Pith. sign in

REVIEW 3 major objections 5 minor 55 references

Thermal rectification in a qubit-resonator system

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A qubit-resonator junction reverses its preferred heat-flow direction as their coupling enters the ultrastrong regime.

desk verdict New physics in the QRM heat junction; the USC rectification sign-change is credible because analytical formulas back it, but the missing large-g truncation convergence needs to be supplied. read the letter →

arxiv 2507.10282 v1 pith:7SFESGN5 submitted 2025-07-14 quant-ph cond-mat.mes-hall

Luca Magazzù , Elisabetta Paladino , Jukka P. Pekola , Milena Grifoni This is my paper · ORCID
classification quant-phcond-mat.mes-hall
keywords thermalrectificationheatdiodequantumRabimodelultrastrongcouplingcircuitQEDRedfieldmasterequationsteady-statecoherencegeneralizedrotatingwaveapproximation
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

Growing the coupling between a superconducting flux qubit and a resonator, in a junction described by the quantum Rabi model, can flip the preferred direction of heat flow through the device. The paper computes heat current and thermal rectification for such a junction weakly coupled to two bosonic heat baths, using a Redfield master equation that keeps steady-state coherences where they matter. The central finding is that the rectification $R$ changes sign as the qubit-resonator coupling $g$ enters the ultrastrong regime: for zero qubit bias and detuning $\Delta$ below the resonator frequency $\omega_r$, $R$ is positive at weak coupling and negative at large $g$, with an analytical crossing point given by Eq. (22), while at resonance $R$ is always negative. In the nonlinear regime, the temperature-bias scaling of the current turns from super-linear to sub-linear as $g$ grows, and the rectification changes sign accordingly. These are testable signatures because circuit QED platforms already reach ultrastrong coupling strengths.

What carries the argument

The load-bearing object is the quantum Rabi junction—a flux qubit of frequency $\omega_q = \sqrt{\Delta^2 + \epsilon^2}$ coupled with strength $g$ to a resonator mode of frequency $\omega_r$, with the two sides coupled to separate bosonic baths through the operators $Q_L = a + a^\dagger$ and $Q_R = \sigma_z$. The transport calculations use a leading-order Redfield master equation that avoids the secular and Markovian approximations, together with a partial secular reduction that retains the coherences of the quasi-degenerate doublets. The analytical engine is the generalized rotating wave approximation (GRWA) applied to a two-level truncation of the Rabi model, which yields the rectification formula $R = \chi [n_L(\omega_{10}) - n_R(\omega_{10})]/[1 + n_R(\omega_{10}) + n_L(\omega_{10})]$ with asymmetry parameter $\chi = (|Q_{R01}|^2 - |Q_{L01}|^2)/(|Q_{R01}|^2 + |Q_{L01}|^2)$. Setting $\chi = 0$ gives the zero-rectification condition, whose approximate solution is Eq. (22); this condition is what pins the sign flip of $R$.

What would settle it

Sweep the qubit-resonator coupling $g$ in a galvanically coupled flux-qubit-resonator device with asymmetric couplings to two heat baths, at fixed temperatures $T$ and $\Delta T$ and zero qubit bias, and measure the rectification $R$ from the steady-state currents $I_+$ and $I_-$; if $R$ does not change sign near the coupling $g^*$ predicted by Eq. (22) for $\Delta < \omega_r$, the central claim fails. A non-perturbative numerical calculation at system-bath couplings beyond the Redfield regime that finds no sign inversion would likewise falsify the weak-coupling extrapolation.

Watch

Extended reading notes

Core claim

The paper claims that for a qubit-resonator junction described by the quantum Rabi model, weakly connected to two ohmic baths, the thermal rectification is not monotonic in the qubit-resonator coupling but changes sign when the coupling becomes ultrastrong. At zero qubit bias, for qubit splittings below resonance ($\Delta < \omega_r$), the forward current is larger in the direction where the hot bath sits on the resonator side at weak coupling ($R > 0$), but this preference inverts ($R < 0$) once $g$ is increased past a coupling $g^*$ that the paper approximates analytically in Eq. (22); at resonance the rectification is always negative. The sign change is traced to the dressed matrix elements of the system-bath coupling operators crossing $|Q_{L01}| = |Q_{R01}|$. In the nonlinear transport regime, the current's growth with temperature bias switches from super-linear to sub-linear as $g$ increases for off-resonant detunings, with the rectification turning from positive to negative correspondingly, while at resonance the scaled current always grows sub-linearly. The paper also shows that steady-state coherences, which become relevant when the bath coupling is comparable to the quasi-degenerate doublet splittings, suppress the current and enhance rectification, and proposes a galvanic flux-qubit implementation that could realize these regimes.

Load-bearing premise

The quantitative predictions rest on the assumption that the junction-bath coupling is weak enough for the leading-order Redfield equation (with partial secular coherences) to be accurate, so that the strong system-bath coupling regime, where this treatment loses quantitative validity, is not covered.

Editorial extensions

If this is right

  • The sign flip of $R$ at the coupling $g^*$ of Eq. (22) gives a transport signature of the transition from two weakly coupled subsystems (resonant sequential transport) to a single hybridized ultrastrongly coupled junction.
  • At resonance, $\Delta = \omega_r$, the rectification is always non-positive and the current scaled by the linear conductance grows sub-linearly with the temperature bias, independent of the qubit-resonator coupling.
  • Off resonance, increasing $g$ reverses the current's temperature-bias scaling from super-linear to sub-linear and flips $R$ from positive to negative; the magnitude of $R$ grows with the temperature bias in all regimes studied.
  • For quasi-degenerate doublets and finite system-bath coupling, steady-state coherences suppress the heat current and enhance rectification, so that $I_+/\alpha$ depends on $\alpha$ through the partial secular master equation.
  • A two-resonator galvanic circuit with strongly different resonator frequencies realizes the model and is proposed as an experimental platform for observing these effects.

Reading between the lines

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

  • If the sign inversion is confirmed experimentally, tuning $g$ in situ would let the same device operate as a heat diode with switchable preferred direction, which the paper itself does not explicitly propose as a control feature.
  • The zero-rectification coupling $g^*$ in Eq. (22) is temperature-independent within the two-level truncation; measuring how $g^*$ shifts with temperature would directly probe where the two-level description of the Rabi junction breaks down.
  • The coherence-induced current suppression suggests that tailoring quasi-degenerate level doublets could be a general strategy to enhance thermal rectification in other multi-level quantum junctions, an idea that extends beyond the specific Rabi model studied here.
  • The crossover from super-linear to sub-linear current scaling with temperature bias, tied to the sign of $R$, may offer a generic probe of whether a multi-component junction behaves as a sequential conductor or as a single hybridized body—an interpretation the paper motivates but does not elevate to a general criterion.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies steady-state heat transport through a flux-qubit-resonator junction modeled by the quantum Rabi Hamiltonian, with the junction weakly coupled to two bosonic ohmic baths at different temperatures. The authors compute heat current and rectification using a Redfield master equation in both full-secular and partial-secular versions, and they supplement the numerics with analytical TLS, GRWA, and Van Vleck perturbation-theory results. The central claims are that, at zero qubit bias, the rectification changes sign from positive to negative when the qubit-resonator coupling enters the ultrastrong-coupling regime for negative detuning, that the rectification is always negative at resonance, that in the nonlinear regime the temperature-bias scaling of the current crosses from superlinear to sublinear as the coupling increases, and that steady-state coherences suppress the current and enhance rectification. An experimental implementation based on a galvanically coupled flux qubit is proposed.

Significance. If the central claims hold, the paper identifies a new transport signature of the ultrastrong-coupling regime and provides analytic control over the zero-rectification condition, which is of direct interest for thermal-diode design. The manuscript has clear strengths: the Redfield formalism is standard and carefully presented, the partial-secular master equation is solved analytically for a three-level truncation, and the numerical results are cross-checked against Van Vleck perturbation theory and the RWA in appropriate limits. The main caveat is the lack of demonstrated truncation convergence for the numerical 'full Rabi model' results on which the sign-change claim rests.

major comments (3)
  1. [Secs. IV A-C, Figs. 3-6] The numerical curves labeled as results for the 'full Rabi model' never state the number of Rabi states retained, nor is a truncation-convergence test reported. This is load-bearing because the central claim of a sign change in R rests on the solid curves in Figs. 3-6, and the paper's own Appendix D (Fig. 10) shows that the rectification is qualitatively different between three-level and five-level truncations at g/omega_r = 0.01. The same risk applies at the larger couplings where the sign change occurs, since the relevant dressed states have multi-photon components and the matrix elements QL01 and QR01 that control the sign through Eq. (19) are basis dependent. Please specify the basis size for each figure and provide convergence tests of I+/alpha and R as a function of truncation level N, in particular at g/omega_r near 1 and along the zero-rectification contour in Fig. 4(b).
  2. [Sec. IV D, Figs. 7-8] The five-level truncation used in the PSME results is called 'converged,' but no convergence evidence is given. Since the coherence effects involve the second quasi-degenerate doublet (omega_43) and Appendix D shows that a three-level truncation fails qualitatively for the rectification, the assertion that five levels are sufficient needs support. Please report a systematic convergence check (e.g., 5LS versus 7LS versus 9LS) for the PSME results and state the convergence criterion used.
  3. [Eq. (22), Fig. 4] The zero-rectification condition g* in Eq. (22) is derived in a TLS truncation of the quantum Rabi model under the GRWA and under a 'small Delta/omega_r' approximation, and the paper itself notes that the TLS truncation is inappropriate at high temperatures. Yet Eq. (22) is used to draw the dashed zero-rectification contour in Fig. 4(b) over a broad range of detunings. Please state the quantitative validity region of Eq. (22) in the (Delta/g) plane and either restrict the contour to that region or demonstrate that the contour is insensitive to higher Rabi levels in the plotted range.
minor comments (5)
  1. [Sec. III] The definition of the Bohr frequencies reads 'omega_nm := omega_n - omega_n'; this should be omega_n - omega_m.
  2. [Sec. IV C] There are typos in the text: 'usinng the FSME' should be 'using the FSME,' and 'accordingly to what what was found in [10]' should read 'according to what was found in [10].'
  3. [Appendix D, Eq. (D5)] The symbol B1 is defined twice in Eq. (D5); the second definition should presumably be B2, which would be consistent with the expressions for rho_11 and rho_22.
  4. [Fig. 4(b)] The dashed line marking the zero-rectification condition would be easier to interpret if the figure caption stated that it is obtained from the approximate formula (22) and is therefore expected to be accurate only in a limited parameter range.
  5. [Sec. V] Reference [51] is cited as an arXiv preprint; if a published version is available, it should be cited instead or in addition.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the rectification sign change is computed from independent Redfield/GRWA evaluations, not from fitted or self-referential inputs.

full rationale

The paper's central derivation is self-contained. Transport currents and rectification are obtained from the Redfield equation (Eq. (9)) with transition rates computed from the quantum Rabi eigenstates, using GRWA, second-order Van Vleck perturbation theory, and numerical diagonalization, all of which are independent of the target rectification result. The analytical TLS formula, Eq. (18)-(20), is a re-derivation of the known spin-boson heat-rectifier expression in terms of the coupling matrix elements QL01 and QR01, and the zero-rectification condition g* is derived from |QL01| = |QR01| in Eq. (22), not fitted to the numerics; the numerics in Figs. 3-6 independently corroborate the analytical prediction. Self-citations [27,28] provide the Redfield kernel and prior conductance formalism, but the present heat-current and rectification results are computed from the equations stated in this paper, and the cited work is not invoked to forbid alternatives or to supply the sign-change conclusion. Appendix D's demonstration that 3LS truncation gives qualitatively different rectification than 5LS truncation is a numerical-convergence caveat, not a circularity: it does not mean any result reduces by definition to its input. Accordingly, no circular step meets the evidentiary bar of Eq. X = Eq. Y by construction or fitted parameter renamed as prediction.

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

No new particles, forces, or entities are introduced. The free parameters are standard model parameters and bath parameters. The main burden is the perturbative master equation treatment and the spectral approximations, which are standard but not fully validated beyond leading order.

free parameters (4)
  • qubit-oscillator coupling g = 0.01 to 1.0 omega_r in figures
    Control parameter varied across the weak to USC regimes; not fitted, but the central qualitative results depend on its value.
  • detuning Delta/omega_r and bias epsilon/omega_r = 0.4 to 2.5 and -2 to 2
    Control parameters swept in figures.
  • bath coupling alpha = 0.1 to 5 x 10^-3 in coherence figures; otherwise small
    Chosen to be in the weak-coupling regime; the PSME results depend on it, and it is not fixed by any experimental value here.
  • bath cutoff omega_c = 5 omega_r
    Fixed ad hoc for numerics, not derived from a specific experimental realization.
assumptions (5)
  • domain assumption Born-Markov and weak junction-bath coupling for the Redfield equation, Eq. (9).
    The central transport results assume leading order in the junction-bath coupling; the paper explicitly states this and uses FSME/PSME consistently.
  • domain assumption Caldeira-Leggett form of the baths with ohmic-Drude spectral density G(omega) = alpha omega/(1+(omega/omega_c)^2).
    The model choice for the environment; the qualitative results, especially the sign changes, are not shown to be independent of the bath spectral form.
  • domain assumption Bath-induced renormalization included as mu_l Q_l^2; assumed small or absorbed.
    The paper handles this term, but some analytical results in Appendix D neglect it, and the comparison shows it matters at finite alpha.
  • ad hoc to paper GRWA spectrum, Eq. (2), is valid for Delta < omega_r and perturbative in the renormalized qubit gap.
    The analytical formulas and g* use the GRWA; the paper notes this approximation is not valid at high temperatures for the TLS truncation.
  • domain assumption Truncation of the Rabi model to 4 or 5 levels is converged for the computed currents.
    The 3LS truncation is explicitly shown to be insufficient, and 5LS is used; convergence to higher levels is not demonstrated.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Thermal rectification in a qubit-resonator system." pith.science (2026). https://pith.science/paper/7SFESGN5

@misc{pith2026250710282,
  author       = {Pith},
  title        = {Pith review of: Thermal rectification in a qubit-resonator system},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7SFESGN5}},
  note         = {Machine review of arXiv:2507.10282}
}
read the original abstract

A qubit-oscillator junction connecting as a series two bosonic heat baths at different temperatures can display heat valve and diode effects. In particular, the rectification can change in magnitude and even in sign, implying an inversion of the preferential direction for the heat current with respect to the temperature bias. We perform a systematic study of these effects in a circuit QED model of qubit-oscillator system and find that the features of current and rectification crucially depend on the qubit-oscillator coupling. While at small coupling, transport occurs via a resonant mechanism between the sub-systems, in the ultrastrong coupling regime the junction is a unique, highly hybridized system and the current becomes largely insensitive to the detuning. Correspondingly, the rectification undergoes a change of sign. In the nonlinear transport regime, the coupling strength determines whether the current scales sub- or super-linearly with the temperature bias and whether the rectification, which increases in magnitude with the bias, is positive or negative. We also find that steady-state coherence largely suppresses the current and enhances rectification. An insight on these behaviors with respect to changes in the system parameters is provided by analytical approximate formulas.

Figures

Figures reproduced from arXiv: 2507.10282 by the authors.

Figure 1
Figure 1. FIG. 1. Heat transport setup. The system is formed [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Excitation spectrum of the quantum Rabi [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Ultrastrong coupling effects in transport at [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Transition to negative rectification at zero [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Signatures of transition to the USC regime by tuning the bias. Heat current and rectification [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Superlinear to sublinear turnover in the current and change of sign of rectification. Current, scaled [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Effects of coherence at zero bias. Heat current [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Schematic of the experimental implementa [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Forward current and rectification vs. ∆ at zero qubit bias. Dashed lines: Three-level-system (3LS) [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

55 extracted references · 53 canonical work pages

  1. [1]

    Thermal rectification in clas- sical and quantum systems: Searching for efficient thermal diodes(a),

    Emmanuel Pereira, “Thermal rectification in clas- sical and quantum systems: Searching for efficient thermal diodes(a),” EPL 126, 14001 (2019)

    work page 2019

  2. [2]

    Dy- namics of the dissipative two-state system,

    A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, “Dy- namics of the dissipative two-state system,” Rev. Mod. Phys. 59, 1–85 (1987)

    work page 1987

  3. [3]

    Spin-Boson thermal rec- tifier,

    D. Segal and A. Nitzan, “Spin-Boson thermal rec- tifier,” Phys. Rev. Lett. 94, 034301 (2005)

    work page 2005

  4. [4]

    Heat flow in nonlinear molecular junc- tions: Master equation analysis,

    D. Segal, “Heat flow in nonlinear molecular junc- tions: Master equation analysis,” Phys. Rev. B 73, 205415 (2006)

    work page 2006

  5. [5]

    Heat transport and rectification via quantum sta- tistical and coherence asymmetries,

    Stephania Palafox, Ricardo Rom´ an-Ancheyta, Barı ¸ s C ¸ akmak, and¨Ozg¨ ur E. M¨ ustecaplıo˘ glu, “Heat transport and rectification via quantum sta- tistical and coherence asymmetries,” Phys. Rev. E 106, 054114 (2022)

    work page 2022

  6. [6]

    Dark-state-induced heat rectification,

    K. Poulsen and N. T. Zinner, “Dark-state-induced heat rectification,” Phys. Rev. E 106, 034116 (2022)

    work page 2022

  7. [7]

    Thermal rectification through a nonlinear quantum resonator,

    B. Bhandari, P. A. Erdman, R. Fazio, E. Paladino, and F. Taddei, “Thermal rectification through a nonlinear quantum resonator,” Phys. Rev. B 103, 155434 (2021)

    work page 2021

  8. [8]

    Rectification of heat currents across nonlinear quantum chains: a versatile ap- proach beyond weak thermal contact,

    T. Motz, M. Wiedmann, J. T. Stockburger, and J. Ankerhold, “Rectification of heat currents across nonlinear quantum chains: a versatile ap- proach beyond weak thermal contact,” New J. Phys. 20, 113020 (2018)

    work page 2018

Show all 55 references
  1. [9]

    Photonic heat rectification in a system of coupled qubits,

    A. Iorio, E. Strambini, G. Haack, M. Campisi, and F. Giazotto, “Photonic heat rectification in a system of coupled qubits,” Phys. Rev. Appl. 15, 054050 (2021)

    2021

  2. [10]

    Quantum heat valve 19 and diode of strongly coupled defects in amor- phous material,

    Yu-qiang Liu, Yi-jia Yang, Ting-ting Ma, Zheng Liu, and Chang-shui Yu, “Quantum heat valve 19 and diode of strongly coupled defects in amor- phous material,” Phys. Rev. E109, 014137 (2024)

    2024

  3. [11]

    Circuit quantum electrodynamics,

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, “Circuit quantum electrodynamics,” Rev. Mod. Phys. 93, 025005 (2021)

    2021

  4. [12]

    Colloquium: Quan- tum heat transport in condensed matter systems,

    J. P. Pekola and B. Karimi, “Colloquium: Quan- tum heat transport in condensed matter systems,” Rev. Mod. Phys. 93, 041001 (2021)

    2021

  5. [13]

    Mesoscopic photon heat transistor,

    T. Ojanen and A.-P. Jauho, “Mesoscopic photon heat transistor,” Phys. Rev. Lett. 100, 155902 (2008)

    2008

  6. [14]

    Tun- able photonic heat transport in a quantum heat valve,

    A. Ronzani, B. Karimi, J. Senior, Y.-C. Chang, J. T. Peltonen, C. Chen, and J. P. Pekola, “Tun- able photonic heat transport in a quantum heat valve,” Nat. Phys. 14, 991–995 (2018)

    2018

  7. [15]

    Ther- mal rectification in nonlinear quantum circuits,

    T. Ruokola, T. Ojanen, and A.-P. Jauho, “Ther- mal rectification in nonlinear quantum circuits,” Phys. Rev. B 79, 144306 (2009)

    2009

  8. [16]

    Coupled qubits as a quantum heat switch,

    B Karimi, J P Pekola, M Campisi, and R Fazio, “Coupled qubits as a quantum heat switch,” Quantum Sci. Technol. 2, 044007 (2017)

    2017

  9. [17]

    Photonic heat transport across a josephson junction,

    George Thomas, Jukka P. Pekola, and Dmitry S. Golubev, “Photonic heat transport across a josephson junction,” Phys. Rev. B 100, 094508 (2019)

    2019

  10. [18]

    The qutrit as a heat diode and circulator,

    Israel D ´ ıaz and Rafael S´ anchez, “The qutrit as a heat diode and circulator,” New J. Phys. 23, 125006 (2021)

    2021

  11. [19]

    Heat rec- tification via a superconducting artificial atom,

    J. Senior, A. Gubaydullin, B. Karimi, J. T. Pelto- nen, J. Ankerhold, and J. P. Pekola, “Heat rec- tification via a superconducting artificial atom,” Commun. Phys. 3, 40 (2020)

    2020

  12. [20]

    Microwave quantum diode,

    R. Upadhyay, D. S. Golubev, Y-C. Chang, G. Thomas, A. Guthrie, J. T. Peltonen, and J. P. Pekola, “Microwave quantum diode,” Nat. Com- mun. 15, 630 (2024)

    2024

  13. [21]

    Tuning nonequi- librium heat current and two-photon statistics via composite qubit-resonator interaction,

    Ze-Huan Chen, Han-Xin Che, Zhe-Kai Chen, Chen Wang, and Jie Ren, “Tuning nonequi- librium heat current and two-photon statistics via composite qubit-resonator interaction,” Phys. Rev. Research 4, 013152 (2022)

    2022

  14. [22]

    Quantum heat diode versus light emission in circuit quantum electrodynamical system,

    Yu-qiang Liu, Yi-jia Yang, and Chang-shui Yu, “Quantum heat diode versus light emission in circuit quantum electrodynamical system,” Phys. Rev. E 107, 044121 (2023)

    2023

  15. [23]

    Superconducting qubit- oscillator circuit beyond the ultrastrong-coupling regime,

    F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, “Superconducting qubit- oscillator circuit beyond the ultrastrong-coupling regime,” Nat. Phys. 13, 44 (2016)

    2016

  16. [24]

    Ultrastrong coupling regimes of light- matter interaction,

    P. Forn-D ´ ıaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light- matter interaction,” Rev. Mod. Phys. 91, 025005 (2019)

    2019

  17. [25]

    Ultrastrong coupling between light and matter,

    F. A. Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, “Ultrastrong coupling between light and matter,” Nat. Rev. Phys. 1, 19– 40 (2019)

    2019

  18. [26]

    Detecting virtual pho- tons in ultrastrongly coupled superconducting quantum circuits,

    L. Giannelli, E. Paladino, M. Grajcar, G. S. Paraoanu, and G. Falci, “Detecting virtual pho- tons in ultrastrongly coupled superconducting quantum circuits,” Phys. Rev. Res. 6, 013008 (2024)

    2024

  19. [27]

    Uni- fied diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model,

    L. Magazz` u, E. Paladino, and M. Grifoni, “Uni- fied diagrammatic approach to quantum transport in few-level junctions for bosonic and fermionic reservoirs: Application to the quantum Rabi model,” Phys. Rev. B 110, 085419 (2024)

    2024

  20. [28]

    Heat transport in the quantum Rabi model: univer- sality and ultrastrong coupling effects,

    L. Magazz` u, E. Paladino, and M. Grifoni, “Heat transport in the quantum Rabi model: univer- sality and ultrastrong coupling effects,” Quantum Sci. Technol. 10, 025013 (2025)

    2025

  21. [29]

    Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultra- strong Coupling Regime,

    P. Forn-D ´ ıaz, J. Lisenfeld, D. Marcos, J. J. Garc ´ ıa- Ripoll, E. Solano, C. J. P. M. Harmans, and J. E. Mooij, “Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultra- strong Coupling Regime,” Phys. Rev. Lett. 105, 237001 (2010)

    2010

  22. [30]

    The Jaynes- Cummings Model,

    B. W. Shore and P. L. Knight, “The Jaynes- Cummings Model,” J. Mod. Opt. 40, 1195–1238 (1993)

    1993

  23. [31]

    Integrability of the Rabi model,

    D. Braak, “Integrability of the Rabi model,” Phys. Rev. Lett. 107, 100401 (2011)

    2011

  24. [32]

    Generalized rotating- Wave approximation for arbitrarily large cou- pling,

    E. K. Twyeffort Irish, “Generalized rotating- Wave approximation for arbitrarily large cou- pling,” Phys. Rev. Lett. 99, 173601 (2007)

    2007

  25. [33]

    Qubit-oscillator systems in the ultrastrong-coupling regime and their po- tential for preparing nonclassical states,

    S. Ashhab and F. Nori, “Qubit-oscillator systems in the ultrastrong-coupling regime and their po- tential for preparing nonclassical states,” Phys. Rev. A 81, 042311 (2010)

    2010

  26. [34]

    Dissipative dynam- ics of a biased qubit coupled to a harmonic oscil- lator: analytical results beyond the rotating wave approximation,

    J. Hausinger and M. Grifoni, “Dissipative dynam- ics of a biased qubit coupled to a harmonic oscil- lator: analytical results beyond the rotating wave approximation,” New J. Phys. 10, 115015 (2008)

    2008

  27. [35]

    Qubit-oscillator system: An analytical treatment of the ultra- strong coupling regime,

    J. Hausinger and M. Grifoni, “Qubit-oscillator system: An analytical treatment of the ultra- strong coupling regime,” Phys. Rev. A 82, 062320 (2010)

    2010

  28. [36]

    Theoretical methods for ultrastrong light–matter interactions,

    A. Le Boit´ e, “Theoretical methods for ultrastrong light–matter interactions,” Adv. Quantum Tech- nol. 3, 1900140 (2020)

    2020

  29. [37]

    Analytical solution of the open dis- persive Jaynes-Cummings model and perturba- tive analytical solution of the open quantum Rabi model,

    A. Vaaranta, M. Cattaneo, and P. Muratore- Ginanneschi, “Analytical solution of the open dis- persive Jaynes-Cummings model and perturba- tive analytical solution of the open quantum Rabi model,” arXiv:2411.18310 (2025)

    2025 arXiv

  30. [38]

    General- ized rotating-wave approximation to biased qubit- oscillator systems,

    Y. Y. Zhang, Q. H. Chen, and Y. Zhao, “General- ized rotating-wave approximation to biased qubit- oscillator systems,” Phys. Rev. A 87, 033827 (2013)

    2013

  31. [39]

    Influence of dissipation on quantum tunneling in macroscopic systems,

    A. O. Caldeira and A. J. Leggett, “Influence of dissipation on quantum tunneling in macroscopic systems,” Phys. Rev. Lett. 46, 211–214 (1981). 20

    1981

  32. [40]

    Quantum tun- nelling in a dissipative system,

    A. O Caldeira and A. J Leggett, “Quantum tun- nelling in a dissipative system,” Ann. Phys. 149, 374–456 (1983)

    1983

  33. [41]

    Heat rectification in molecular junctions,

    D. Segal and A. Nitzan, “Heat rectification in molecular junctions,” J. Chem. Phys. 122, 194704 (2005)

    2005

  34. [42]

    Heat rectifica- tion through single and coupled quantum dots,

    L. Tesser, B. Bhandari, P. A. Erdman, E. Pal- adino, R. Fazio, and F. Taddei, “Heat rectifica- tion through single and coupled quantum dots,” New J. Phys. 24, 035001 (2022)

    2022

  35. [43]

    Characterizing the performance of heat rectifiers,

    S. Khandelwal, M. Perarnau-Llobet, S. Seah, N. Brunner, and G. Haack, “Characterizing the performance of heat rectifiers,” Phys. Rev. Res. 5, 013129 (2023)

    2023

  36. [44]

    Steady-state thermal transport in anhar- monic systems: Application to molecular junc- tions,

    J. Thingna, J. L. Garc ´ ıa-Palacios, and J.-S. Wang, “Steady-state thermal transport in anhar- monic systems: Application to molecular junc- tions,” Phys. Rev. B 85, 195452 (2012)

    2012

  37. [45]

    Ac- curacy assessment of perturbative master equa- tions: Embracing nonpositivity,

    Richard Hartmann and Walter T. Strunz, “Ac- curacy assessment of perturbative master equa- tions: Embracing nonpositivity,” Phys. Rev. A 101, 012103 (2020)

    2020

  38. [46]

    Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approxima- tion,

    M. Cattaneo, G. L. Giorgi, S. Maniscalco, and R. Zambrini, “Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approxima- tion,” New J. Phys. 21, 113045 (2019)

    2019

  39. [47]

    Unified Gorini-Kossakowski- Lindblad-Sudarshan quantum master equation be- yond the secular approximation,

    A. Trushechkin, “Unified Gorini-Kossakowski- Lindblad-Sudarshan quantum master equation be- yond the secular approximation,” Phys. Rev. A 103, 062226 (2021)

    2021

  40. [48]

    Quantum coherence-control of thermal energy transport: the V model as a case study,

    F. Ivander, N. Anto-Sztrikacs, and D. Segal, “Quantum coherence-control of thermal energy transport: the V model as a case study,” New J. Phys. 24, 103010 (2022)

    2022

  41. [49]

    Quasidegenerate perturbation theories. A canonical van Vleck for- malism and its relationship to other approaches,

    I. Shavitt and L. T. Redmon, “Quasidegenerate perturbation theories. A canonical van Vleck for- malism and its relationship to other approaches,” J. Chem. Phys. 73, 5711–5717 (1980)

    1980

  42. [50]

    Thermal rectification and heat amplification in a nonequi- librium V-type three-level system,

    C. Wang, D. Xu, H. Liu, and X. Gao, “Thermal rectification and heat amplification in a nonequi- librium V-type three-level system,” Phys. Rev. E 99, 042102 (2019)

    2019

  43. [51]

    Strong-coupling quantum thermodynamics using a superconducting flux qubit,

    R. Upadhyay, B. Karimi, D. Subero, C. D. Satrya, J. Peltonen, T.Yu-Cheng Chang, and J. P. Pekola, “Strong-coupling quantum thermodynamics using a superconducting flux qubit,” arXiv:2411.10774 (2025)

    2025

  44. [52]

    Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong- Coupling Regime,

    F. Yoshihara, T. Fuse, Z. Ao, S. Ashhab, K. Kakuyanagi, S. Saito, T. Aoki, K. Koshino, and K. Semba, “Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong- Coupling Regime,” Phys. Rev. Lett. 120, 183601 (2018)

    2018

  45. [53]

    Effect of friction on electron transfer in biomolecules,

    A. Garg, J. N. Onuchic, and V. Ambe- gaokar, “Effect of friction on electron transfer in biomolecules,” J. Chem. Phys. 83, 4491–4503 (1985)

    1985

  46. [54]

    Compari- son of quantum and semiclassical radiation theo- ries with application to the beam maser,

    E. T. Jaynes and F. W. Cummings, “Compari- son of quantum and semiclassical radiation theo- ries with application to the beam maser,” IEEE Proc 51, 89–109 (1963)

    1963

  47. [55]

    Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2012, 4th ed.)

    U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 2012, 4th ed.)

    2012

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.