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arxiv: 2505.05202 · v1 · submitted 2025-05-08 · 🪐 quant-ph

Switching Dynamics of Metastable Open Quantum Systems

Ya-Xin Xiang , Weibin Li , Zhengyang Bai , Yu-Qiang Ma This is my paper

Pith reviewed 2026-05-22 16:04 UTC · model grok-4.3

classification 🪐 quant-ph
keywords open quantum systemsmetastabilityquantum jumpsLiouvillian gapstochastic switchingArrhenius lawlarge deviationsinstantons
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The pith

Stochastic switching in bistable open quantum systems erases initial condition memory and limits relaxation to rare transitions obeying an Arrhenius law with inverse system size as effective temperature.

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

This paper shows that in Markovian open quantum systems with bistability, noise-induced stochastic switching between metastable states quickly erases the memory of initial conditions, making relaxation depend on the rare switching events rather than the initial state. This contrasts with cases lacking switching, where a small Liouvillian gap may or may not slow relaxation depending on starting conditions. The switching rates follow the Arrhenius law, with the inverse system size acting as the nonequilibrium analog of temperature, consistent with the exponential scaling of the Liouvillian gap. The authors extend large-deviation and instanton methods to the quantum jump process using dynamical path integrals to connect quasipotentials to rare fluctuation probabilities. This matters for understanding relaxation in dissipative quantum systems far from the thermodynamic limit, such as qubits and Rydberg atoms.

Core claim

In Markovian open quantum systems with bistability, trajectory-level stochastic switching due to quantum jumps causes the memory of initial conditions to be lost rapidly, with relaxation governed by the infrequent transitions between metastable states. Without such switching, slow relaxation from a small spectral gap depends on the choice of initial state. The switching rates conform to the Arrhenius law, where the inverse system size plays the role of an effective temperature, aligning with the exponential dependence of the Liouvillian gap on system size. The connection between the quasipotential functional and probabilities of rare fluctuations is extended to the quantum domain through the

What carries the argument

Distinction between spectrum-level metastability via small Liouvillian gap and trajectory-level metastability via stochastic switching in quantum jumps, analyzed with large-deviation principles and instanton methods.

If this is right

  • Relaxation dynamics become independent of initial states when stochastic switching is active.
  • Switching rates scale exponentially with system size according to the Arrhenius form.
  • Inverse system size functions as the nonequilibrium analog of temperature for relaxation rates.
  • Large-deviation theory connects quasipotentials to rare-event probabilities in the quantum jump process.

Where Pith is reading between the lines

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

  • Measurements of switching times in Rydberg-atom or qubit arrays could test the predicted dependence on system size.
  • The approach may offer a route to predict long-term stability in engineered dissipative quantum devices.
  • Similar Arrhenius behavior could appear in other nonequilibrium quantum systems dominated by rare jumps.

Load-bearing premise

The open quantum system is Markovian and bistable in a manner that produces both a small Liouvillian gap and observable trajectory-level switching, allowing large-deviation and instanton formalisms to extend directly to the quantum jump process.

What would settle it

A quantum-jump simulation or experiment in which measured switching rates deviate from Arrhenius scaling with inverse system size, or in which relaxation times remain sensitive to initial conditions despite the presence of switching.

Figures

Figures reproduced from arXiv: 2505.05202 by Weibin Li, Ya-Xin Xiang, Yu-Qiang Ma, Zhengyang Bai.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of quantum metastability and collective quan [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) MF stable (unstable) fixed points as a function of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Real part of the Liouvillian eigenvalues for (a) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Average excited population according to the density [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Finite-size scaling of the ratio of the steady-state [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Optimal switching paths (instantons) obtained within [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Average excitation population of simulated quantum [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a) The difference in the normalized effective en [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
read the original abstract

Classical metastability manifests as noise-driven switching between disjoint basins of attraction and slowing down of relaxation, quantum systems like qubits and Rydberg atoms exhibit analogous behavior through collective quantum jumps and long-lived Liouvillian modes with a small spectral gap. Though any metastable mode is expected to decay after a finite time, stochastic switching persists indefinitely. Here, we elaborate on the connection between switching dynamics and quantum metastability through the lens of the large deviation principles, spectral decomposition, and quantum-jump simulations. Specifically, we distinguish the trajectory-level noise-induced metastability (stochastic switching) from the spectrum-level deterministic metastability (small Liouvillian gap) in a Markovian open quantum system with bistability. Without stochastic switching, whether a small spectral gap leads to slow relaxation depends on initial states. In contrast, with switching, the memory of initial conditions is quickly lost, and the relaxation is limited by the rare switching between the metastable states. Consistent with the exponential scaling of the Liouvillian gap with system size, the switching rates conform to the Arrhenius law, with the inverse system size serving as the nonequilibrium analog of temperature. Using the dynamical path integral and the instanton approach, we further extend the connection between the quasipotential functional and the probabilities of rare fluctuations to the quantum realm. These results provide new insights into quantum bistability and the relaxation processes of strongly interacting, dissipative quantum systems far away from the thermodynamic limit.

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 examines metastability in Markovian open quantum systems with bistability, distinguishing spectral-level metastability (small Liouvillian gap) from trajectory-level stochastic switching. It claims that switching rates obey an Arrhenius law with inverse system size 1/N as the effective nonequilibrium temperature, that relaxation is limited by rare switches once switching is present, and that the classical large-deviation/instanton formalism extends to quantum jump processes via a dynamical path integral, yielding a quasipotential that governs rare-event probabilities.

Significance. If the extension of the instanton method to quantum trajectories is placed on a rigorous footing with controlled error estimates, the work would usefully connect spectral properties of the Liouvillian to observable switching statistics in dissipative quantum systems such as Rydberg arrays or driven qubits. The distinction between initial-state-dependent relaxation and switching-limited relaxation is conceptually clear and could guide experiments that monitor both ensemble averages and single-shot trajectories.

major comments (2)
  1. [§4] §4 (instanton approach and dynamical path integral): the central identification of the quasipotential with the rate function for quantum-jump trajectories assumes that coherent evolution between jumps produces no leading-order correction to the large-deviation rate function. No explicit bound or scaling argument is supplied that controls the size of these corrections when the coherent Hamiltonian is non-negligible relative to the jump rates.
  2. [§3] §3 (quantum-jump simulations and Arrhenius scaling): the reported switching rates are stated to conform to Arrhenius behavior with 1/N as temperature, yet the manuscript supplies neither a direct comparison against exact diagonalization for small N nor an error estimate on the extracted rates. Without such a check, it remains unclear whether the observed scaling is limited by the Liouvillian gap or by finite-sampling effects in the trajectory ensemble.
minor comments (2)
  1. The notation for the quasipotential functional is introduced without an explicit comparison to its classical counterpart; a short paragraph clarifying the precise definition would aid readability.
  2. Several references to prior work on Liouvillian spectral gaps in driven-dissipative systems are cited only in passing; adding one or two sentences that locate the present Arrhenius claim relative to those earlier results would strengthen the introduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major comment below and will revise the manuscript to incorporate additional arguments and validations as indicated.

read point-by-point responses

  1. Referee: §4 (instanton approach and dynamical path integral): the central identification of the quasipotential with the rate function for quantum-jump trajectories assumes that coherent evolution between jumps produces no leading-order correction to the large-deviation rate function. No explicit bound or scaling argument is supplied that controls the size of these corrections when the coherent Hamiltonian is non-negligible relative to the jump rates.

    Authors: We agree that an explicit control on corrections arising from coherent evolution between jumps would strengthen the presentation. In the revised manuscript we add a scaling analysis in §4. For the bistable models considered, the jump rates scale linearly with system size N while coherent terms remain O(1); under these conditions the coherent contribution to the leading large-deviation rate function is sub-exponential. We include a brief derivation that bounds the relative error by the ratio of coherent frequency to jump rate, which vanishes in the large-N limit relevant to the Arrhenius scaling. revision: yes

  2. Referee: §3 (quantum-jump simulations and Arrhenius scaling): the reported switching rates are stated to conform to Arrhenius behavior with 1/N as temperature, yet the manuscript supplies neither a direct comparison against exact diagonalization for small N nor an error estimate on the extracted rates. Without such a check, it remains unclear whether the observed scaling is limited by the Liouvillian gap or by finite-sampling effects in the trajectory ensemble.

    Authors: We acknowledge the value of this validation. Although exact diagonalization is infeasible for the system sizes at which switching becomes observable, we have added a new subsection in §3 that compares switching rates extracted from quantum-jump trajectories with the inverse Liouvillian gap for small N (N≤10). The two agree within statistical uncertainties. We also report bootstrap error estimates on the trajectory-derived rates (based on 10^4 independent realizations) and confirm that the 1/N Arrhenius scaling persists after accounting for sampling variance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation extends classical methods independently

full rationale

The paper distinguishes trajectory-level stochastic switching from spectrum-level small Liouvillian gap, then invokes large-deviation principles and the dynamical path integral plus instanton formalism to connect quasipotentials to rare-event probabilities in the quantum-jump process. The Arrhenius-law statement is presented as consistent with (not derived from) the known exponential gap scaling, while the core technical step is the claimed direct applicability of the classical instanton construction to the quantum unraveling. No equation is shown to reduce to a fitted parameter or to a self-citation that itself assumes the target result; the extension is offered as an independent argument rather than a renaming or tautology. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard open-quantum-system assumptions (Markovian master equation, existence of bistable steady states) and classical large-deviation theory; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption The dynamics are governed by a Markovian Lindblad master equation.
    Invoked throughout the abstract when discussing Liouvillian spectrum and quantum jumps.
  • domain assumption Large-deviation principles and instanton methods apply to the quantum jump process.
    Used to connect quasipotential to rare switching probabilities.

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Forward citations

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