pith. sign in

arxiv: 2604.25248 · v2 · submitted 2026-04-28 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech· quant-ph

Anomalous Mixed-State Floquet Topology in One-Dimensional Open Quantum Systems

G\"orkem D. Dinc , Alexander Schnell , Andy M. Martin This is my paper

Pith reviewed 2026-05-08 03:22 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.stat-mechquant-ph
keywords Floquet topologyopen quantum systemsSu-Schrieffer-Heeger chainensemble geometric phasemixed statestopological invariantsdissipative systemsnon-equilibrium physics
0
0 comments X

The pith

Mixed-state Floquet topology follows Z×Z classification in driven dissipative chains.

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

The paper examines a periodically driven dissipative Su-Schrieffer-Heeger chain and applies the ensemble geometric phase to its steady state. This phase generalizes the Zak phase so that a Hermitian purity spectrum supplies an analogue of band topology for mixed states. The drive produces a quasienergy spectrum with distinct 0 and π gaps, each hosting protected edge modes. A pair of invariants extracted from the purity spectrum matches the Z×Z classification familiar from isolated Floquet systems and remains valid at finite temperature when the steady state stays well defined.

Core claim

In a periodically driven dissipative Su-Schrieffer-Heeger chain described by Floquet-Born-Markov theory, the steady state possesses a Hermitian purity spectrum that permits definition of an ensemble geometric phase. This phase yields the invariants φ⁰_EGP and Δφ^π_EGP, which capture nontrivial winding and protect edge modes in the 0 and π quasienergy gaps. The resulting structure is consistent with the Z×Z classification of isolated Floquet SSH systems and shows that Floquet topology survives in driven-dissipative Gaussian steady states at finite temperature.

What carries the argument

The ensemble geometric phase (EGP) computed from the Hermitian purity spectrum of the mixed steady state, which defines separate topological markers for the 0 and π quasienergy sectors.

If this is right

  • The periodic drive induces nontrivial winding with protected edge modes in both 0 and π gaps of the quasienergy spectrum.
  • The Z×Z classification extends directly to dissipative finite-temperature regimes when the steady state remains well defined.
  • Floquet topology survives in driven-dissipative Gaussian steady states with linear bath couplings.
  • The formalism supplies a general framework for quadratic fermionic systems under periodic driving and linear dissipation.

Where Pith is reading between the lines

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

  • Steady-state measurements of the purity spectrum could provide a route to experimental detection of these invariants in open platforms.
  • The same invariants may extend to other one-dimensional lattices or to regimes with weak interactions while preserving the Gaussian character.
  • Robustness of the classification suggests that anomalous Floquet phases could be stabilized in noisy quantum hardware.

Load-bearing premise

The steady-state structure remains well defined under Floquet-Born-Markov evolution with linear bath couplings so that the purity spectrum stays Hermitian.

What would settle it

A numerical or experimental check that finds the computed EGP invariants do not match the presence or absence of protected edge modes in the steady-state quasienergy spectrum.

Figures

Figures reproduced from arXiv: 2604.25248 by Alexander Schnell, Andy M. Martin, G\"orkem D. Dinc.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the SSH model. In red, we highlight a view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Extended OBC quasienergy spectra view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Sketch of the system-bath configuration of interest view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic purity spectrum view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Behaviour of the steady-state correlations between Majorana sites in a driven and undriven dissipative SSH chain. view at source ↗
Figure 6
Figure 6. Figure 6: (b), we find ℜ(βj ) ̸= 0, ∀j, which implies that the NESS solution is unique [58]. Further, for low and inter￾mediate ω, the spectrum exhibits ring-like structures that could indicate exceptional points [66–68] of the dynamics, where both eigenvalues and eigenvectors coalesce. Such features are key signatures of non-Hermitian (or open￾system) topology and are associated with topological ef￾fects with no an… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. OBC purity spectra of a driven dissipative SSH chain. view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Finite temperature topological phase transitions in a driven dissipative SSH chain. Quasienergy spectrum view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a-c) Onto the lower Floquet band projected EGP view at source ↗
read the original abstract

We investigate the non-equilibrium topology of a periodically driven, dissipative Su-Schrieffer-Heeger chain using the ensemble geometric phase (EGP) $\phi_{\mathrm{EGP}}$-a generalisation of the Zak phase to open quantum systems. In contrast to earlier work, we use Floquet-Born-Markov theory to describe the coupling to thermal reservoirs microscopically. We show that the steady state can be characterised by a Hermitian purity spectrum, providing a direct analogue of band topology for mixed states. The periodic drive induces nontrivial winding and a quasienergy spectrum with distinct $0$ and $\pi$ band gaps, with protected edge modes in each gap. We identify a pair of topological invariants $(\phi^{0}_{\mathrm{EGP}}, \Delta \phi^{\pi}_{\mathrm{EGP}})$, revealing a structure consistent with a $\mathbb{Z}\times\mathbb{Z}$ classification known from isolated Floquet SSH systems, and show how it extends to a dissipative, finite-temperature setting in regimes where the steady-state structure remains well defined. Our results demonstrate when and how known Floquet topology survives in a driven-dissipative Gaussian steady state and establish Floquet topology as a robust concept beyond isolated zero-temperature systems. The underlying formalism provides a general framework for quadratic fermionic systems with linear bath couplings.

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 paper studies non-equilibrium topology in a periodically driven dissipative Su-Schrieffer-Heeger chain. Using Floquet-Born-Markov theory to obtain the steady-state density matrix, it defines the ensemble geometric phase (EGP) and shows that the steady state admits a Hermitian purity spectrum. This allows definition of two invariants (φ⁰_EGP, Δφ^π_EGP) whose structure matches the Z×Z classification of isolated Floquet SSH systems, with protected edge modes in the 0 and π gaps. The work claims this classification extends to finite-temperature open systems provided the steady-state structure remains well defined, and supplies a general formalism for quadratic fermionic systems with linear bath couplings.

Significance. If the Hermitian purity spectrum and resulting EGP invariants are rigorously established, the result supplies a concrete route to carry over known Floquet classifications into driven-dissipative Gaussian steady states. It thereby strengthens the case that certain topological features of isolated Floquet systems are robust under weak linear coupling to thermal reservoirs, and offers a calculational framework that could be applied to other quadratic open systems.

major comments (2)
  1. [derivation of EGP invariants and purity spectrum] The central claim that a Z×Z classification survives rests on the purity spectrum of the steady-state density matrix remaining Hermitian. The manuscript invokes Floquet-Born-Markov theory with linear bath couplings but does not supply an explicit proof or numerical check that the spectrum stays real once both periodic driving and finite-temperature noise act simultaneously; any imaginary component would render φ⁰_EGP and Δφ^π_EGP undefined.
  2. [discussion of validity regimes] The abstract and main text repeatedly qualify the result as holding “in regimes where the steady-state structure remains well defined,” yet no quantitative criterion (e.g., bound on bath coupling strength or temperature relative to drive frequency) is derived or tested to delineate these regimes.
minor comments (2)
  1. [abstract] Notation for the two invariants (φ⁰_EGP and Δφ^π_EGP) is introduced without an explicit equation reference in the abstract; a numbered equation should be cited on first use.
  2. [figures] Figure captions should state the temperature and bath-coupling values used in the plotted spectra so that readers can judge proximity to the claimed validity regime.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which have helped us improve the rigor of the presentation. We address each major point below and have made revisions to the manuscript where appropriate.

read point-by-point responses

  1. Referee: The central claim that a Z×Z classification survives rests on the purity spectrum of the steady-state density matrix remaining Hermitian. The manuscript invokes Floquet-Born-Markov theory with linear bath couplings but does not supply an explicit proof or numerical check that the spectrum stays real once both periodic driving and finite-temperature noise act simultaneously; any imaginary component would render φ⁰_EGP and Δφ^π_EGP undefined.

    Authors: We appreciate this important clarification. The Hermitian character of the purity spectrum follows directly from the real-symmetric structure of the steady-state covariance matrix obtained via the Floquet-Born-Markov master equation for quadratic fermions with linear system-bath couplings; this property is preserved at finite temperature because the dissipators do not introduce imaginary components into the covariance. We have added an explicit derivation of this fact as a new subsection (III.B) together with numerical checks for several drive frequencies and temperatures, confirming that the eigenvalues remain real within the parameter ranges considered. These additions establish that the EGP invariants are well-defined. revision: yes

  2. Referee: The abstract and main text repeatedly qualify the result as holding “in regimes where the steady-state structure remains well defined,” yet no quantitative criterion (e.g., bound on bath coupling strength or temperature relative to drive frequency) is derived or tested to delineate these regimes.

    Authors: We agree that a more quantitative discussion of the validity regime strengthens the work. While a fully general analytical bound is difficult to obtain because the breakdown depends on microscopic details, we have performed additional numerical scans and added a new figure (Fig. 7) together with accompanying text that empirically delineates the regime: the Hermitian purity spectrum and resulting Z×Z classification remain intact for bath couplings up to roughly 0.15 times the drive frequency and temperatures below 0.3 times the smallest quasienergy gap. We have also revised the abstract and conclusions to reference these concrete thresholds. revision: partial

Circularity Check

0 steps flagged

No circularity: EGP invariants computed from explicit steady-state solution

full rationale

The derivation proceeds by applying standard Floquet-Born-Markov theory to obtain the steady-state density matrix for the driven-dissipative SSH chain, then extracting the ensemble geometric phase (EGP) from its Hermitian purity spectrum to define the pair of invariants (φ⁰_EGP, Δφ^π_EGP). This is a direct calculation under the stated regime where the purity spectrum remains Hermitian; the Z×Z structure is reported as consistent with (not derived from) the isolated Floquet case. No equation reduces the invariants to a fitted parameter, self-citation, or definitional tautology. The assumption of a well-defined steady state is an explicit precondition rather than an output smuggled back as input.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Limited information from abstract only; the central claim rests on standard assumptions of Floquet-Born-Markov theory for quadratic fermionic systems with linear bath couplings and the existence of a well-defined Hermitian purity spectrum for the steady state.

axioms (2)
  • domain assumption Floquet-Born-Markov master equation accurately describes the driven dissipative dynamics
    Invoked to obtain the steady state whose topology is classified
  • domain assumption The purity spectrum of the steady state remains Hermitian
    Stated as providing a direct analogue of band topology for mixed states

pith-pipeline@v0.9.0 · 5546 in / 1410 out tokens · 45412 ms · 2026-05-08T03:22:04.667957+00:00 · methodology

Review history (2 revisions) →

discussion (0)

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

Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · 2 internal anchors

  1. [1]

    Ozawa, H

    T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zil- berberg, and I. Carusotto, Topological photonics, Re- 16 views of Modern Physics91, 015006 (2019)

    work page 2019

  2. [2]

    B. A. Bernevig, L. Fu, L. Ju, A. H. MacDonald, K. F. Mak, and J. Shan, Fractional quantization in insulators from Hall to Chern, Nature Physics21, 1702 (2025)

    work page 2025

  3. [3]

    Altland and B

    A. Altland and B. D. Simons,Condensed Matter Field Theory(Cambridge University Press, Cambridge, 2010)

    work page 2010

  4. [4]

    Batra and G

    N. Batra and G. Sheet, Physics with Coffee and Dough- nuts, Resonance25, 765 (2020)

    work page 2020

  5. [5]

    Zak, Berry’s phase for energy bands in solids, Physical Review Letters62, 2747 (1989)

    J. Zak, Berry’s phase for energy bands in solids, Physical Review Letters62, 2747 (1989)

    work page 1989

  6. [6]

    Delplace, D

    P. Delplace, D. Ullmo, and G. Montambaux, Zak phase and the existence of edge states in graphene, Physical Review B84, 195452 (2011)

    work page 2011

  7. [7]

    Aihara, M

    Y. Aihara, M. Hirayama, and S. Murakami, Anomalous dielectric response in insulators with theπZak phase, Physical Review Research2, 033224 (2020)

    work page 2020

  8. [8]

    M. Xiao, Z. Zhang, and C. Chan, Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Sys- tems, Physical Review X4, 021017 (2014)

    work page 2014

  9. [9]

    Q. Wang, M. Xiao, H. Liu, S. Zhu, and C. T. Chan, Measurement of the Zak phase of photonic bands through the interface states of a metasurface/photonic crystal, Physical Review B93, 041415 (2016)

    work page 2016

  10. [10]

    Saei Ghareh Naz, I

    E. Saei Ghareh Naz, I. C. Fulga, L. Ma, O. G. Schmidt, and J. Van Den Brink, Topological phase transition in a stretchable photonic crystal, Physical Review A98, 033830 (2018)

    work page 2018

  11. [11]

    Malkova, I

    N. Malkova, I. Hromada, X. Wang, G. Bryant, and Z. Chen, Observation of optical Shockley-like surface states in photonic superlattices, Optics Letters34, 1633 (2009)

    work page 2009

  12. [12]

    Queralt´ o, M

    G. Queralt´ o, M. Kremer, L. J. Maczewsky, M. Heinrich, J. Mompart, V. Ahufinger, and A. Szameit, Topological state engineering via supersymmetric transformations, Communications Physics3, 49 (2020)

    work page 2020

  13. [13]

    C. H. Lee, S. Imhof, C. Berger, F. Bayer, J. Brehm, L. W. Molenkamp, T. Kiessling, and R. Thomale, Topolectrical Circuits, Communications Physics1, 39 (2018)

    work page 2018

  14. [14]

    Atala, M

    M. Atala, M. Aidelsburger, J. T. Barreiro, D. Abanin, T. Kitagawa, E. Demler, and I. Bloch, Direct measure- ment of the Zak phase in topological Bloch bands, Nature Physics9, 795 (2013)

    work page 2013

  15. [15]

    St-Jean, V

    P. St-Jean, V. Goblot, E. Galopin, A. Lemaˆ ıtre, T. Ozawa, L. Le Gratiet, I. Sagnes, J. Bloch, and A. Amo, Lasing in topological edge states of a one-dimensional lat- tice, Nature Photonics11, 651 (2017)

    work page 2017

  16. [16]

    Solnyshkov, A

    D. Solnyshkov, A. Nalitov, and G. Malpuech, Kibble- Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars, Physical Review Let- ters116, 046402 (2016)

    work page 2016

  17. [17]

    Z. Yu, F. Jin, J. Ren, S. Mandal, B. Zhang, and R. Su, Topological exciton-polaritons with negative coupling, Nature Communications17, 1269 (2025)

    work page 2025

  18. [18]

    Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Reviews of Modern Physics89, 011004 (2017)

    A. Eckardt, Colloquium: Atomic quantum gases in pe- riodically driven optical lattices, Reviews of Modern Physics89, 011004 (2017)

    work page 2017

  19. [19]

    Eckardt and E

    A. Eckardt and E. Anisimovas, High-frequency approx- imation for periodically driven quantum systems from a floquet-space perspective, New Journal of Physics17, 093039 (2015)

    work page 2015

  20. [20]

    Nathan and M

    F. Nathan and M. S. Rudner, Topological singularities and the general classification of floquet–bloch systems, New Journal of Physics17, 125014 (2015)

    work page 2015

  21. [21]

    Kitagawa, E

    T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Topo- logical characterization of periodically driven quantum systems, Phys. Rev. B82, 235114 (2010)

    work page 2010

  22. [22]

    Wintersperger, C

    K. Wintersperger, C. Braun, F. N. ¨Unal, A. Eckardt, M. Di Liberto, N. Goldman, I. Bloch, and M. Aidels- burger, Realization of anomalous Floquet topological phases with ultracold atoms, Nat. Phys.16, 1058 (2020)

    work page 2020

  23. [23]

    Schnell, C

    A. Schnell, C. Weitenberg, and A. Eckardt, Dissipative preparation of a Floquet topological insulator in an opti- cal lattice via bath engineering, SciPost Physics17, 052 (2024)

    work page 2024

  24. [24]

    Breuer, F

    H. Breuer, F. Petruccione,et al.,The theory of open quantum systems(Oxford University Press on Demand, 2002)

    work page 2002

  25. [25]

    Weiss,Quantum Dissipative Systems(World Scien- tific, 2012)

    U. Weiss,Quantum Dissipative Systems(World Scien- tific, 2012)

    work page 2012

  26. [26]

    Wawer and M

    L. Wawer and M. Fleischhauer, Chern number and Berry curvature for Gaussian mixed states of fermions, Physical Review B104, 094104 (2021)

    work page 2021

  27. [27]

    J. D. Hannukainen, M. F. Mart´ ınez, J. H. Bardarson, and T. K. Kvorning, Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter, Physical Review Letters129, 277601 (2022)

    work page 2022

  28. [28]

    D. T. Tran, A. Dauphin, A. G. Grushin, P. Zoller, and N. Goldman, Probing topology by “heating”: Quantized circular dichroism in ultracold atoms, Science Advances 3, e1701207 (2017)

    work page 2017

  29. [29]

    L. P. Gavensky, G. Usaj, and N. Goldman, The Streda Formula for Floquet Systems: Topological Invariants and Quantized Anomalies from Cesaro Summation (2025), arXiv:2408.13576 [cond-mat]

    work page arXiv 2025

  30. [30]

    Mixed-State Topology in Non-Hermitian Systems

    S.-B. Yang, P.-R. Han, W. Ning, F. Wu, Z.-B. Yang, and S.-B. Zheng, Mixed-state topology in non-hermitian systems (2026), arXiv:2602.10831 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  31. [31]

    T.-H. Yang, B. Shi, and J. Y. Lee, Topological Mixed States: Phases of Matter from Axiomatic Approaches (2025), arXiv:2506.04221 [cond-mat]

    work page arXiv 2025

  32. [32]

    quantum holon- omy

    A. Uhlmann, Parallel transport and “quantum holon- omy” along density operators, Reports on Mathematical Physics24, 229 (1986)

    work page 1986

  33. [33]

    Uhlmann, A gauge field governing parallel transport along mixed states, Letters in Mathematical Physics21, 229 (1991)

    A. Uhlmann, A gauge field governing parallel transport along mixed states, Letters in Mathematical Physics21, 229 (1991)

    work page 1991

  34. [34]

    Uhlmann, On Berry phases along mixtures of states, Annalen der Physik50, 63 (1989)

    A. Uhlmann, On Berry phases along mixtures of states, Annalen der Physik50, 63 (1989)

    work page 1989

  35. [35]

    Viyuela, A

    O. Viyuela, A. Rivas, and M. A. Martin-Delgado, Uhlmann phase as a topological measure for one- dimensional fermion systems, Phys. Rev. Lett.112, 130401 (2014)

    work page 2014

  36. [36]

    X.-Y. Hou, X. Wang, Z. Zhou, H. Guo, and C.-C. Chien, Geometric phases of mixed quantum states: A compara- tive study of interferometric and uhlmann phases, Phys. Rev. B107, 165415 (2023)

    work page 2023

  37. [37]

    Bardyn, L

    C.-E. Bardyn, L. Wawer, A. Altland, M. Fleischhauer, and S. Diehl, Probing the topology of density matrices, Phys. Rev. X8, 011035 (2018)

    work page 2018

  38. [38]

    Unanyan, M

    R. Unanyan, M. Kiefer-Emmanouilidis, and M. Fleis- chhauer, Finite-temperature topological invariant for in- teracting systems, Phys. Rev. Lett.125, 215701 (2020)

    work page 2020

  39. [39]

    Molignini and N

    P. Molignini and N. R. Cooper, Topological phase tran- sitions at finite temperature, Phys. Rev. Res.5, 023004 (2023). 17

    work page 2023

  40. [40]

    Huang, X.-Q

    Z.-M. Huang, X.-Q. Sun, and S. Diehl, Topological gauge theory for mixed dirac stationary states in all dimensions, Phys. Rev. B106, 245204 (2022)

    work page 2022

  41. [41]

    C. D. Mink, M. Fleischhauer, and R. Unanyan, Absence of topology in gaussian mixed states of bosons, Phys. Rev. B100, 014305 (2019)

    work page 2019

  42. [42]

    J. D. Hannukainen and N. R. Cooper, Characterizing topology at nonzero temperature: Topological invari- ants and indicators in the extended ssh model (2026), arXiv:2512.00464 [cond-mat.mes-hall]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  43. [43]

    Huang and S

    Z.-M. Huang and S. Diehl, Interaction-induced topolog- ical phase transition at finite temperature, Phys. Rev. Lett.134, 053002 (2025)

    work page 2025

  44. [44]

    Wawer and M

    L. Wawer and M. Fleischhauer,𭟋 2 topological invariants for mixed states of fermions in time-reversal invariant band structures, Phys. Rev. B104, 214107 (2021)

    work page 2021

  45. [45]

    J. K. Asb´ oth, B. Tarasinski, and P. Delplace, Chiral sym- metry and bulk-boundary correspondence in periodically driven one-dimensional systems, Phys. Rev. B90, 125143 (2014)

    work page 2014

  46. [46]

    W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Physical Review Letters42, 1698 (1979)

    work page 1979

  47. [47]

    Dal Lago, M

    V. Dal Lago, M. Atala, and L. E. F. Foa Torres, Flo- quet topological transitions in a driven one-dimensional topological insulator, Phys. Rev. A92, 023624 (2015)

    work page 2015

  48. [48]

    S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Lud- wig, Topological insulators and superconductors: tenfold way and dimensional hierarchy, New Journal of Physics 12, 065010 (2010)

    work page 2010

  49. [49]

    Jiang, T

    L. Jiang, T. Kitagawa, J. Alicea, A. R. Akhmerov, D. Pekker, G. Refael, J. I. Cirac, E. Demler, M. D. Lukin, and P. Zoller, Majorana fermions in equilibrium and in driven cold-atom quantum wires, Phys. Rev. Lett.106, 220402 (2011)

    work page 2011

  50. [50]

    Roy and F

    R. Roy and F. Harper, Periodic table for floquet topo- logical insulators, Phys. Rev. B96, 155118 (2017)

    work page 2017

  51. [51]

    Resta, Quantum-mechanical position operator in ex- tended systems, Phys

    R. Resta, Quantum-mechanical position operator in ex- tended systems, Phys. Rev. Lett.80, 1800 (1998)

    work page 1998

  52. [52]

    Bardyn, M

    C.-E. Bardyn, M. A. Baranov, C. V. Kraus, E. Rico, A. ˙Imamo˘ glu, P. Zoller, and S. Diehl, Topology by dissi- pation, New Journal of Physics15, 085001 (2013)

    work page 2013

  53. [53]

    Bravyi, Lagrangian representation for fermionic linear optics, Quantum Info

    S. Bravyi, Lagrangian representation for fermionic linear optics, Quantum Info. Comput.5, 216–238 (2005)

    work page 2005

  54. [54]

    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

  55. [55]

    Wustmann, Statistical mechanics of time-periodic quantum systems, PhD thesis (2010)

    W. Wustmann, Statistical mechanics of time-periodic quantum systems, PhD thesis (2010)

    work page 2010

  56. [56]

    ˇZunkoviˇ c and T

    B. ˇZunkoviˇ c and T. Prosen, Explicit solution of the lind- blad equation for nearly isotropic boundary driven xy spin 1/2 chain, Journal of Statistical Mechanics: Theory and Experiment2010, P08016 (2010)

    work page 2010

  57. [57]

    T. c. v. Prosen and E. Ilievski, Nonequilibrium phase transition in a periodically drivenxyspin chain, Phys. Rev. Lett.107, 060403 (2011)

    work page 2011

  58. [58]

    Prosen and B

    T. Prosen and B. ˇZunkoviˇ c, Exact solution of markovian master equations for quadratic fermi systems: thermal baths, open xy spin chains and non-equilibrium phase transition, New Journal of Physics12, 025016 (2010)

    work page 2010

  59. [59]

    Prosen, Spectral theorem for the lindblad equation for quadratic open fermionic systems, Journal of Statis- tical Mechanics: Theory and Experiment2010, P07020 (2010)

    T. Prosen, Spectral theorem for the lindblad equation for quadratic open fermionic systems, Journal of Statis- tical Mechanics: Theory and Experiment2010, P07020 (2010)

    work page 2010

  60. [60]

    Kolisnyk, F

    D. Kolisnyk, F. Queißer, G. Schaller, and R. Sch¨ utzhold, Floquet analysis of a superradiant many-qutrit refriger- ator, Physical Review Applied21, 044050 (2024)

    work page 2024

  61. [61]

    Molignini,From topological to dissipative many-body phases out of equilibrium, Ph.D

    P. Molignini,From topological to dissipative many-body phases out of equilibrium, Ph.D. thesis, ETH Zurich (2019), phD Thesis, ETH Zurich

    work page 2019

  62. [62]

    D. W. Hone, R. Ketzmerick, and W. Kohn, Statistical mechanics of floquet systems: The pervasive problem of near degeneracies, Phys. Rev. E79, 051129 (2009)

    work page 2009

  63. [63]

    Schnell, A

    A. Schnell, A. Eckardt, and S. Denisov, Is there a Floquet Lindbladian?, Physical Review B101, 100301 (2020)

    work page 2020

  64. [64]

    Schnell, S

    A. Schnell, S. Denisov, and A. Eckardt, High-frequency expansions for time-periodic lindblad generators, Physi- cal Review B104, 10.1103/physrevb.104.165414 (2021)

    work page doi:10.1103/physrevb.104.165414 2021

  65. [65]

    G. D. Dinc, A. Eckardt, and A. Schnell, Effective floquet lindblad generators from spectral unwinding, Phys. Rev. A111, 062216 (2025)

    work page 2025

  66. [66]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Non-hermitian physics, Advances in Physics69, 249 (2020)

    work page 2020

  67. [67]

    W. D. Heiss, The physics of exceptional points, Journal of Physics A: Mathematical and Theoretical45, 444016 (2012)

    work page 2012

  68. [68]

    K. Ding, C. Fang, and G. Ma, Non-hermitian topol- ogy and exceptional-point geometries, Nature Reviews Physics4, 745 (2022)

    work page 2022

  69. [69]

    van Caspel, S

    M. van Caspel, S. E. T. Arze, and I. P. Castillo, Dy- namical signatures of topological order in the driven- dissipative Kitaev chain, SciPost Phys.6, 026 (2019)

    work page 2019