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arxiv: 2506.18334 · v3 · pith:LFREKBLAnew · submitted 2025-06-23 · ✦ hep-th · astro-ph.CO· hep-lat· hep-ph· quant-ph

False Vacuum Decay across the Quantum-to-Thermal Crossover: A Comparison of Real-Time Observables

Haiyang Wang , Renhui Qin , Ligong Bian This is my paper

Pith reviewed 2026-05-22 00:00 UTC · model grok-4.3

classification ✦ hep-th astro-ph.COhep-lathep-phquant-ph
keywords false vacuum decayquantum-to-thermal crossoverWigner functional latticenucleation rateconnected cluster criterionglobal survival criterionreal-time observablesmetastable decay
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The pith

A connected-cluster survival criterion extracts accurate false vacuum decay rates across the quantum-to-thermal crossover.

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

The paper develops a real-time Wigner-functional lattice framework with positive Hartree-Gaussian initial sampling to simulate false vacuum decay. It introduces a connected-cluster survival criterion to measure decay rates from the quantum regime to thermal nucleation. At high temperatures this criterion matches the Hartree-resummed thermal nucleation benchmark, while the global-survival criterion underestimates rates because of multi-seed dynamics and global averaging. At low temperatures the two criteria converge in the dilute-event regime, though the false-vacuum fraction observable can be affected by transient spatial conversion and kink-antikink reflection. Clarifying how different real-time observables encode distinct aspects of metastable decay helps interpret numerical results for phase transitions.

Core claim

We develop a real-time Wigner-functional lattice framework with positive Hartree-Gaussian initial sampling and introduce a connected-cluster survival criterion for extracting false-vacuum decay rates across the crossover from quantum fluctuations to thermal nucleation. At high temperatures, the connected-cluster rate agrees well with the Hartree-resummed thermal nucleation benchmark, while the commonly used global-survival criterion can give substantially smaller rates because of multi-seed dynamics and global averaging. At low temperatures, the connected-cluster and global-survival rates approach each other in the dilute-event regime, whereas the false-vacuum fraction observable can be cont

What carries the argument

The connected-cluster survival criterion, which identifies local clusters of field values to determine decay events without relying on global field averages.

If this is right

  • At high temperatures the connected-cluster rate matches the Hartree-resummed benchmark for thermal nucleation.
  • The global-survival criterion underestimates decay rates because of multi-seed dynamics and global averaging.
  • At low temperatures the connected-cluster and global-survival rates converge in the dilute-event regime.
  • The false-vacuum fraction observable can be contaminated by transient spatial conversion and kink-antikink reflection.

Where Pith is reading between the lines

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

  • In large-volume simulations local observables like the connected-cluster criterion may be required to avoid systematic underestimation from multiple nucleation seeds.
  • The real-time lattice framework could be applied to other potentials or higher-dimensional models to test the robustness of the crossover behavior.
  • Results highlight the need for careful observable selection when numerically simulating first-order phase transitions in cosmology or condensed matter.

Load-bearing premise

The positive Hartree-Gaussian initial sampling within the real-time Wigner-functional lattice framework accurately captures the quantum-to-thermal crossover dynamics without introducing uncontrolled artifacts.

What would settle it

Direct comparison of the connected-cluster extracted rate against the known Hartree-resummed analytical expression for thermal nucleation in the high-temperature limit.

Figures

Figures reproduced from arXiv: 2506.18334 by Haiyang Wang, Ligong Bian, Renhui Qin.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic illustration of the solution of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The decay rate as a function of temperature for dif [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The ratio of the initial energy density [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Statistical distribution of initial field values at different temperatures. Here, [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The power spectra evolution under different [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The average power spectrum of the ensemble, where [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Variations of average field values over time. [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Variations of false vacuum probabilities over time. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Evolution of the quasi-wavefunction under different values of [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
read the original abstract

We develop a real-time Wigner-functional lattice framework with positive Hartree-Gaussian initial sampling and introduce a connected-cluster survival criterion for extracting false-vacuum decay rates across the crossover from quantum fluctuations to thermal nucleation. At high temperatures, the connected-cluster rate agrees well with the Hartree-resummed thermal nucleation benchmark, while the commonly used global-survival criterion can give substantially smaller rates because of multi-seed dynamics and global averaging. At low temperatures, the connected-cluster and global-survival rates approach each other in the dilute-event regime, whereas the false-vacuum fraction observable can be contaminated by transient spatial conversion and kink-antikink reflection. Our results clarify how different real-time observables encode distinct aspects of metastable decay.

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

3 major / 2 minor

Summary. The paper develops a real-time Wigner-functional lattice framework employing positive Hartree-Gaussian initial sampling to simulate false vacuum decay across the quantum-to-thermal crossover. It introduces a connected-cluster survival criterion for rate extraction and compares it to the global-survival criterion and false-vacuum fraction observable. The central results are that the connected-cluster rate agrees with a Hartree-resummed thermal nucleation benchmark at high T (while global-survival underestimates due to multi-seed effects), the two rates converge at low T in the dilute regime, and the false-vacuum fraction can be contaminated by transients and kink reflections.

Significance. If the results hold, the work provides a useful clarification of how different real-time observables capture distinct aspects of metastable decay, particularly the role of multi-seed dynamics and global averaging. The lattice framework enables direct access to the crossover regime, which is a technical strength. Credit is due for the explicit comparison of observables and the focus on real-time dynamics rather than Euclidean instantons. However, the shared Hartree-level approximation between the simulation initial state and the benchmark limits the independence of the validation.

major comments (3)
  1. [§3] §3 (Initial state sampling): The positive Hartree-Gaussian ansatz is adopted to guarantee positivity for Monte-Carlo sampling of the Wigner functional. In the crossover regime, where quantum tunneling and thermal activation compete, any truncation of higher moments or non-Gaussian correlations in this ansatz propagates directly into the connected-cluster survival probability. The manuscript should quantify the sensitivity of the extracted rates to this Gaussian restriction, for example by comparing to a non-Gaussian or full Wigner sampling where feasible.
  2. [§5.1] §5.1 (High-T comparison): The reported agreement between the connected-cluster rate and the Hartree-resummed benchmark at high T is presented as validation. Because the benchmark itself is constructed at the same Hartree level, the agreement does not constitute an independent check. A cross-validation against a non-Hartree reference (e.g., classical-statistical field theory or perturbative thermal nucleation rates) is required to establish that the real-time dynamics are accurately captured rather than reproducing a shared approximation artifact.
  3. [§4.2] §4.2 and associated figures (Error analysis): The lattice parameters, statistical error bars, and criteria for excluding rare events or transients are not specified in sufficient detail. Without these, it is difficult to assess whether the reported differences between connected-cluster and global-survival rates, or the convergence at low T, are statistically robust or sensitive to simulation volume and cutoff choices.
minor comments (2)
  1. [§3.3] The definition of the cluster-size threshold used in the connected-cluster criterion should be stated explicitly, including any dependence on lattice spacing.
  2. [Figures 3-5] Figure captions would benefit from indicating the specific temperature or coupling values corresponding to each panel to aid cross-referencing with the text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment point by point below, indicating where we agree and what revisions we will make.

read point-by-point responses

  1. Referee: [§3] §3 (Initial state sampling): The positive Hartree-Gaussian ansatz is adopted to guarantee positivity for Monte-Carlo sampling of the Wigner functional. In the crossover regime, where quantum tunneling and thermal activation compete, any truncation of higher moments or non-Gaussian correlations in this ansatz propagates directly into the connected-cluster survival probability. The manuscript should quantify the sensitivity of the extracted rates to this Gaussian restriction, for example by comparing to a non-Gaussian or full Wigner sampling where feasible.

    Authors: We agree that the positive Hartree-Gaussian ansatz truncates higher moments and non-Gaussian correlations, which could in principle affect results in the crossover regime. This truncation is required to maintain a positive-definite Wigner functional that permits efficient Monte Carlo sampling on the lattice. A systematic comparison to non-Gaussian or full Wigner sampling is not feasible within the present computational framework without substantial new methodological development. In the revised manuscript we will expand §3 to state these limitations explicitly, discuss their expected impact on the connected-cluster criterion, and note that the local nature of the cluster observable is intended to reduce sensitivity to global correlations. revision: partial

  2. Referee: [§5.1] §5.1 (High-T comparison): The reported agreement between the connected-cluster rate and the Hartree-resummed benchmark at high T is presented as validation. Because the benchmark itself is constructed at the same Hartree level, the agreement does not constitute an independent check. A cross-validation against a non-Hartree reference (e.g., classical-statistical field theory or perturbative thermal nucleation rates) is required to establish that the real-time dynamics are accurately captured rather than reproducing a shared approximation artifact.

    Authors: The referee is correct that the high-temperature agreement is obtained within a shared Hartree approximation and therefore constitutes a consistency check rather than a fully independent validation. The primary purpose of the comparison is to demonstrate that the real-time lattice dynamics reproduce the expected thermal nucleation rate while exposing the differences between observables (connected-cluster versus global survival) that arise from multi-seed effects. We will revise the text in §5.1 to clarify this scope and to reference existing classical-statistical or perturbative results in the literature for additional context, without claiming an independent benchmark. revision: partial

  3. Referee: [§4.2] §4.2 and associated figures (Error analysis): The lattice parameters, statistical error bars, and criteria for excluding rare events or transients are not specified in sufficient detail. Without these, it is difficult to assess whether the reported differences between connected-cluster and global-survival rates, or the convergence at low T, are statistically robust or sensitive to simulation volume and cutoff choices.

    Authors: We thank the referee for highlighting this omission. The revised manuscript will include a new subsection (or appendix) that specifies all lattice parameters (spatial volume, lattice spacing, ultraviolet cutoff), the number of Monte Carlo samples, the procedure used to estimate statistical errors, and the explicit criteria applied to identify and discard transients, kink reflections, and rare multi-seed configurations. Updated figures will display error bars, and we will add a short discussion of finite-volume and cutoff sensitivity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; rates extracted numerically and validated against separate Hartree-resummed benchmark

full rationale

The paper develops a real-time lattice framework and extracts decay rates from connected-cluster survival probabilities in the simulated evolution. These rates are then compared to an external Hartree-resummed thermal nucleation benchmark at high temperatures. No step reduces a claimed prediction to a fitted parameter or self-citation by construction; the benchmark is a distinct resummed calculation rather than an internal fit. The positive Hartree-Gaussian sampling is an ansatz chosen for Monte-Carlo positivity, but the reported agreement is presented as a numerical validation rather than a definitional identity. This yields only minor self-consistency risk without load-bearing circularity in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be identified. The framework presumably relies on standard lattice discretization and Hartree approximation assumptions whose details are not provided.

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