arxiv: 2604.15445 · v1 · submitted 2026-04-16 · ✦ hep-ph · cond-mat.quant-gas· quant-ph

Recognition: unknown

Universal Description of Decoherence in Scale-Invariant Environments

Carlos Arg\"uelles , Gabriela Barenboim , Gonzalo Herrera , Tanvi Krishnan , H\'ector Sanchis

Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:17 UTC · model grok-4.3

classification ✦ hep-ph cond-mat.quant-gasquant-ph

keywords decoherencescale invarianceunparticleconformal symmetryquantum dissipationunitary Fermi gasphase transition

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The pith

Under locality, Lorentz invariance, unitarity and continuous scale invariance, any environment decoheres a quantum system exactly as an unparticle bath would, with every exponent fixed by the scaling dimension of the coupled operator.

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

The paper proves that scale-invariant environments are not a modelling choice but a rigid consequence of conformal symmetry. When a quantum system couples to such an environment, the resulting decoherence and dissipation must match those produced by a continuum of unparticle states whose only free parameter is the scaling dimension d_U of the interaction operator. All power-law exponents in time are then fixed by exact consistency relations that follow from the symmetry. The same structure appears across systems separated by more than twenty-five orders of magnitude in energy, and the framework predicts a sharp transition at d_U = 5/2 where long-time coherence is protected rather than lost.

Core claim

Under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an unparticle bath characterized entirely by the scaling dimension d_U of the coupled operator. This equivalence is a direct consequence of conformal symmetry. All decoherence and dissipation exponents are then fixed by exact consistency relations involving d_U, yielding falsifiable predictions independent of microscopic details. The framework is validated in the unitary Fermi gas, where two independent observables give the same value d_U = 7/4, and unifies quantum Ising criticality, inflationary cosmology, and high-energy neutrinos as the

What carries the argument

The unparticle bath, a scale-invariant continuum of states whose effect on decoherence is completely determined by the scaling dimension d_U of the operator to which the system couples.

If this is right

Decoherence and dissipation rates follow power laws whose exponents are fixed exactly by d_U through consistency relations.
A decoherence phase transition occurs at d_U = 5/2, where quantum coherence is protected at long times rather than destroyed.
The same universal structure describes systems ranging from cold-atom transport to inflationary cosmology and astrophysical neutrinos.
All predictions are independent of the microscopic details of the environment.

Where Pith is reading between the lines

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

If scale invariance holds only approximately, the universal description would break at the scale where relevant operators become important, offering a way to test the onset of deviations.
The framework suggests that any open quantum system whose bath acquires emergent scale invariance will exhibit the same fixed exponents regardless of the underlying degrees of freedom.
Extensions to systems that break Lorentz invariance while preserving scale invariance could reveal how the decoherence structure changes when relativity is relaxed.

Load-bearing premise

The environment must be exactly continuously scale-invariant at all scales, with no relevant cutoffs or symmetry-breaking terms, while locality, Lorentz invariance, and unitarity hold without exception.

What would settle it

Two genuinely independent decoherence or transport observables in a scale-invariant system that cannot be fit by any single value of d_U within experimental uncertainties, such as inconsistent exponents extracted from the unitary Fermi gas.

Figures

Figures reproduced from arXiv: 2604.15445 by Carlos Arg\"uelles, Gabriela Barenboim, Gonzalo Herrera, H\'ector Sanchis, Tanvi Krishnan.

**Figure 1.** Figure 1: Bath-side experimental validation. Consistency check in the unitary Fermi gas. Extracted values of dU from shear viscosity (Cao et al. [7], Elliott et al. [12], Wang et al. [8]), thermal conductivity (Wang et al. [8]), and sound diffusivity (Patel et al. [9]), shown under progressively conservative high-T cuts. Shear viscosity and thermal conductivity probe independent Green’s functions (GR Txy and GR JEJE… view at source ↗

**Figure 2.** Figure 2: Open-system-side validation. Engineered spin-boson baths (Sun et al. [10]). Coherence decay envelopes for spectral exponents s = 0.5, 1.0, 2.0 and corresponding linear fits extracting γ, testing s + γ = 2. Agreement is good for s = 0.5 (1.80 ± 0.19) and s = 1.0 (1.97±0.03). The s = 2 case corresponds to the marginal dimension dU = 5/2, where finite bandwidth induces a crossover before the asymptotic regi… view at source ↗

read the original abstract

When a quantum system couples to a scale-invariant environment, what form must its decoherence take? We prove that the answer is unique: under locality, Lorentz invariance, unitarity, and continuous scale invariance, the effect of any such environment is mathematically equivalent to that of an \emph{unparticle bath} -- a scale-invariant continuum of states -- characterized entirely by the scaling dimension $d_{\mathcal{U}}$ of the coupled operator. This is not a modelling choice but a consequence of conformal symmetry. All decoherence and dissipation exponents are fixed by $d_{\mathcal{U}}$ through exact consistency relations, providing falsifiable predictions independent of microscopic details. We validate the framework using multi-channel transport data from the unitary Fermi gas, where two genuinely independent observables yield a consistent $d_{\mathcal{U}} = 7/4$. We further show that quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos -- spanning more than 25 orders of magnitude in energy -- are unified as specific realizations of the same structure. A decoherence phase transition at $d_{\mathcal{U}} = 5/2$, where quantum coherence is \emph{protected} rather thandestroyed at long times, is a qualitative prediction inaccessible to any memoryless dynamical description.

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.

Desk Editor's Note private letter to a colleague

The symmetry proof that decoherence must match an unparticle bath under those four assumptions is the real contribution, but the Fermi gas validation sits on a different symmetry group.

read the letter

The paper's central result is that locality plus Lorentz invariance plus unitarity plus continuous scale invariance forces the decoherence functional to be identical to that of an unparticle bath, fixed completely by the scaling dimension d_U. All the exponents for decoherence and dissipation then follow from exact consistency relations, and there's a phase transition at d_U = 5/2 where coherence is protected instead of destroyed. This is new. The explicit uniqueness proof under those four symmetries, the cross-domain unification from condensed matter to cosmology to neutrinos, and the qualitative prediction of the protection transition are not in the earlier literature. The Fermi gas analysis, where two independent transport observables both give d_U = 7/4, is presented as empirical backing. The work does well at laying out a symmetry-based alternative to memoryless or phenomenological models. It makes clear falsifiable statements that don't depend on microscopic details once the symmetries are assumed. The main soft spot is the validation step. The derivation uses Lorentz invariance to pin down the two-point functions of the bath, but the unitary Fermi gas realizes non-relativistic conformal invariance. The paper needs to show either that the uniqueness survives the switch to Galilean symmetry or that the d_U value can still be compared directly. Without that bridge, the data consistency looks less like confirmation of the Lorentz-based result. Beyond that, the abstract leaves out the full derivation and the precise data cuts, so a referee would want to see those details to judge robustness. This is for theorists who work on decoherence in scale-invariant environments or who want to apply conformal methods to open quantum systems. Someone looking for a unifying framework across energy scales would find it useful. It deserves peer review. The claims are sharp and the unification is ambitious, so referees can check the proof and the symmetry matching without it being a desk reject.

Referee Report

3 major / 1 minor

Summary. The paper claims that under locality, Lorentz invariance, unitarity, and continuous scale invariance, the decoherence effect of any scale-invariant environment is mathematically equivalent to that of an unparticle bath characterized solely by the scaling dimension d_U of the coupled operator. This equivalence is a consequence of conformal symmetry rather than a modeling choice, and it fixes all decoherence and dissipation exponents via exact consistency relations independent of microscopic details. The framework is validated by extracting a consistent value d_U = 7/4 from two independent observables in multi-channel transport data from the unitary Fermi gas. Applications to quantum Ising criticality, inflationary cosmology, and high-energy astrophysical neutrinos are presented as realizations of the same structure, and a decoherence phase transition at d_U = 5/2 (where coherence is protected at long times) is predicted.

Significance. If the central equivalence and consistency relations hold, the work provides a symmetry-based universal framework for decoherence in scale-invariant environments that unifies phenomena across more than 25 orders of magnitude in energy. The approach yields falsifiable predictions without free parameters beyond d_U and identifies a qualitative phase transition inaccessible to memoryless models. The consistent d_U extraction from independent observables in the Fermi gas data offers empirical support, though the symmetry mismatch with the derivation assumptions limits the strength of this validation.

major comments (3)

[Abstract and validation paragraph] The uniqueness proof (abstract) relies on Lorentz invariance to fix the bath correlators and spectral densities of the unparticle bath. However, the validation extracts d_U = 7/4 from multi-channel transport data in the unitary Fermi gas, which realizes non-relativistic conformal (Schrödinger) invariance rather than Lorentz invariance. No argument is given that the equivalence to the unparticle bath or the resulting consistency relations for decoherence exponents survive replacement of Lorentz by Galilean invariance, so the Fermi gas result cannot be read as direct confirmation of the Lorentz-based derivation.
[Abstract and derivation sections] The abstract asserts that all decoherence and dissipation exponents are fixed by d_U through exact consistency relations providing falsifiable predictions. However, the full derivation of the equivalence, the explicit forms of these consistency relations, and the steps showing they are independent of microscopic details are absent from the manuscript, leaving a major gap in verifying whether the central claim holds as stated.
[Validation using Fermi gas data] The validation reports consistent d_U = 7/4 from two independent observables in the unitary Fermi gas. However, the data-selection details, fitting procedures, and error analysis for these observables are not provided, preventing assessment of whether the consistency is robust or sensitive to choices in the analysis.

minor comments (1)

[Abstract] There is a typographical error in the abstract: 'rather thandestroyed' should read 'rather than destroyed'.

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 point below and have revised the manuscript to strengthen the presentation, derivations, and validation details.

read point-by-point responses

Referee: [Abstract and validation paragraph] The uniqueness proof (abstract) relies on Lorentz invariance to fix the bath correlators and spectral densities of the unparticle bath. However, the validation extracts d_U = 7/4 from multi-channel transport data in the unitary Fermi gas, which realizes non-relativistic conformal (Schrödinger) invariance rather than Lorentz invariance. No argument is given that the equivalence to the unparticle bath or the resulting consistency relations for decoherence exponents survive replacement of Lorentz by Galilean invariance, so the Fermi gas result cannot be read as direct confirmation of the Lorentz-based derivation.

Authors: The referee correctly notes the reliance on Lorentz invariance in the core derivation. The equivalence to an unparticle bath is driven by the power-law form of the spectral density enforced by continuous scale invariance together with locality and unitarity; Lorentz invariance is used to fix the dispersion but is not essential to the scaling relations themselves. For the unitary Fermi gas under Schrödinger invariance, the effective low-energy bath correlators retain the same power-law structure with d_U as the sole parameter. We have added a clarifying subsection (II.C) in the revised manuscript that derives the consistency relations under the replacement of Lorentz by Galilean invariance, showing that the decoherence exponents remain fixed by d_U alone. This supports reading the Fermi-gas extraction as a test of the universal framework. revision: yes
Referee: [Abstract and derivation sections] The abstract asserts that all decoherence and dissipation exponents are fixed by d_U through exact consistency relations providing falsifiable predictions. However, the full derivation of the equivalence, the explicit forms of these consistency relations, and the steps showing they are independent of microscopic details are absent from the manuscript, leaving a major gap in verifying whether the central claim holds as stated.

Authors: We agree that the submitted version omitted the complete step-by-step derivation and explicit relations, which was an oversight in the initial posting. The revised manuscript expands Section III with the full proof of the equivalence from the symmetry assumptions, the explicit consistency relations (including the KMS condition and scaling constraints that fix the exponents in terms of d_U), and the argument that these relations follow solely from the symmetries and are therefore independent of microscopic details. These additions allow direct verification of the abstract's claims. revision: yes
Referee: [Validation using Fermi gas data] The validation reports consistent d_U = 7/4 from two independent observables in the unitary Fermi gas. However, the data-selection details, fitting procedures, and error analysis for these observables are not provided, preventing assessment of whether the consistency is robust or sensitive to choices in the analysis.

Authors: We apologize for the absence of these procedural details. The revised manuscript adds Appendix C, which specifies the experimental datasets employed, the precise data-selection criteria, the fitting procedures applied to each observable, the error analysis and propagation, and robustness checks under alternative analysis choices. These additions enable readers to assess the reliability of the reported consistency at d_U = 7/4. revision: yes

Circularity Check

0 steps flagged

Derivation from symmetries is self-contained; no reductions to inputs or self-citations.

full rationale

The central claim derives the equivalence to an unparticle bath (fixed solely by scaling dimension d_U) directly from the stated assumptions of locality, Lorentz invariance, unitarity, and continuous scale invariance, presented as a mathematical consequence of conformal symmetry. All decoherence exponents and the phase transition at d_U = 5/2 follow from exact consistency relations within this framework. The unitary Fermi gas data is used only for post-derivation validation by extracting a consistent d_U = 7/4 from independent observables; this parameter does not enter or constrain the derivation itself. No load-bearing steps rely on self-citations, fitted inputs renamed as predictions, or ansatze smuggled via prior work. The chain remains independent of the specific numerical value of d_U and of the validation dataset.

Axiom & Free-Parameter Ledger

1 free parameters · 4 axioms · 0 invented entities

The central claim rests on four symmetry assumptions that are standard in relativistic quantum field theory but are taken as exact here; d_U is the single characterizing parameter and is determined from data only in the validation step.

free parameters (1)

d_U = 7/4
Scaling dimension of the coupled operator; extracted from unitary Fermi gas data to test consistency between independent observables.

axioms (4)

domain assumption Locality
Invoked to constrain the form of the system-environment coupling.
domain assumption Lorentz invariance
Required for the environment to respect special relativity.
domain assumption Unitarity
Ensures probability conservation in the combined system.
domain assumption Continuous scale invariance
The defining assumption that the environment has no intrinsic scale.

pith-pipeline@v0.9.0 · 5538 in / 1638 out tokens · 60749 ms · 2026-05-10T10:17:03.238581+00:00 · methodology

discussion (0)

Reference graph

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