Pith. sign in

REVIEW 3 major objections 4 minor 71 references

Non-Markovian dynamics of the giant atom beyond the rotating-wave approximation

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read The paper establishes that HEOM simulations with an ESPRIT-based bath fit are numerically exact for giant-atom dynamics beyond the rotating-wave and weak-coupling approximations, and that at strong coupling and zero temperature a long-lived

desk verdict Solid HEOM-ESPRIT methods paper, but the two-contact bound-state claim needs a single-contact control and N_c convergence before it can be taken seriously. read the letter →

arxiv 2601.03383 v2 pith:3IAFFXOV submitted 2026-01-06 quant-ph

Mei Yu , Walter T. Strunz , Stefan Nimmrichter This is my paper · ORCID
classification quant-ph
keywords giantatomnon-MarkoviandynamicshierarchicalequationsofmotionESPRITbathcorrelationfunctionrotating-waveapproximationboundstatesinthecontinuumopenquantumsystems
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

The paper establishes that combining the hierarchical equations of motion with an ESPRIT-based exponential decomposition of the bath correlation function gives numerically exact reduced dynamics for a two-level giant atom in a one-dimensional acoustic waveguide, valid beyond the rotating-wave approximation, at finite temperature, and at strong coupling. In the weak-coupling zero-temperature limit the simulation matches the exact single-excitation analytical solution, while the standard second-order perturbative master equation fails as soon as the propagation delay between the two coupling points becomes comparable to the atomic relaxation time. At finite temperature, the non-Markovian revivals in population and coherence survive thermal noise. The paper's central new physical claim is that at zero temperature and sufficient coupling, a long-lived atom-phonon bound state forms with only two contacts, trapping population and residual coherence. If correct, this provides a reliable non-perturbative toolbox for giant-atom physics and a concrete route to protecting quantum coherence in waveguide platforms.

What carries the argument

The load-bearing mechanism is the pairing of HEOM with an ESPRIT-based fit of the bath correlation function (BCF). HEOM converts the Gaussian bath influence functional into a hierarchy of coupled auxiliary density operators; the hierarchy is exact only if the real and imaginary parts of the BCF are represented as sums of exponentials. The paper's optimized ESPRIT routine samples the BCF in the time domain, forms a Hankel matrix, uses an SVD to estimate the number of exponentials, and iteratively prunes the set until the L2 relative error falls below 10^-3. For the linear low-frequency spectral density of the waveguide, the BCF has sharp peaks at t=0 and t=τ with flat regions between, a struc

What would settle it

Run the strong-coupling zero-temperature giant-atom simulation (e.g., dimensionless coupling η=5×10^-2, spectral cutoff ω_c=2ω0, delay ω0τ/2π=20) with hierarchy depths N_c=3 and N_c=4 and watch the long-time excited-state population and coherence. If the residual plateau shrinks or disappears as N_c increases, the two-contact bound-state claim would be falsified; if it persists, the claim is supported.

Watch

Extended reading notes

Core claim

The central claim is that HEOM, fed with an optimized ESPRIT exponential fit of the bath correlation function, captures the exact dynamics of a giant atom in regimes where rotating-wave and weak-coupling assumptions break down. At zero temperature and weak coupling, the HEOM result agrees with the exact single-excitation analytical solution, whereas a second-order perturbative master equation shows clear deviations once the delay-induced memory time becomes long. Beyond the weak-coupling limit, the simulations show that non-Markovian features become more pronounced as the system-bath coupling grows, and at zero temperature the atom retains a long-lived excited-state population and coherence.

Load-bearing premise

Numerical exactness rests on truncating the HEOM hierarchy at depth N_c=2 and on the ESPRIT fit's L2 tolerance of 10^-3, with no reported convergence study over N_c in the strong-coupling or finite-temperature regimes; if N_c=2 is insufficient there, the predicted two-contact bound state could be a numerical artifact.

Editorial extensions

If this is right

  • Second-order perturbative master equations are inadequate for giant atoms once the delay τ approaches the atomic relaxation time, so HEOM-type simulations become the reference tool for benchmarking approximate non-Markovian methods.
  • Non-Markovian excitation and coherence revivals persist at finite temperature, meaning the memory effect is not a zero-temperature artifact and can be studied in realistic thermal environments.
  • Stronger system-bath coupling enhances the revivals and leads to population trapping and long-lived coherence at zero temperature, implying a two-contact bound-state branch in the continuum.
  • The stationary state at strong coupling differs from the bare thermal state, with the difference consistent with a second-order mean-force Hamiltonian, so standard Gibbs-state thermalization predictions fail in this regime.

Reading between the lines

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

  • If the two-contact bound state is real, it gives a minimal geometric setup for protecting a qubit against decay using only two spatial coupling points, which could simplify experimental implementations in surface-acoustic-wave or circuit-QED platforms.
  • The ESPRIT exponential-fitting strategy is likely transferable to other structured environments with multiple delayed-feedback peaks, such as multi-contact giant atoms or photonic-crystal waveguides, where conventional spectral decompositions struggle.
  • Because the paper reports no hierarchy-depth convergence study in the strong-coupling regime, the bound-state claim should be re-checked at N_c=3 and above; until then, the residual coherence is a prediction pending convergence verification, not a settled fact.
  • The observed ratio C(0)/C(τ)≈2 for large delay, extracted from the BCF line shapes, could serve as a simple experimental probe of the memory time in the noise spectrum of a giant-atom device.
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 / 4 minor

Summary. The manuscript studies a two-level giant atom coupled to a one-dimensional surface-acoustic-waveguide bath beyond the rotating-wave and weak-coupling approximations. The authors use HEOM with an ESPRIT-based exponential decomposition of the bath correlation function, benchmark the method at zero temperature and weak coupling against an independent RWA single-excitation analytical solution, demonstrate that Redfield theory fails in the delay-memory regime, and then extend the simulations to finite temperature and stronger coupling. The central new physical claim is that at stronger coupling a long-lived atom-phonon bound state can form with only two contact points, inferred from a residual excited-state population and coherence at zero temperature.

Significance. The weak-coupling zero-temperature benchmark is convincing: the HEOM-ESPRIT results agree with an independent analytical RWA solution, and the demonstrated failure of Redfield theory in the delay-memory regime is a useful cautionary result. The finite-temperature robustness of non-Markovian revivals is also a meaningful extension. However, the headline claim of a two-contact bound state at stronger coupling is not presently supported by the evidence: no hierarchy-depth convergence is reported, no single-contact control is shown, and the residual zero-temperature coherence can be explained by ordinary counter-rotating vacuum dressing. The methodological contribution is potentially valuable, but the strong-coupling bound-state claim needs substantial additional evidence.

major comments (3)
  1. [§VI, Fig. 5(b,d), Table I] The claim of a long-lived two-contact bound state is not distinguished from ordinary counter-rotating vacuum dressing. At η=5×10^-2, P_ee≈0.009 is of the order (g/ω0)^2 expected from the RWA-breaking dressing of the ground state. No τ=0 (single-contact) simulation at η=5×10^-2 is shown, so the two-contact interference cannot be isolated. The RWA benchmark of §V removes counter-rotating terms and therefore cannot validate a zero-temperature residual. The second-order mean-force Hamiltonian in App. C is diagonal and gives P*_ee=0 at β→∞, so it provides no support. Please add a single-contact control at the same coupling, a spectral analysis of the phonon distribution around the atom, and preferably a coupling-strength sweep to show a nonperturbative onset rather than an η^2 dressing effect.
  2. [§III after Eq. (5), §VI] All strong-coupling and finite-temperature results are obtained with a fixed HEOM truncation depth N_c=2, and no convergence study over N_c is reported. The text states that 'several hundreds of exponential terms' were needed 'at a HEOM depth of N_c=2', but this is not a convergence test. In a regime advertised as 'multi-phonon', N_c=2 may be insufficient, and the inferred bound state could be a truncation artifact. Please report P_ee(t) and |P_eg(t)| for at least N_c=1,2,3,4 at η=5×10^-2, βω0=∞ and at one finite temperature, and also check the sensitivity to ε_r and to the ESPRIT term counts. Without this, the 'numerically exact' claim in the abstract is overreaching.
  3. [§VI and App. C, Table I] The zero-temperature discrepancy between HEOM (P_ee=0.009, residual |P_eg|) and the second-order mean-force result (P*_ee=0) is attributed to 'higher-order corrections', but no such corrections are computed. Because the second-order mean-force Hamiltonian in Eq. (C7) is diagonal, it cannot produce any coherence at all, and the finite-temperature agreement in Table I does not address the zero-temperature residual. The alternative explanation — that the residual is simply the dressed ground state of the σ_x-coupled spin-boson model — remains viable. A concrete higher-order mean-force calculation, an exact small-system diagonalization of the two-contact model, or a time-asymptotic analysis with N_c convergence would be needed to support the bound-state interpretation.
minor comments (4)
  1. [Fig. 5 caption] The legend labels '0 = 1.0', '0 = 0.5', '0 = 0.1' appear to be missing the β prefix (likely βω0). Please correct the caption.
  2. [Eq. (5)] The superoperators O× and O◦ are defined after the equation, but their action on the ADO indices would be clearer if the definition appeared before the equation and if the anti-commutator convention {·,·} were stated explicitly in the main text.
  3. [§IV] For the ESPRIT fitting, only the global L2 tolerance ε_r=1e-3 is reported. A brief statement on how the fit error propagates into observables, or a plot of the fit error as a function of t, would strengthen confidence in the long-time strong-coupling results.
  4. [§II] The BCF expression in Eq. (6) is written for finite β; the zero-temperature limit β→∞ used in Fig. 2 is not explicitly stated in the main text. Please state how the limit is taken and whether any additional fitting terms are needed near βω0→∞.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the only fit is the exponential decomposition of the analytically known bath correlation function, the central benchmark is an independent RWA analytical solution, and the self-citations are not load-bearing.

full rationale

The derivation chain is not circular. The only fitted quantities are the parameters of exponential decompositions of the analytically known bath correlation function C(t) of Eq. (6), obtained by the ESPRIT algorithm with a stated L2 tolerance; these fits serve as inputs to HEOM and are not informed by the target atomic dynamics (P_ee or P_eg). The zero-temperature benchmark in Sec. V compares HEOM against an independently derived RWA single-excitation solution (App. A, Eqs. (A1)-(A5)); that solution is not used to set any HEOM parameter. Likewise, the Redfield comparison is an independent perturbative result, and the finite-temperature/strong-coupling simulations use the same independent BCF fits. The stationary populations are compared with a separately computed mean-force Gibbs state (App. C), not derived from it. The self-citation [24] and other co-authored methodological references are background or future-work citations and are not load-bearing for the main claims. The paper itself flags numerical-convergence limitations such as hierarchy depth N_c=2, fit tolerance epsilon_r=1e-3, and second-order mean-force deviations; these concern numerical accuracy, not circularity. No equation reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claims rest primarily on standard open-quantum-system modeling choices plus the assumed convergence of HEOM with N_c=2 and ESPRIT-fitted BCFs. No exotic invented entities are introduced; the bound state is a physical inference, not a new degree of freedom.

free parameters (6)
  • eta (dimensionless coupling) = 1e-2 (weak), 5e-2 (strong)
    Model parameter set by hand; controls the strength of memory effects and the bound-state behavior.
  • omega_c (bath cutoff) = 2 omega0
    Chosen to regularize the Ohmic spectrum; sets the short-time memory scale.
  • omega0 tau (delay phase) = 20 x 2pi (omega0 tau / 2pi = 20)
    Chosen to realize the long-memory regime; controls the peak structure of the bath correlation function.
  • ESPRIT fit tolerance epsilon_r = 1e-3
    Balances BCF fit accuracy against the number of exponentials; directly affects HEOM convergence.
  • HEOM truncation depth N_c = 2
    Formally infinite hierarchy; truncation is a numerical free choice whose adequacy is asserted but not scanned.
  • ESPRIT exponential counts (N_R, N_I) = up to (743, 750)
    Fitted coefficients of the BCF decomposition; the central numerical input to the HEOM hierarchy.
assumptions (6)
  • domain assumption Initial system-bath product state rho(0)=rho_S(0) tensor rho_B(0) with a thermal bath and Hamiltonian Eq. (1).
    HEOM derivation (Sec. III) and BCF Eq. (3) assume this initial preparation; all simulations start from it.
  • domain assumption The bath correlation function is accurately represented by a finite sum of exponentials (Eq. 4) with ESPRIT fit at epsilon_r=1e-3.
    HEOM's exactness is conditional on this decomposition; the paper uses up to ~750 terms but does not prove convergence for strong coupling.
  • domain assumption Truncating the hierarchy at depth N_c=2 captures the relevant dynamics.
    Sec. III states N_c=2 was used; no convergence scan over N_c is shown for the strong-coupling or finite-temperature regime.
  • standard math RWA single-excitation analytical solution (App. A) is the correct benchmark at zero temperature and weak coupling.
    Used to validate HEOM in Sec. V; it relies on the single-phonon subspace and rotating-wave approximation.
  • domain assumption Ohmic spectral density gamma(omega)=eta omega e^{-omega/omega_c} with omega_c=2 omega0 describes the SAW waveguide.
    Chosen for physical realism and convergence (Sec. II); quantitative results depend on this choice.
  • standard math Redfield master equation is a correct second-order perturbative baseline (App. B).
    Used for comparison to demonstrate perturbative breakdown; not an assumption of the main method.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Non-Markovian dynamics of the giant atom beyond the rotating-wave approximation." pith.science (2026). https://pith.science/paper/3IAFFXOV

@misc{pith2026260103383,
  author       = {Pith},
  title        = {Pith review of: Non-Markovian dynamics of the giant atom beyond the rotating-wave approximation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3IAFFXOV}},
  note         = {Machine review of arXiv:2601.03383}
}
read the original abstract

We study the non-Markovian dynamics of a giant artificial atom coupled to a one-dimensional acoustic waveguide beyond the rotating-wave and weak-coupling approximations. By combining an optimized ESPRIT-based decomposition of the bath correlation function with the hierarchical equations of motion (HEOM), we achieve numerically exact simulations in regimes with long memory times, finite temperature, and strong system-bath coupling. Benchmarking against analytical results reveals the breakdown of perturbative non-Markovian approaches such as Redfield theory even at weak coupling in the presence of delay-induced memory. We further show that non-Markovian features, including excitation revivals, remain robust at finite temperature and can be enhanced by increasing the system-bath coupling strength. Our approach provides a versatile framework for studying non-Markovian quantum dynamics in structured environments relevant to giant-atom platforms.

Figures

Figures reproduced from arXiv: 2601.03383 by the authors.

Figure 1
Figure 1. FIG. 1. Two-level giant atom coupled to the left- and right [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Effective bath spectral density of the SAW field [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Excited-state probability of the giant atom as a func [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Real part of the thermal BCF for the SAW field as [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Time evolution of the excited-state population [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 1 linked inside Pith

  1. [1]

    L. Du, Y. Zhang, J.-H. Wu, A. F. Kockum, and Y. Li, Giant atoms in a synthetic frequency dimension, Phys. Rev. Lett.128, 223602 (2022)

    2022

  2. [2]

    In (a), the dashed lines mark the Gibbs steady-state population for 0.0 0.2 0.4 Pee (a) (b) 0 40 80 120 0t/2 0.0 0.2 0.4 |Peg| (c) 0 = 0 = 1.0 0 = 0.5 0 = 0.1 0 80 160 240 0t/2 (d) FIG. 5. Time evolution of the excited-state populationP ee [panels (a), (b)] and coherence|P eg|[panels (c), (d)] of a two- level giant atom at different temperatures. Results ...

  3. [3]

    A. M. Vadiraj, A. Ask, T. G. McConkey, I. Nsanzineza, C. W. S. Chang, A. F. Kockum, and C. M. Wilson, En- gineering the level structure of a giant artificial atom in waveguide quantum electrodynamics, Phys. Rev. A103, 023710 (2021)

    2021

  4. [4]

    Kannan, M

    B. Kannan, M. J. Ruckriegel, D. L. Campbell, A. Frisk Kockum, J. Braum¨ uller, D. K. Kim, M. Kjaer- gaard, P. Krantz, A. Melville, B. M. Niedzielski,et al., Waveguide quantum electrodynamics with superconduct- ing artificial giant atoms, Nature583, 775 (2020)

    2020

  5. [5]

    Manenti, A

    R. Manenti, A. F. Kockum, A. Patterson, T. Behrle, J. Rahamim, G. Tancredi, F. Nori, and P. J. Leek, Circuit quantum acoustodynamics with surface acoustic waves, Nature communications8, 975 (2017)

    2017

  6. [6]

    Andersson, B

    G. Andersson, B. Suri, L. Guo, T. Aref, and P. Delsing, Non-exponential decay of a giant artificial atom, Nature Physics15, 1123 (2019)

    2019

  7. [7]

    Frisk Kockum, P

    A. Frisk Kockum, P. Delsing, and G. Johansson, De- signing frequency-dependent relaxation rates and lamb shifts for a giant artificial atom, Phys. Rev. A90, 013837 (2014)

    2014

  8. [8]

    S. Guo, Y. Wang, T. Purdy, and J. Taylor, Beyond spon- taneous emission: Giant atom bounded in the continuum, Phys. Rev. A102, 033706 (2020)

    2020

Show all 71 references
  1. [10]

    Zhao and Z

    W. Zhao and Z. Wang, Single-photon scattering and bound states in an atom-waveguide system with two or multiple coupling points, Phys. Rev. A101, 053855 (2020)

    2020

  2. [11]

    Zhou, X.-L

    J. Zhou, X.-L. Yin, and J.-Q. Liao, Chiral and nonrecip- rocal single-photon scattering in a chiral-giant-molecule waveguide-qed system, Phys. Rev. A107, 063703 (2023)

    2023

  3. [12]

    A. F. Kockum, G. Johansson, and F. Nori, Decoherence- free interaction between giant atoms in waveguide quan- tum electrodynamics, Phys. Rev. Lett.120, 140404 (2018)

    2018

  4. [13]

    L. Du, L. Guo, and Y. Li, Complex decoherence-free interactions between giant atoms, Phys. Rev. A107, 023705 (2023)

    2023

  5. [14]

    Yin, W.-B

    X.-L. Yin, W.-B. Luo, and J.-Q. Liao, Non-markovian disentanglement dynamics in double-giant-atom waveguide-qed systems, Phys. Rev. A106, 063703 (2022). 8

    2022

  6. [15]

    Yin and J.-Q

    X.-L. Yin and J.-Q. Liao, Generation of two-giant-atom entanglement in waveguide-qed systems, Phys. Rev. A 108, 023728 (2023)

    2023

  7. [16]

    H. Yu, Z. Wang, and J.-H. Wu, Entanglement prepa- ration and nonreciprocal excitation evolution in giant atoms by controllable dissipation and coupling, Phys. Rev. A104, 013720 (2021)

    2021

  8. [17]

    A. C. Santos and R. Bachelard, Generation of maximally entangled long-lived states with giant atoms in a waveg- uide, Phys. Rev. Lett.130, 053601 (2023)

    2023

  9. [18]

    Chen and A

    G. Chen and A. Frisk Kockum, Simulating open quantum systems with giant atoms, Quantum Science and Tech- nology10, 025028 (2025)

    2025

  10. [19]

    L. Du, X. Wang, A. F. Kockum, and J. Splettstoesser, Dressed interference in giant superatoms: Entanglement generation and transfer, Phys. Rev. Lett.135, 223601 (2025)

    2025

  11. [20]

    A. L. Grimsmo, Time-delayed quantum feedback control, Phys. Rev. Lett.115, 060402 (2015)

    2015

  12. [21]

    Pichler and P

    H. Pichler and P. Zoller, Photonic circuits with time de- lays and quantum feedback, Phys. Rev. Lett.116, 093601 (2016)

    2016

  13. [22]

    Caruso, V

    F. Caruso, V. Giovannetti, C. Lupo, and S. Mancini, Quantum channels and memory effects, Rev. Mod. Phys. 86, 1203 (2014)

    2014

  14. [23]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, J. Piilo, and B. Vacchini, Col- loquium: Non-markovian dynamics in open quantum sys- tems, Rev. Mod. Phys.88, 021002 (2016)

    2016

  15. [24]

    de Vega and D

    I. de Vega and D. Alonso, Dynamics of non-markovian open quantum systems, Rev. Mod. Phys.89, 015001 (2017)

    2017

  16. [25]

    Yu, T.-A

    M. Yu, T.-A. Ohst, H.-C. Nguyen, and S. Nimmrichter, Quantum memory in spontaneous emission processes (2025), arXiv:2504.08605 [quant-ph]

    2025 arXiv

  17. [26]

    Y. Wang, M. Um, J. Zhang, S. An, M. Lyu, J.-N. Zhang, L.-M. Duan, D. Yum, and K. Kim, Single-qubit quan- tum memory exceeding ten-minute coherence time, Na- ture Photonics11, 646 (2017)

    2017

  18. [27]

    Binder, L

    F. Binder, L. Correa, C. Gogolin, J. Anders, and G. Adesso,Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions, Fundamental Theories of Physics (Springer International Publishing, 2019)

    2019

  19. [28]

    Newman, F

    D. Newman, F. Mintert, and A. Nazir, Performance of a quantum heat engine at strong reservoir coupling, Phys. Rev. E95, 032139 (2017)

    2017

  20. [29]

    Valentini, Non-local correlations in quantum electro- dynamics, Physics Letters A153, 321 (1991)

    A. Valentini, Non-local correlations in quantum electro- dynamics, Physics Letters A153, 321 (1991)

    1991

  21. [30]

    Le´ on and C

    J. Le´ on and C. Sab ´ ın, Generation of atom-atom corre- lations inside and outside the mutual light cone, Phys. Rev. A79, 012304 (2009)

    2009

  22. [31]

    Sab ´ ın, J

    C. Sab ´ ın, J. J. Garc ´ ıa-Ripoll, E. Solano, and J. Le´ on, Dy- namics of entanglement via propagating microwave pho- tons, Phys. Rev. B81, 184501 (2010)

    2010

  23. [32]

    Pichler, S

    H. Pichler, S. Choi, P. Zoller, and M. D. Lukin, Uni- versal photonic quantum computation via time-delayed feedback, Proceedings of the National Academy of Sci- ences114, 11362 (2017)

    2017

  24. [33]

    L. R. Sletten, B. A. Moores, J. J. Viennot, and K. W. Lehnert, Resolving phonon fock states in a multimode cavity with a double-slit qubit, Phys. Rev. X9, 021056 (2019)

    2019

  25. [34]

    L. Guo, A. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson, Giant acoustic atom: A single quantum system with a deterministic time delay, Phys. Rev. A95, 053821 (2017)

    2017

  26. [35]

    Magnifico, M

    G. Magnifico, M. Maffei, D. Pomarico, D. Das, P. Facchi, S. Pascazio, and F. V. Pepe, Non-markovian dynamics of generation of bound states in the continuum via single- photon scattering, Phys. Rev. Res.7, 033249 (2025)

    2025

  27. [36]

    A. W. Chin, A. Rivas, S. F. Huelga, and M. B. Ple- nio, Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogo- nal polynomials, Journal of Mathematical Physics51, 092109 (2010)

    2010

  28. [37]

    Strathearn, P

    A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Efficient non-markovian quantum dynamics using time-evolving matrix product operators, Nature commu- nications9, 3322 (2018)

    2018

  29. [38]

    Link, H.-H

    V. Link, H.-H. Tu, and W. T. Strunz, Open quantum sys- tem dynamics from infinite tensor network contraction, Phys. Rev. Lett.132, 200403 (2024)

    2024

  30. [39]

    Suess, A

    D. Suess, A. Eisfeld, and W. T. Strunz, Hierarchy of stochastic pure states for open quantum system dynam- ics, Phys. Rev. Lett.113, 150403 (2014)

    2014

  31. [40]

    Tanimura and R

    Y. Tanimura and R. Kubo, Two-time correlation func- tions of a system coupled to a heat bath with a gaussian- markoffian interaction, Journal of the Physical Society of Japan58, 1199 (1989)

    1989

  32. [41]

    Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (heom), The Journal of Chemical Physics153, 020901 (2020)

    Y. Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (heom), The Journal of Chemical Physics153, 020901 (2020)

    2020

  33. [42]

    Lambert, T

    N. Lambert, T. Raheja, S. Cross, P. Menczel, S. Ahmed, A. Pitchford, D. Burgarth, and F. Nori, Qutip-bofin: A bosonic and fermionic numerical hierarchical-equations- of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics, Phys...

    2023

  34. [43]

    Tanimura, Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath, Phys

    Y. Tanimura, Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath, Phys. Rev. A41, 6676 (1990)

    1990

  35. [44]

    Ishizaki and Y

    A. Ishizaki and Y. Tanimura, Quantum dynamics of sys- tem strongly coupled to low-temperature colored noise bath: Reduced hierarchy equations approach, Journal of the Physical Society of Japan74, 3131 (2005)

    2005

  36. [45]

    Ding, R.-X

    J.-J. Ding, R.-X. Xu, and Y. Yan, Optimizing hierar- chical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum trans- fer mechanisms, The Journal of Chemical Physics136, 224103 (2012)

    2012

  37. [46]

    Hu, R.-X

    J. Hu, R.-X. Xu, and Y. Yan, Communication: Pad´ e spectrum decomposition of fermi function and bose func- tion, The Journal of Chemical Physics133, 101106 (2010)

    2010

  38. [47]

    J. Hu, M. Luo, F. Jiang, R.-X. Xu, and Y. Yan, Pad´ e spectrum decompositions of quantum distribution func- tions and optimal hierarchical equations of motion con- struction for quantum open systems, The Journal of Chemical Physics134, 244106 (2011)

    2011

  39. [48]

    Roy and T

    R. Roy and T. Kailath, Esprit-estimation of signal parameters via rotational invariance techniques, IEEE Transactions on Acoustics, Speech, and Signal Process- ing37, 984 (1989)

    1989

  40. [49]

    Takahashi, S

    H. Takahashi, S. Rudge, C. Kaspar, M. Thoss, and R. Borrelli, High accuracy exponential decomposition of bath correlation functions for arbitrary and structured spectral densities: Emerging methodologies and new ap- 9 proaches, The Journal of Chemical Physics160, 204105 (2024)

    2024

  41. [50]

    Cui, H.-D

    L. Cui, H.-D. Zhang, X. Zheng, R.-X. Xu, and Y. Yan, Highly efficient and accurate sum-over-poles expansion of fermi and bose functions at near zero temperatures: Fano spectrum decomposition scheme, The Journal of Chemical Physics151, 024110 (2019)

    2019

  42. [51]

    Zhang, L

    H.-D. Zhang, L. Cui, H. Gong, R.-X. Xu, X. Zheng, and Y. Yan, Hierarchical equations of motion method based on fano spectrum decomposition for low tempera- ture environments, The Journal of Chemical Physics152, 064107 (2020)

    2020

  43. [52]

    M. Xu, Y. Yan, Q. Shi, J. Ankerhold, and J. T. Stock- burger, Taming quantum noise for efficient low temper- ature simulations of open quantum systems, Phys. Rev. Lett.129, 230601 (2022)

    2022

  44. [53]

    Vanhuffel, H

    S. Vanhuffel, H. Chen, C. Decanniere, and P. Vanhecke, Algorithm for time-domain nmr data fitting based on to- tal least squares, Journal of Magnetic Resonance, Series A110, 228 (1994)

    1994

  45. [54]

    Aushev, A

    T. Aushev, A. N. Kozhinov, and Y. O. Tsybin, Least- squares fitting of time-domain signals for fourier trans- form mass spectrometry, Journal of the American Society for Mass Spectrometry25, 1263 (2014), pMID: 24789745

    2014

  46. [55]

    Hartmann, M

    R. Hartmann, M. Werther, F. Grossmann, and W. T. Strunz, Exact open quantum system dynamics: Opti- mal frequency vs time representation of bath correlations, The Journal of Chemical Physics150, 234105 (2019)

    2019

  47. [56]

    Z.-H. Chen, Y. Wang, X. Zheng, R.-X. Xu, and Y. Yan, Universal time-domain prony fitting decomposition for optimized hierarchical quantum master equations, The Journal of Chemical Physics156, 221102 (2022)

    2022

  48. [57]

    Schaubert, Application of prony’s method to time- domain reflectometer data and equivalent circuit synthe- sis, IEEE Transactions on Antennas and Propagation27, 180 (1979)

    D. Schaubert, Application of prony’s method to time- domain reflectometer data and equivalent circuit synthe- sis, IEEE Transactions on Antennas and Propagation27, 180 (1979)

    1979

  49. [58]

    Abramowitz and I

    M. Abramowitz and I. Stegun,Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Applied mathematics series (Dover Publications, 1965)

    1965

  50. [59]

    Van Kampen,Stochastic Processes in Physics and Chemistry, North-Holland Personal Library (North Hol- land, 2011)

    N. Van Kampen,Stochastic Processes in Physics and Chemistry, North-Holland Personal Library (North Hol- land, 2011)

    2011

  51. [60]

    M. J. W. Hall, J. D. Cresser, L. Li, and E. Andersson, Canonical form of master equations and characterization of non-markovianity, Phys. Rev. A89, 042120 (2014)

    2014

  52. [61]

    Hartmann and W

    R. Hartmann and W. T. Strunz, Accuracy assessment of perturbative master equations: Embracing nonpositivity, Phys. Rev. A101, 012103 (2020)

    2020

  53. [62]

    Scali, J

    S. Scali, J. Anders, and L. A. Correa, Local master equa- tions bypass the secular approximation, Quantum5, 451 (2021)

    2021

  54. [63]

    Frisk Kockum, Quantum optics with giant atoms— the first five years, inInternational Symposium on Math- ematics, Quantum Theory, and Cryptography, edited by T

    A. Frisk Kockum, Quantum optics with giant atoms— the first five years, inInternational Symposium on Math- ematics, Quantum Theory, and Cryptography, edited by T. Takagi, M. Wakayama, K. Tanaka, N. Kunihiro, K. Ki- moto, and Y. Ikematsu (Springer Singapore, Singapore,

  55. [64]

    Campisi, P

    M. Campisi, P. Talkner, and P. H¨ anggi, Fluctuation the- orem for arbitrary open quantum systems, Phys. Rev. Lett.102, 210401 (2009)

    2009

  56. [65]

    Rivas, Strong coupling thermodynamics of open quan- tum systems, Phys

    A. Rivas, Strong coupling thermodynamics of open quan- tum systems, Phys. Rev. Lett.124, 160601 (2020)

    2020

  57. [66]

    L. Guo, A. F. Kockum, F. Marquardt, and G. Johansson, Oscillating bound states for a giant atom, Phys. Rev. Res. 2, 043014 (2020)

    2020

  58. [67]

    Li and X

    L. Li and X. Cao, Coherent destruction of tunneling of quantum energy transport in a driven nonequilibrium spin-boson model, Phys. Rev. B110, 075403 (2024)

    2024

  59. [68]

    Ritter, D

    M. Ritter, D. M. Long, Q. Yue, A. Chandran, and A. J. Koll´ ar, Autonomous stabilization of floquet states using static dissipation, Phys. Rev. X15, 031028 (2025)

    2025

  60. [69]

    B¨ acker, K

    C. B¨ acker, K. Beyer, and W. T. Strunz, Local disclosure of quantum memory in non-markovian dynamics, Phys. Rev. Lett.132, 060402 (2024)

    2024

  61. [70]

    Breuer and F

    H. Breuer and F. Petruccione,The Theory of Open Quan- tum Systems(Oxford University Press, 2002)

    2002

  62. [71]

    Lobejko, M

    M. Lobejko, M. Winczewski, G. Su´ arez, R. Alicki, and M. Horodecki, Corrections to the hamiltonian induced by finite-strength coupling to the environment, Phys. Rev. E110, 014144 (2024). Appendix A: Exact master equation in R W A at zero temperature Here we derive the master ...

    2024

  63. [72]

    (A3), we obtain an integro-differential equation for the amplitudee(t)

    Using the Schr¨ odinger equationiℏ∂ t|Ψ(t)⟩= ˆHI (t)|Ψ(t)⟩, we obtain the coupled equations of motion for the 10 probability amplitudes ˙e(t) =−i X j=1,2 Z ∞ 0 dω r γ(ω) π cos ωτ 2 αjω (t)ei(ω0−ω)t,(A3) ˙αjω (t) =−i r γ(ω) π cos ωτ 2 e(t)e−i(ω0−ω)t.(A4) By formally solvingα jω...

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.