page 2018

[3] [3]

Deﬀner and S

S. Deﬀner and S. Campbell, Quantum Thermodynamics: An in troduction to the ther- modynamics of quantum information (Morgan and Claypool Pub lishers, 2019)

work page 2019

[4] [4]

Alicki and M

R. Alicki and M. Fannes, Phys. Rev. E 87, 042123 (2013)

2013

[5] [5]

G. M. Andolina, D. Farina, A. Mari, V. Pellegrini, V. Giov annetti, and M. Polini, Phys. Rev. B 98, 205423 (2018)

work page 2018

[6] [6]

Farina, G

D. Farina, G. M. Andolina, A. Mari, M. Polini, and V. Giova nnetti, Charger-mediated energy transfer for quantum batteries: An open-system appr oach, Phys. Rev. B 99, 035421 (2019)

work page 2019

[7] [7]

A. C. Santos, A. Saguia, and M. S. Sarandy, Phys. Rev. E 101 , 062114 (2020)

work page 2020

[8] [8]

T. P. Le, J. Levinsen, K. Modi, M. M. Parish, and F. A. Pollo ck, Phys. Rev. A 97, 022106 (2018)

work page 2018