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REVIEW 2 major objections 1 minor 71 references

Large Fluctuations in Open Quantum Systems

T0 review · 2 major / 1 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read In driven dissipative quantum systems the large-deviation function for rare fluctuations develops lines and surfaces of discontinuous derivatives.

desk verdict The paper shows non-analytic large-deviation functions in driven open systems from competing instantons, but the semiclassical claim needs checking against quantum corrections. read the letter →

arxiv 2606.11822 v1 pith:XHPN23BT submitted 2026-06-10 quant-ph cond-mat.mes-hall

V. Yu. Mylnikov , S. O. Potashin , A. Kamenev This is my paper · ORCID
classification quant-phcond-mat.mes-hall
keywords large-deviationfunctionopenquantumsystemsdrivendissipativeinstantontrajectoriesKeldysh-LindbladactionKerroscillatornon-analyticityrarefluctuations
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

In equilibrium the probability distribution over phase space, such as the Wigner function, is analytic. The paper shows that this analyticity is generically lost once the system is both driven and dissipative. The large-deviation function that governs the statistics of atypical steady-state outcomes then contains lines or surfaces where its derivatives jump. These discontinuities arise because the same rare fluctuation can be produced by several distinct semiclassical trajectories whose dominance switches abruptly. The effect is demonstrated for a parametrically driven Kerr oscillator coupled linearly or nonlinearly to a bath.

What carries the argument

Competition among multiple distinct semiclassical instanton trajectories of the Keldysh-Lindblad action that realize the same rare fluctuation.

What would settle it

A calculation or measurement of the large-deviation function for the parametrically driven Kerr oscillator that remains everywhere differentiable would show that the claimed non-analyticities do not appear.

Watch

Extended reading notes

Core claim

We show that this property is generically lost in driven dissipative systems: their large-deviation function develops lines and surfaces across which its derivatives are discontinuous. Rare fluctuations in the amplitude and phase of the induced oscillations are governed by semiclassical instanton trajectories of the corresponding Keldysh-Lindblad action. We demonstrate that a given fluctuation can be realized through multiple distinct instanton trajectories. The competition between these trajectories leads to abrupt switching of the dominant instanton and, consequently, to non-analytic features in the large-deviation function.

Load-bearing premise

Rare fluctuations are governed by semiclassical instanton trajectories of the Keldysh-Lindblad action, and a given fluctuation can be realized through multiple distinct such trajectories whose competition produces the non-analyticity.

Editorial extensions

If this is right

  • The probabilities of atypical measurement outcomes in driven open systems can change abruptly across certain surfaces in phase space.
  • In the Kerr-oscillator example the statistics of amplitude and phase fluctuations exhibit these derivative discontinuities.
  • The dominant instanton trajectory switches at the locations of the non-analytic lines or surfaces.
  • The non-analyticity is presented as a generic feature of driven dissipative steady states rather than a special case.

Reading between the lines

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

  • Similar competition between trajectories could produce non-analytic large-deviation functions in other open quantum models that admit multiple instanton solutions.
  • Numerical sampling of rare events in driven dissipative systems may need to account for the abrupt switches rather than assuming smooth interpolation.
  • The locations of the non-analytic surfaces might serve as signatures that distinguish driven-dissipative dynamics from equilibrium ones in experiments.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The paper claims that in driven dissipative quantum systems the large-deviation function for atypical steady-state measurement outcomes develops lines and surfaces across which its derivatives are discontinuous, in contrast to the analytic phase-space distributions (e.g., Wigner function) found in equilibrium. This non-analyticity is attributed to competition among multiple distinct semiclassical instanton trajectories of the Keldysh-Lindblad action; the claim is illustrated with a parametrically driven Kerr oscillator coupled linearly or nonlinearly to a bath, where abrupt switching between dominant instantons produces the kinks or cusps.

Significance. If substantiated, the result would establish a qualitative distinction between equilibrium and driven open quantum systems in the structure of large-deviation functions, with potential consequences for the statistics of rare events in quantum optics and related platforms. The mechanistic identification of instanton competition as the origin of the non-analyticity supplies a concrete, falsifiable picture within the standard Keldysh-Lindblad formalism.

major comments (2)
  1. [Kerr-oscillator example (semiclassical treatment)] The central claim that non-analyticities survive generically rests on the semiclassical saddle-point approximation; the Kerr-oscillator example supplies no explicit bound on the magnitude of subleading fluctuation determinants or interference terms that could round the discontinuities across the switching surface.
  2. [Abstract and illustrative example] Generality is asserted from a single model without a parameter-free argument showing that the same multiple-trajectory competition mechanism persists in other driven-dissipative systems; the abstract states the property is 'generically lost' but the supporting analysis is model-specific.
minor comments (1)
  1. Notation for the large-deviation function I(observable) and the precise definition of the observable (amplitude/phase) should be introduced earlier for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments point by point below, clarifying the scope of the semiclassical analysis and the generality of the proposed mechanism.

read point-by-point responses

  1. Referee: [Kerr-oscillator example (semiclassical treatment)] The central claim that non-analyticities survive generically rests on the semiclassical saddle-point approximation; the Kerr-oscillator example supplies no explicit bound on the magnitude of subleading fluctuation determinants or interference terms that could round the discontinuities across the switching surface.

    Authors: The large-deviation function is defined as the leading exponential rate I = -lim (1/N) log P, obtained from the saddle-point evaluation of the Keldysh-Lindblad path integral. This rate is exactly the minimum action among competing instantons; at a switching surface the rate function is the lower envelope of two smooth branches and is therefore non-analytic whenever the gradients differ. Sub-exponential corrections arising from fluctuation determinants or interference enter only the prefactor and cannot remove the non-analyticity of the leading rate function itself. In open dissipative systems the environment further suppresses coherent interference between macroscopically distinct trajectories. We will add a short clarifying paragraph on this point in the revised manuscript. revision: partial

  2. Referee: [Abstract and illustrative example] Generality is asserted from a single model without a parameter-free argument showing that the same multiple-trajectory competition mechanism persists in other driven-dissipative systems; the abstract states the property is 'generically lost' but the supporting analysis is model-specific.

    Authors: The mechanism follows from the general structure of the Keldysh-Lindblad action for driven systems: the drive term renders the effective potential non-Hermitian, permitting multiple distinct instanton solutions that can cross in action. In equilibrium the corresponding action reduces to a form whose minimizing trajectory is unique for each observable, restoring analyticity. This distinction is independent of the specific Kerr parameters and holds for any driven dissipative system whose steady-state manifold supports multiple attractors. The Kerr oscillator serves only as an explicit illustration; we will revise the abstract and introduction to separate the general structural argument from the concrete example. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: derivation applies standard Keldysh-Lindblad instanton analysis to derive non-analyticity

full rationale

The paper's central result follows from minimizing the Keldysh-Lindblad action over semiclassical trajectories for the driven Kerr oscillator model; multiple distinct instantons compete to produce switching and kinks in the large-deviation function as a direct consequence of the variational problem. No step reduces by definition to the target non-analyticity, no parameters are fitted to the observable being predicted, and no load-bearing self-citation or imported uniqueness theorem is required. The derivation remains self-contained within the established formalism.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claim rests on the validity of the semiclassical instanton approximation within the Keldysh-Lindblad framework for large deviations; no free parameters or new entities are introduced in the abstract description.

assumptions (1)
  • domain assumption Semiclassical instanton trajectories of the Keldysh-Lindblad action govern rare fluctuations in driven open quantum systems.
    Invoked directly in the abstract as the method for describing atypical measurement outcomes.

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Cite this review

Pith. "Pith review of Large Fluctuations in Open Quantum Systems." pith.science (2026). https://pith.science/paper/XHPN23BT

@misc{pith2026260611822,
  author       = {Pith},
  title        = {Pith review of: Large Fluctuations in Open Quantum Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XHPN23BT}},
  note         = {Machine review of arXiv:2606.11822}
}
read the original abstract

We study statistics of atypical measurement outcomes in the steady states of driven open quantum systems. In equilibrium, the probability distribution over the phase space, as encoded in, e.g., the Wigner function, is analytic in the phase-space coordinates. We show that this property is generically lost in driven dissipative systems: their {\it large-deviation function} develops lines and surfaces across which its derivatives are discontinuous. As an illustrative example, we consider a parametrically driven Kerr oscillator coupled linearly and/or nonlinearly to a dissipative bath. Rare fluctuations in the amplitude and phase of the induced oscillations are governed by semiclassical instanton trajectories of the corresponding Keldysh-Lindblad action. We demonstrate that a given fluctuation can be realized through multiple distinct instanton trajectories. The competition between these trajectories leads to abrupt switching of the dominant instanton and, consequently, to non-analytic features in the large-deviation function.

Figures

Figures reproduced from arXiv: 2606.11822 by the authors.

Figure 1
Figure 1. (a,b) Stationary Wigner function W0(α, α∗ ) and effective potential − ln W0(α, α∗ ) (c,d) vs. phase-space coordinates Re(α) and Im(α). The first row presents the case of zero dephasing (κϕ = 0), where the exact (a,c) and WKB (d) solutions present (see Eqs. (15)-(17) and Appendix A). The second row shows the nonzero dephasing case (κϕ = 0.2), which does not admit the holomorphic decomposition (15) and is calculated n… view at source ↗
Figure 2
Figure 2. The real-time instanton trajectories, Eq. 37, spanning the fluctuation Riemann surface, [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Stokes lines (red) on the complex α plane, as de￾fined by Eq. (47). Within the inner Stokes region (blue), only the instanton with S− action contributes to the Wigner func￾tion. Within the outer Stokes region (green), both instantons with S± contribute. The two actions equalize along the anti￾Stokes lines (black), given by Eq. (23). The large deviation function is non-analytic along these lines. One possible choice … view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: (a,b) The large-deviation function from the in [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: The α-plane flow and the phase-slip instanton path (orange line) in the bistable regime. The phase-slip path starts at the classical fixed point α = α0 and ends at the saddle point α = 0 (red dots). From the saddle point to the opposite stationary point, the system evo…
Figure 6
Figure 6. Figure 6: (a-b) The large deviation function S(α, α¯) = min{S−(α, α¯), S+(α, α¯)} vs. phase-space coordinates Re(α) and Im(α). It is calculated numerically for zero dephasing rate κϕ = 0 (a) and finite dephasing κϕ = 0.03 (b) using Eq. (57). Red and blue curves correspond to non…
Figure 7
Figure 7. Figure 7: Stokes regions near the turning point z = 1. Within the inner Stokes region (blue), there is only one WKB solution Ψ−. Within the outer Stokes region (green), the solution is the sum of two WKB terms Ψ− + Ψ+. The Stokes lines are shown in red. A possible branch cut is …

Discussion (0). Continue with ORCID to comment.

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