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arxiv: 2606.18340 · v1 · pith:VCN2GQ7Xnew · submitted 2026-06-16 · 🪐 quant-ph · cond-mat.stat-mech· nlin.CD

Chaos from quantum bath fluctuations

Ilan Baud , Tamoghna Ray , Mahaveer Prasad , Manas Kulkarni , Camille Aron This is my paper

Pith reviewed 2026-06-27 00:36 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechnlin.CD
keywords dissipative Dicke modelquantum fluctuationsstrange attractorLyapunov exponentsuperradiant regimeshear-induced chaosquantum noisesemiclassical dynamics
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The pith

Quantum noise from the bath generates a strange attractor with positive Lyapunov exponent in the classically regular superradiant regime of the dissipative Dicke model at large but finite spin.

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

The paper asks whether quantum fluctuations from a large environment can create chaos in a quantum system whose classical limit is non-chaotic. It examines the dissipative Dicke model, in which a large spin couples to a lossy harmonic mode. Working in the semiclassical regime at large but finite spin, the authors show that the added quantum noise produces a strange attractor possessing a fractal dimension and a positive Lyapunov exponent. The mechanism is linked to shear-induced chaos. A reader would care because dissipation is usually expected to stabilize motion, yet here the accompanying quantum fluctuations destabilize it instead.

Core claim

Starting from a classically regular phase space in the superradiant regime, quantum noise generates a strange attractor with fractal dimension and a positive Lyapunov exponent in the dissipative Dicke model at large but finite spin.

What carries the argument

Semiclassical stochastic equations for the dissipative Dicke model at large but finite spin, whose quantum noise term drives shear-induced chaos.

If this is right

  • The superradiant phase of the dissipative Dicke model becomes chaotic once quantum fluctuations are retained at finite spin.
  • A positive Lyapunov exponent and fractal dimension appear directly from the quantum noise term.
  • The same mechanism connects the model to shear-induced chaos studied in the mathematical literature.
  • Dissipation alone does not guarantee regularity when quantum fluctuations are present.

Where Pith is reading between the lines

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

  • Similar quantum-noise-induced chaos may appear in other open quantum optical models once treated at finite but large system size.
  • Experiments in cavity QED with controlled dissipation could test whether the predicted strange attractor is observable.
  • The result raises the question of how quantum fluctuations affect long-time predictability in other dissipative many-body systems.

Load-bearing premise

The semiclassical regime at large but finite spin is enough to capture how quantum bath fluctuations produce chaos without needing a full quantum many-body treatment.

What would settle it

Numerical integration of the stochastic semiclassical equations at large but finite spin that yields only regular bounded orbits with zero or negative Lyapunov exponents instead of a strange attractor.

Figures

Figures reproduced from arXiv: 2606.18340 by Camille Aron, Ilan Baud, Mahaveer Prasad, Manas Kulkarni, Tamoghna Ray.

Figure 1
Figure 1. Figure 1: FIG. 1. Noise-induced chaotic attractor for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effects of the dissipative environment on the Lya [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dynamical phase diagram in the coupling [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

The effect of a large environment on a finite-size quantum mechanical system is two-fold: It brings dissipation, but also fluctuations of thermal and quantum origin. While dissipation tends to stabilize the dynamics, we question if and how environmental quantum fluctuations can generate chaos in an otherwise classically non-chaotic system. We work out a paradigmatic model of quantum optics: the dissipative Dicke model, where a large spin interacts with a dissipative harmonic mode. We dial in the classical/quantum correspondence by working in the semiclassical regime at large but finite spin. We demonstrate that, starting from a classically regular phase space in the superradiant regime, quantum noise can generate a strange attractor with fractal dimension and a positive Lyapunov exponent. We unveil the deep connection with shear-induced chaos that was recently developed in the mathematical community.

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 / 1 minor

Summary. The manuscript examines the dissipative Dicke model in the semiclassical regime at large but finite spin. It claims that quantum bath fluctuations generate a strange attractor possessing a fractal dimension and a positive Lyapunov exponent in the superradiant regime, which is classically regular, and links the mechanism to shear-induced chaos developed in the mathematical literature.

Significance. If the central numerical observation holds after methodological clarification, the result would illustrate how quantum environmental fluctuations can induce chaos in an otherwise non-chaotic dissipative quantum-optical system. The explicit connection to shear-induced chaos supplies a concrete mathematical interpretation and is a positive feature. The semiclassical truncation at large but finite spin is a standard and appropriate bridge between quantum and classical descriptions.

major comments (2)
  1. [Abstract] Abstract: the central numerical observation is stated without any description of the integration scheme, the algorithm used to extract the Lyapunov exponent, the method for estimating the fractal dimension, or the controls applied for finite-size effects; these omissions leave the primary claim without a verifiable computational foundation.
  2. [Model setup] Model setup and semiclassical regime: the effective stochastic differential equations obtained from the quantum truncation can be reproduced by classical additive or multiplicative noise whose second moments are matched to the quantum ones; no test is reported that isolates the quantum origin of the fluctuations from a purely classical stochastic drive, which is load-bearing for the claim that quantum bath fluctuations are essential.
minor comments (1)
  1. [Introduction] The introduction would benefit from a concise paragraph summarizing the key mathematical result on shear-induced chaos before invoking it to interpret the numerics.

Simulated Author's Rebuttal

2 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.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central numerical observation is stated without any description of the integration scheme, the algorithm used to extract the Lyapunov exponent, the method for estimating the fractal dimension, or the controls applied for finite-size effects; these omissions leave the primary claim without a verifiable computational foundation.

    Authors: We agree that the abstract would benefit from a concise mention of the numerical methods to strengthen the presentation of the central claim. In the revised manuscript we will add one sentence to the abstract noting the integration scheme for the stochastic differential equations, the algorithm employed for the Lyapunov exponent, the estimator used for the fractal dimension, and that finite-size effects were controlled via explicit scaling checks with system size. Full technical details remain in the Methods section. revision: yes

  2. Referee: [Model setup] Model setup and semiclassical regime: the effective stochastic differential equations obtained from the quantum truncation can be reproduced by classical additive or multiplicative noise whose second moments are matched to the quantum ones; no test is reported that isolates the quantum origin of the fluctuations from a purely classical stochastic drive, which is load-bearing for the claim that quantum bath fluctuations are essential.

    Authors: This is a substantive point. The stochastic terms in our equations are obtained by truncating the quantum master equation at large but finite spin; their second moments therefore inherit the specific structure dictated by the quantum bath operators. While classical noise with identical second moments could in principle be written down, the quantum derivation fixes both the form and the higher-order correlations that are not arbitrary. We did not perform an explicit side-by-side comparison with purely classical noise in the submitted version. In the revision we will add a paragraph clarifying this origin and, space permitting, include a short numerical comparison to classical noise with matched moments to illustrate the distinction. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained against external benchmarks

full rationale

The paper's central demonstration proceeds from the dissipative Dicke model in the semiclassical large-but-finite-spin regime, replacing quantum dynamics with stochastic differential equations whose noise statistics are fixed by the truncation (e.g., truncated Wigner). The emergence of a strange attractor and positive Lyapunov exponent is then shown numerically and linked to the independently developed mathematical theory of shear-induced chaos. No step reduces a claimed prediction to a fitted parameter by construction, no load-bearing uniqueness theorem is imported from the authors' own prior work, and the shear-chaos connection is invoked as an external insight rather than a self-citation that closes the argument. The result is therefore falsifiable against classical stochastic models of matched noise strength and does not collapse to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the semiclassical large-spin limit as a faithful representation of quantum bath fluctuations and on the numerical identification of a positive Lyapunov exponent and fractal dimension.

axioms (1)
  • domain assumption The semiclassical regime at large but finite spin captures the essential quantum noise effects without full quantum many-body treatment.
    Invoked in the abstract when the authors dial in the classical/quantum correspondence.

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    Schwinger boson representation Let us first use the Schwinger boson representation of the spin degrees of freedom. It involves two auxiliary bosonic degrees of freedom,b ↓ (b† ↓) andb ↑ (b† ↑), and the mapping Sz = n↑ −n ↓ 2 , S + =b † ↑b↓,withn ↑ :=b † ↑b↑, n ↓ :=b † ↓b↓,(A.1) where the total number of Schwinger bosonsN b :=n ↑ +n ↓ is constrained:N b = ...

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    Phase space formalism We briefly construct the phase space representation of quantum mechanics based on the Wigner representation. We refer the reader to Ref. [48] for a pedagogical introduction. Wigner transform.Collecting the different bosonic degrees of freedom in a vector fashion, ⃗ α:= (α, β↑, β↓) and⃗ α ∗ := (α∗, β∗ ↑ , β∗ ↓),(A.3) the density matri...

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