pith. machine review for the scientific record. sign in

arxiv: 2511.08754 · v3 · submitted 2025-11-11 · 🪐 quant-ph

Exact Floquet dynamics of strongly damped driven quantum systems

Konrad Mickiewicz , Valentin Link , Walter T. Strunz This is my paper

Pith reviewed 2026-05-17 23:08 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Floquet dynamicsopen quantum systemsmatrix product operatorsinfluence functionalnon-Markovian dynamicsspin-boson modeldriven quantum systemsdissipative Floquet
0
0 comments X

The pith

A periodic matrix product operator representation of the influence functional yields a numerically exact Floquet propagator for non-Markovian dynamics in strongly damped driven quantum systems.

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

The paper develops a numerical method for quantum systems that experience both strong environmental damping and periodic driving. It encodes the bath's cumulative effect in a periodic matrix product operator form of the influence functional. From this encoding the authors construct a propagator that advances the system state exactly over each driving period while retaining non-Markovian memory. A sympathetic reader would care because the same tool can be used to track both the long-time heating of a bath and the transient build-up or stabilization of entanglement between driven qubits.

Core claim

The central claim is that representing the influence functional as a periodic matrix product operator enables construction of a numerically exact Floquet propagator that captures the non-Markovian open-system dynamics, thereby supplying a dissipative counterpart to the Floquet Hamiltonian used for isolated driven systems.

What carries the argument

The periodic matrix product operator representation of the influence functional, which encodes bath memory in a compact, periodically repeating structure that supports exact propagation over many drive cycles.

If this is right

  • The method characterizes the asymptotic heating of a reservoir in spin-boson models and quantifies its deviation from equilibrium.
  • Local driving applied to two qubits can stabilize a transient entanglement that originates from their shared environment.
  • Stationary and transient regimes of strongly damped driven systems become directly accessible inside a single transparent numerical framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same periodic representation may extend to other bath spectral densities or non-periodic but slowly varying drives without loss of the exact-propagator property.
  • Exact long-time trajectories generated this way could serve as benchmarks for approximate master-equation or perturbative treatments in the strong-damping regime.
  • The construction supplies a concrete route to Floquet engineering of steady-state properties in open quantum systems.

Load-bearing premise

The influence functional for strongly damped driven systems admits an efficient and accurate periodic matrix product operator representation that preserves numerical exactness without uncontrolled truncation errors over many periods.

What would settle it

A direct numerical comparison in a solvable spin-boson model that shows accumulating deviation from the known exact dynamics after propagation through many driving periods would falsify the claim of sustained numerical exactness.

Figures

Figures reproduced from arXiv: 2511.08754 by Konrad Mickiewicz, Valentin Link, Walter T. Strunz.

Figure 1
Figure 1. Figure 1: FIG. 1. Quantum circuit representation of a periodic Floquet [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Spin-boson dynamics with transversal driving [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time-averaged asymptotic heat current density in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Extensions to general driving One limitation of our numerical technique is that we require the driving to be local in order to construct a Floquet IF from a semi-group IF. This excludes the important case of time-dependent coupling, often encountered in thermodynamical cycles [23, 24, 72–74]. Specifically, one considers a time depen￾dent coupling operator S(t + T) = S(t). In order to construct a Floquet-IF… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Entanglement dynamics in a driven two-spin-boson [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Total time-averaged heat current (25) as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Spectral analysis of undriven entanglement dynamics [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We present an approach for efficiently simulating strongly damped quantum systems subjected to periodic driving, employing a periodic matrix product operator representation of the influence functional. This representation enables the construction of a numerically exact Floquet propagator that captures the non-Markovian open system dynamics, thus providing a dissipative analogue to the Floquet Hamiltonian of driven isolated quantum systems. We apply this method to study the asymptotic heating of a reservoir in spin-boson models, characterizing the deviation from equilibrium conditions. Moreover, we show how a local driving of two qubits can be utilized to stabilize a transient entanglement buildup of the qubits originating from the interaction with a common environment. Our results make it possible to directly study both stationary and transient dynamics of strongly damped and driven quantum systems within a transparent theoretical and numerical framework.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a periodic matrix product operator (MPO) representation of the influence functional for strongly damped, periodically driven quantum systems. This construction is used to build a numerically exact Floquet propagator that captures non-Markovian open-system dynamics, positioned as a dissipative analogue to the Floquet Hamiltonian for closed systems. Applications include analysis of asymptotic reservoir heating in spin-boson models and stabilization of transient entanglement in locally driven two-qubit systems coupled to a common bath.

Significance. If the numerical exactness and error control are established, the approach would offer a transparent and efficient framework for long-time dynamics in driven dissipative systems, enabling direct access to stationary states and transient entanglement without Markovian approximations. It extends influence-functional methods to periodic driving and could support studies in quantum thermodynamics and control.

major comments (2)
  1. [§3] §3 (Floquet propagator construction): The claim that the periodic MPO yields a numerically exact propagator rests on the assumption that the representation of the influence functional requires no uncontrolled truncation. The manuscript must supply explicit error bounds or a proof that finite-bond-dimension truncation errors remain bounded independently of the number of Floquet periods; without this, iteration of the propagator can accumulate approximation errors, undermining the central 'exact' claim.
  2. [§4.1] §4.1 (spin-boson heating results): The reported deviation from equilibrium heating is presented as a direct consequence of the exact propagator, yet no convergence tests versus MPO bond dimension or versus exact benchmarks for small bath discretizations are shown. This is load-bearing because any hidden truncation error would directly affect the claimed non-equilibrium characterization.
minor comments (2)
  1. [§2] Notation for the periodic MPO bond dimension and the discretization of the bath correlation function should be introduced once in §2 and used consistently; current usage mixes symbols across equations.
  2. [Figures] Figure 2 and Figure 4 captions should explicitly state the bond dimension, time-step discretization, and number of periods used, to allow readers to assess the numerical exactness.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We are pleased that the referee recognizes the potential of our periodic MPO approach for studying driven dissipative quantum systems. We address each major comment below and describe the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Floquet propagator construction): The claim that the periodic MPO yields a numerically exact propagator rests on the assumption that the representation of the influence functional requires no uncontrolled truncation. The manuscript must supply explicit error bounds or a proof that finite-bond-dimension truncation errors remain bounded independently of the number of Floquet periods; without this, iteration of the propagator can accumulate approximation errors, undermining the central 'exact' claim.

    Authors: We agree that clarifying the error control is important for substantiating the 'numerically exact' claim. The construction in the manuscript relies on the fact that for strongly damped systems, the influence functional can be accurately represented by an MPO with modest bond dimension due to the short correlation time of the bath. While we do not provide a rigorous mathematical proof that errors are bounded for all possible parameters independently of the number of periods, our numerical experiments indicate that the results stabilize with increasing bond dimension and do not show accumulation of errors over multiple Floquet periods. In the revised version, we will expand §3 to include a discussion of the truncation error, supported by additional convergence plots demonstrating stability over long times. revision: partial

  2. Referee: [§4.1] §4.1 (spin-boson heating results): The reported deviation from equilibrium heating is presented as a direct consequence of the exact propagator, yet no convergence tests versus MPO bond dimension or versus exact benchmarks for small bath discretizations are shown. This is load-bearing because any hidden truncation error would directly affect the claimed non-equilibrium characterization.

    Authors: The referee correctly points out the need for explicit convergence tests to support the results in §4.1. Although the original manuscript selects parameters where the MPO representation is expected to be accurate based on prior literature on influence functional methods, we acknowledge that direct evidence was not provided. We will revise this section to include convergence tests with respect to the MPO bond dimension for the asymptotic heating rates. Additionally, for small bath discretizations, we will add comparisons to exact diagonalization or other benchmarks to validate the deviation from equilibrium heating. revision: yes

standing simulated objections not resolved
  • A general analytical proof that truncation errors remain bounded independently of the number of Floquet periods for arbitrary finite bond dimensions.

Circularity Check

0 steps flagged

No circularity: method extends influence-functional formalism with periodic MPO representation

full rationale

The paper introduces a periodic matrix product operator representation of the influence functional to build a Floquet propagator for strongly damped driven systems. This construction is presented as a direct extension of the standard influence-functional approach rather than a self-referential definition or a fitted parameter renamed as a prediction. No quoted equations or steps in the abstract reduce the claimed numerically exact propagator to its own inputs by construction, nor do they rely on load-bearing self-citations or imported uniqueness theorems. The central claim rests on the independent assumption that the influence functional admits an efficient periodic MPO representation that preserves exactness, which is an external methodological choice verifiable against tensor-network benchmarks and not equivalent to the result by definition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard influence-functional formalism of open quantum systems together with the new periodic MPO representation; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The system-bath interaction is captured by a standard influence functional that can be represented as a matrix product operator.
    The method presupposes the validity of the influence-functional approach for strongly damped systems.

pith-pipeline@v0.9.0 · 5423 in / 1223 out tokens · 47607 ms · 2026-05-17T23:08:05.698587+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

91 extracted references · 91 canonical work pages · 2 internal anchors

  1. [1]

    or process tensor [35, 36], in terms of a large tensor [34, 37, 38] I (µN µ′ N )...(µ1µ′

    work page

  2. [2]

    Exact Floquet dynamics of strongly damped driven quantum systems

    = trU µN µ′ N N · · · Uµ2µ′ 2 2 U µ1µ′ 1 1 ρenv.(2) The Greek indicesµ= 1. . .dim(H sys)2 label the Liouville-space (density matrix space) of the system, and can be contracted with the operatorsO n to recover the corresponding local observable. Note that, in the influ- ence functional, the environment degrees of freedom are completely traced out and are n...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  3. [3]

    The boundary vectors⃗ vl/r also live in the auxiliary space and resem- ble the initial state and trace of the environment

    are square matrices that are independent ofNand act on a auxiliary (bond) space, replacing the original full environment state space. The boundary vectors⃗ vl/r also live in the auxiliary space and resem- ble the initial state and trace of the environment. For Gaussian bosonic baths, this form can be obtained us- ing either tailored Markovian embedding me...

    work page

  4. [4]

    This allows us to include reaction coordi- nate into the system, while treating the residual bath as a new stationary environment for which a semi-group IF can be constructed

    where the RC modea 0 is coupled linearly to a modified residual environment. This allows us to include reaction coordi- nate into the system, while treating the residual bath as a new stationary environment for which a semi-group IF can be constructed. The reaction coordinate can then be included back into the bath IF [38], recovering a pe- riodic Floquet...

    work page

  5. [5]

    T. N. Ikeda and A. Polkovnikov, Fermi’s golden rule for heating in strongly driven Floquet systems, Phys. Rev. B104, 134308 (2021)

    work page 2021

  6. [6]

    Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Rev

    A. Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Rev. Mod. Phys.89, 011004 (2017)

    work page 2017

  7. [7]

    Reitter, J

    M. Reitter, J. N¨ ager, K. Wintersperger, C. Str¨ ater, I. Bloch, A. Eckardt, and U. Schneider, Interaction De- pendent Heating and Atom Loss in a Periodically Driven Optical Lattice, Phys. Rev. Lett.119, 200402 (2017)

    work page 2017

  8. [8]

    Y. Chen, Z. Zhu, and K. Viebahn, Mitigating higher- band heating in Floquet-Hubbard lattices via two-tone driving, Phys. Rev. A112, L021301 (2025)

    work page 2025

  9. [9]

    Shirai, J

    T. Shirai, J. Thingna, T. Mori, S. Denisov, P. H¨ anggi, and S. Miyashita, Effective Floquet–Gibbs states for dis- sipative quantum systems, New J. Phys.18, 053008 (2016)

    work page 2016

  10. [10]

    S. A. Sato, U. De Giovannini, S. Aeschlimann, I. Gierz, H. H¨ ubener, and A. Rubio, Floquet states in dissipative open quantum systems, J. Phys. B: At. Mol. Opt. Phys. 53, 225601 (2020)

    work page 2020

  11. [11]

    Petiziol and A

    F. Petiziol and A. Eckardt, Cavity-Based Reservoir En- gineering for Floquet-Engineered Superconducting Cir- cuits, Physical Review Letters129, 233601 (2022)

    work page 2022

  12. [12]

    Mori, Floquet States in Open Quantum Systems, Annu

    T. Mori, Floquet States in Open Quantum Systems, Annu. Rev. Condens. Matter Phys. , 35 (2023)

    work page 2023

  13. [13]

    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)

    work page 2024

  14. [14]

    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)

    work page 2025

  15. [15]

    de Vega and D

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

    work page 2017

  16. [16]

    Hartmann and W

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

    work page 2020

  17. [17]

    C. S. Tello Breuer, T. Becker, and A. Eckardt, Bench- marking quantum master equations beyond ultraweak coupling, Phys. Rev. B110, 064319 (2024)

    work page 2024

  18. [18]

    Gul´ acsi and G

    B. Gul´ acsi and G. Burkard, Temporally correlated quan- tum noise in driven quantum systems with applications to quantum gate operations, Phys. Rev. Res.7, 023073 (2025)

    work page 2025

  19. [19]

    Kohler, T

    S. Kohler, T. Dittrich, and P. H¨ anggi, Floquet-Markovian description of the parametrically driven, dissipative har- monic quantum oscillator, Phys. Rev. E55, 300 (1997)

    work page 1997

  20. [20]

    Marthaler and M

    M. Marthaler and M. I. Dykman, Switching via quantum activation: A parametrically modulated oscillator, Phys. Rev. A73, 042108 (2006)

    work page 2006

  21. [21]

    Ketzmerick and W

    R. Ketzmerick and W. Wustmann, Statistical mechanics of Floquet systems with regular and chaotic states, Phys. Rev. E82, 021114 (2010)

    work page 2010

  22. [22]

    Lazarides, S

    A. Lazarides, S. Roy, F. Piazza, and R. Moessner, Time crystallinity in dissipative Floquet systems, Phys. Rev. 6 Res.2, 022002 (2020)

    work page 2020

  23. [23]

    Gunderson, J

    J. Gunderson, J. Muldoon, K. W. Murch, and Y. N. Joglekar, Floquet exceptional contours in Lindblad dy- namics with time-periodic drive and dissipation, Phys. Rev. A103, 023718 (2021)

    work page 2021

  24. [24]

    H. Z. Shen, Q. Wang, and X. X. Yi, Dispersive readout with non-Markovian environments, Phys. Rev. A105, 023707 (2022)

    work page 2022

  25. [25]

    D. K. J. Boneß, W. Belzig, and M. I. Dykman, Resonant- force-induced symmetry breaking in a quantum paramet- ric oscillator, Phys. Rev. Res.6, 033240 (2024)

    work page 2024

  26. [26]

    Direkci, K

    S. Direkci, K. Winkler, C. Gut, M. Aspelmeyer, and Y. Chen, Universality of stationary entanglement in an optomechanical system driven by non-Markovian noise and squeezed light, arXiv 10.48550/arXiv.2502.02979 (2025), 2502.02979

    work page doi:10.48550/arxiv.2502.02979 2025

  27. [27]

    Koyanagi and Y

    S. Koyanagi and Y. Tanimura, Numerically “exact” sim- ulations of a quantum Carnot cycle: Analysis using ther- modynamic work diagrams, J. Chem. Phys.157, 084110 (2022)

    work page 2022

  28. [28]

    Boettcher, R

    V. Boettcher, R. Hartmann, K. Beyer, and W. T. Strunz, Dynamics of a strongly coupled quantum heat engine—Computing bath observables from the hierarchy of pure states, J. Chem. Phys.160, 10.1063/5.0192075 (2024)

    work page doi:10.1063/5.0192075 2024

  29. [29]

    Kolisnyk, F

    D. Kolisnyk, F. Queißer, G. Schaller, and R. Sch¨ utzhold, Floquet analysis of a superradiant many-qutrit refriger- ator, Phys. Rev. Appl.21, 044050 (2024)

    work page 2024

  30. [30]

    Alamo, F

    M. Alamo, F. Petiziol, and A. Eckardt, Minimal quan- tum heat pump based on high-frequency driving and non- Markovianity, Phys. Rev. E109, 064121 (2024)

    work page 2024

  31. [31]

    J. V. Koski, A. J. Landig, A. P´ alyi, P. Scarlino, C. Re- ichl, W. Wegscheider, G. Burkard, A. Wallraff, K. En- sslin, and T. Ihn, Floquet Spectroscopy of a Strongly Driven Quantum Dot Charge Qubit with a Microwave Resonator, Phys. Rev. Lett.121, 043603 (2018)

    work page 2018

  32. [32]

    von Horstig, L

    F.-E. von Horstig, L. Peri, S. Barraud, S. N. Shevchenko, C. J. B. Ford, and M. F. Gonzalez-Zalba, Floquet in- terferometry of a dressed semiconductor quantum dot, arXiv 10.48550/arXiv.2407.14241 (2024), 2407.14241

    work page doi:10.48550/arxiv.2407.14241 2024

  33. [33]

    N. E. Frattini, R. G. Corti˜ nas, J. Venkatraman, X. Xiao, Q. Su, C. U. Lei, B. J. Chapman, V. R. Joshi, S. M. Girvin, R. J. Schoelkopf, S. Puri, and M. H. Devoret, Ob- servation of pairwise level degeneracies and the quantum regime of the arrhenius law in a double-well parametric oscillator, Phys. Rev. X14, 031040 (2024)

    work page 2024

  34. [34]

    O. V. Ivakhnenko, C. D. Satrya, Y.-C. Chang, R. Upad- hyay, J. T. Peltonen, S. N. Shevchenko, F. Nori, and J. P. Pekola, Probing strongly driven and strongly coupled superconducting qubit-resonator system, arXiv 10.48550/arXiv.2508.03188 (2025), 2508.03188

    work page doi:10.48550/arxiv.2508.03188 2025

  35. [35]

    Link, H.-H

    V. Link, H.-H. Tu, and W. T. Strunz, Open Quan- tum System Dynamics from Infinite Tensor Network Contraction, arXiv 10.48550/arXiv.2307.01802 (2023), 2307.01802

    work page doi:10.48550/arxiv.2307.01802 2023

  36. [36]

    Sonner, V

    M. Sonner, V. Link, and D. A. Abanin, Semi-group influence matrices for non-equilibrium quantum impu- rity models, arXiv 10.48550/arXiv.2502.00109 (2025), 2502.00109

    work page doi:10.48550/arxiv.2502.00109 2025

  37. [37]

    R. P. Feynman and F. L. Vernon, The theory of a gen- eral quantum system interacting with a linear dissipative system, Ann. Phys.24, 118 (1963)

    work page 1963

  38. [38]

    Sonner, A

    M. Sonner, A. Lerose, and D. A. Abanin, Influence func- tional of many-body systems: Temporal entanglement and matrix-product state representation, Ann. Phys. 435, 168677 (2021)

    work page 2021

  39. [39]

    M. R. Jørgensen and F. A. Pollock, Exploiting the Causal Tensor Network Structure of Quantum Processes to Ef- ficiently Simulate Non-Markovian Path Integrals, Phys. Rev. Lett.123, 240602 (2019)

    work page 2019

  40. [40]

    Verifying Quantum Memory in the Dynamics of Spin Boson Models

    C. B¨ acker, V. Link, and W. T. Strunz, Verifying Quan- tum Memory in the Dynamics of Spin Boson Models (2025), arXiv:2505.13067 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  41. [41]

    F. A. Pollock, C. Rodr´ ıguez-Rosario, T. Frauenheim, M. Paternostro, and K. Modi, Non-Markovian quantum processes: Complete framework and efficient characteri- zation, Phys. Rev. A97, 012127 (2018)

    work page 2018

  42. [42]

    Cygorek, M

    M. Cygorek, M. Cosacchi, A. Vagov, V. M. Axt, B. W. Lovett, J. Keeling, and E. M. Gauger, Simulation of open quantum systems by automated compression of arbitrary environments, Nat. Phys.18, 662 (2022)

    work page 2022

  43. [43]

    Lerose, M

    A. Lerose, M. Sonner, and D. A. Abanin, Influence Ma- trix Approach to Many-Body Floquet Dynamics, Phys. Rev. X11, 021040 (2021)

    work page 2021

  44. [44]

    Bukov, L

    M. Bukov, L. D’Alessio, and A. Polkovnikov, Univer- sal high-frequency behavior of periodically driven sys- tems: from dynamical stabilization to Floquet engineer- ing, Adv. Phys. (2015)

    work page 2015

  45. [45]

    Vilkoviskiy, M

    I. Vilkoviskiy, M. Sonner, Q. C. Huang, W. W. Ho, A. Lerose, and D. A. Abanin, Temporal entanglement transition in chaotic quantum many-body dynamics (2025), arXiv:2511.03846 [quant-ph]

    work page arXiv 2025

  46. [46]

    Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of mo- tion (HEOM), J

    Y. Tanimura, Numerically “exact” approach to open quantum dynamics: The hierarchical equations of mo- tion (HEOM), J. Chem. Phys.153, 020901 (2020)

    work page 2020

  47. [47]

    Mascherpa, A

    F. Mascherpa, A. Smirne, A. D. Somoza, P. Fern´ andez- Acebal, S. Donadi, D. Tamascelli, S. F. Huelga, and M. B. Plenio, Optimized auxiliary oscillators for the simulation of general open quantum systems, Phys. Rev. A101, 052108 (2020)

    work page 2020

  48. [48]

    Huang, G

    Z. Huang, G. Park, G. K.-L. Chan, and L. Lin, Coupled Lindblad pseudomode theory for simulating open quan- tum systems, arXiv 10.48550/arXiv.2506.10308 (2025), 2506.10308

    work page doi:10.48550/arxiv.2506.10308 2025

  49. [49]

    Vilkoviskiy and D

    I. Vilkoviskiy and D. A. Abanin, Bound on approximat- ing non-Markovian dynamics by tensor networks in the time domain, Phys. Rev. B109, 205126 (2024)

    work page 2024

  50. [50]

    Thoenniss, I

    J. Thoenniss, I. Vilkoviskiy, and D. A. Abanin, Efficient Pseudomode Representation and Complexity of Quan- tum Impurity Models, arXiv 10.48550/arXiv.2409.08816 (2024), 2409.08816

    work page doi:10.48550/arxiv.2409.08816 2024

  51. [51]

    M. C. Ba˜ nuls, M. B. Hastings, F. Verstraete, and J. I. Cirac, Matrix Product States for Dynamical Simulation of Infinite Chains, Phys. Rev. Lett.102, 240603 (2009)

    work page 2009

  52. [52]

    Strathearn, P

    A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Efficient non-Markovian quantum dynamics us- ing time-evolving matrix product operators, Nat. Com- mun.9, 3322 (2018)

    work page 2018

  53. [53]

    Ye and G

    E. Ye and G. K.-L. Chan, Constructing tensor network influence functionals for general quantum dynamics, J. Chem. Phys.155, 044104 (2021)

    work page 2021

  54. [54]

    Gribben, D

    D. Gribben, D. M. Rouse, J. Iles-Smith, A. Strathearn, H. Maguire, P. Kirton, A. Nazir, E. M. Gauger, and B. W. Lovett, Exact dynamics of nonadditive environ- ments in non-markovian open quantum systems, PRX Quantum3, 010321 (2022)

    work page 2022

  55. [55]

    Thoenniss, A

    J. Thoenniss, A. Lerose, and D. A. Abanin, Nonequi- librium quantum impurity problems via matrix-product 7 states in the temporal domain, Phys. Rev. B107, 195101 (2023)

    work page 2023

  56. [56]

    R. Chen, X. Xu, and C. Guo, Grassmann time-evolving matrix product operators for quantum impurity models, Phys. Rev. B109, 045140 (2024)

    work page 2024

  57. [57]

    Fr´ ıas-P´ erez, L

    M. Fr´ ıas-P´ erez, L. Tagliacozzo, and M. C. Ba˜ nuls, Con- verting Long-Range Entanglement into Mixture: Tensor- Network Approach to Local Equilibration, Phys. Rev. Lett.132, 100402 (2024)

    work page 2024

  58. [58]

    Cygorek and E

    M. Cygorek and E. M. Gauger, Understanding and utilizing the inner bonds of process tensors, arXiv 10.48550/arXiv.2404.01287 (2024), 2404.01287

    work page doi:10.48550/arxiv.2404.01287 2024

  59. [59]

    Cygorek and E

    M. Cygorek and E. M. Gauger, ACE: A general- purpose non-Markovian open quantum systems sim- ulation toolkit based on process tensors, arXiv 10.48550/arXiv.2405.19319 (2024), 2405.19319

    work page doi:10.48550/arxiv.2405.19319 2024

  60. [60]

    Schnell, A

    A. Schnell, A. Eckardt, and S. Denisov, Is there a floquet lindbladian?, Phys. Rev. B101, 100301 (2020)

    work page 2020

  61. [61]

    Chen, Y.-M

    H. Chen, Y.-M. Hu, W. Zhang, M. A. Kurniawan, Y. Shao, X. Chen, A. Prem, and X. Dai, Periodically driven open quantum systems: Spectral properties and nonequilibrium steady states, Phys. Rev. B109, 184309 (2024)

    work page 2024

  62. [62]

    Casas, J

    F. Casas, J. A. Oteo, and J. Ros, Floquet theory: expo- nential perturbative treatment, J. Phys. A: Math. Gen. 34, 3379 (2001)

    work page 2001

  63. [63]

    Rahav, I

    S. Rahav, I. Gilary, and S. Fishman, Effective Hamilto- nians for periodically driven systems, Phys. Rev. A68, 013820 (2003)

    work page 2003

  64. [64]

    A. Dey, D. Lonigro, K. Yuasa, and D. Burgarth, Error bounds for the Floquet-Magnus expansion and their ap- plication to the semiclassical quantum Rabi model, arXiv 10.48550/arXiv.2504.20533 (2025), 2504.20533

    work page doi:10.48550/arxiv.2504.20533 2025

  65. [65]

    Lendi, Extension of quantum dynamical semigroup generators for open systems to time-dependent hamilto- nians, Phys

    K. Lendi, Extension of quantum dynamical semigroup generators for open systems to time-dependent hamilto- nians, Phys. Rev. A33, 3358 (1986)

    work page 1986

  66. [66]

    Breuer, E.-M

    H.-P. Breuer, E.-M. Laine, and J. Piilo, Measure for the degree of non-markovian behavior of quantum processes in open systems, Phys. Rev. Lett.103, 210401 (2009)

    work page 2009

  67. [67]

    Kato and Y

    A. Kato and Y. Tanimura, Quantum heat current under non-perturbative and non-Markovian conditions: Appli- cations to heat machines, J. Chem. Phys.145, 224105 (2016)

    work page 2016

  68. [68]

    Gribben, A

    D. Gribben, A. Strathearn, G. E. Fux, P. Kirton, and B. W. Lovett, Using the Environment to Understand non-Markovian Open Quantum Systems, Quantum6, 847 (2022), 2106.04212v2

    work page arXiv 2022

  69. [69]

    Albarelli, B

    F. Albarelli, B. Vacchini, and A. Smirne, Pseudomode treatment of strong-coupling quantum thermodynamics, Quantum Sci. Technol.10, 015041 (2024)

    work page 2024

  70. [70]

    Koyanagi and Y

    S. Koyanagi and Y. Tanimura, Classical and quantum thermodynamics described as a system–bath model: The dimensionless minimum work principle, J. Chem. Phys. 160, 234112 (2024)

    work page 2024

  71. [71]

    Keeling, E

    J. Keeling, E. M. Stoudenmire, M.-C. Ba˜ nuls, and D. R. Reichman, Process Tensor Approaches to Non-Markovian Quantum Dynamics, arXiv 10.48550/arXiv.2509.07661 (2025), 2509.07661

    work page doi:10.48550/arxiv.2509.07661 2025

  72. [72]

    D. F. Walls and G. J. Milburn,Quantum Optics (Springer Berlin Heidelberg, 2008)

    work page 2008

  73. [73]

    Hartmann and W

    R. Hartmann and W. T. Strunz, Environmentally In- duced Entanglement – Anomalous Behavior in the Adi- abatic Regime, Quantum4, 347 (2020), 2006.04412v2

    work page arXiv 2020

  74. [74]

    M. W. S.R.J. Patrick, Fu-li Li and Y. Yang, Controlling entanglement dynamics of two qubits coupled to a common reservoir via a coherent field, Journal of Modern Optics57, 295 (2010), https://doi.org/10.1080/09500340903548887

    work page doi:10.1080/09500340903548887 2010

  75. [75]

    M. E. Kimchi-Schwartz, L. Martin, E. Flurin, C. Aron, M. Kulkarni, H. E. Tureci, and I. Siddiqi, Stabilizing en- tanglement via symmetry-selective bath engineering in superconducting qubits, Phys. Rev. Lett.116, 240503 (2016)

    work page 2016

  76. [76]

    H. T. Quan, Y.-x. Liu, C. P. Sun, and F. Nori, Quantum thermodynamic cycles and quantum heat engines, Phys. Rev. E76, 031105 (2007)

    work page 2007

  77. [77]

    Kosloff and Y

    R. Kosloff and Y. Rezek, The quantum harmonic otto cycle, Entropy19, 10.3390/e19040136 (2017)

    work page doi:10.3390/e19040136 2017

  78. [78]

    Alamo, F

    M. Alamo, F. Petiziol, and A. Eckardt, Minimal quan- tum heat pump based on high-frequency driving and non- Markovianity, Physical Review E109, 064121 (2024)

    work page 2024

  79. [79]

    K. H. Hughes, C. D. Christ, and I. Burghardt, Effective- mode representation of non-Markovian dynamics: A hi- erarchical approximation of the spectral density. I. Ap- plication to single surface dynamics, J. Chem. Phys.131, 024109 (2009)

    work page 2009

  80. [80]

    A. W. Chin, ´A. Rivas, S. F. Huelga, and M. B. Plenio, Ex- act mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal poly- nomials, J. Math. Phys.51, 092109 (2010)

    work page 2010

Showing first 80 references.