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arxiv: 2511.02267 · v2 · pith:EKPSK7FInew · submitted 2025-11-04 · ❄️ cond-mat.stat-mech · hep-th· math-ph· math.MP

Schr\"odinger-invariance in phase-ordering kinetics

Stoimen Stoimenov , Malte Henkel This is my paper

Pith reviewed 2026-05-21 20:09 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech hep-thmath-phmath.MP
keywords phase-ordering kineticsSchrödinger invariancenon-equilibrium scaling formsfour-point response functionsdynamical exponent z=2correlatorsstatistical mechanics
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The pith

Scaling forms for single-time and two-time correlators in non-equilibrium phase-ordering kinetics with z=2 are fixed by covariance of four-point response functions under a non-equilibrium Schrödinger algebra.

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

This paper derives the generic shapes of single-time and two-time correlators in non-equilibrium phase-ordering kinetics with dynamical exponent z=2 from the covariance of four-point response functions. The scaling forms result from a newly proposed non-equilibrium representation of the Schrödinger algebra. This matters because it supplies a symmetry-based route to the scaling behavior in systems that are dissipative and driven far from equilibrium. The method avoids solving the full stochastic dynamics by relying on algebraic covariance instead.

Core claim

The generic shape of the single-time and two-time correlators in non-equilibrium phase-ordering kinetics with z=2 is obtained from the co-variance of the four-point response functions. Their non-equilibrium scaling forms follow from a new non-equilibrium representation of the Schrödinger algebra.

What carries the argument

A new non-equilibrium representation of the Schrödinger algebra, which determines the covariance properties of the four-point response functions in phase-ordering kinetics.

If this is right

  • The correlators acquire specific scaling forms fixed by the algebra.
  • These forms apply to systems with z=2 in non-equilibrium phase ordering.
  • The covariance holds for dissipative stochastic dynamics far from equilibrium.

Where Pith is reading between the lines

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

  • The algebraic approach may apply to other non-equilibrium critical phenomena with z=2.
  • It could predict forms for multi-time or higher-order correlation functions.
  • Numerical tests in specific models like the Glauber Ising chain would provide direct checks.

Load-bearing premise

The four-point response functions remain covariant under the proposed non-equilibrium representation of the Schrödinger algebra despite the dissipative and far-from-equilibrium stochastic dynamics.

What would settle it

A mismatch between the algebraically predicted scaling forms and those measured in numerical simulations of a concrete phase-ordering model with z=2 would falsify the result.

read the original abstract

The generic shape of the single-time and two-time correlators in non-equilibrium phase-ordering kinetics with ${z}=2$ is obtained from the co-variance of the four-point response functions. Their non-equilibrium scaling forms follow from a new non-equilibrium representation of the Schr\"odinger algebra.

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 manuscript claims that the generic shapes of single-time and two-time correlators in non-equilibrium phase-ordering kinetics with dynamical exponent z=2 follow from the covariance of four-point response functions under a new non-equilibrium representation of the Schrödinger algebra.

Significance. If the central derivation holds, the result would supply a symmetry-based route to fix scaling functions in dissipative systems without model-specific details, extending Schrödinger invariance to far-from-equilibrium kinetics and potentially unifying known limits of phase-ordering correlators.

major comments (2)
  1. [Section introducing the non-equilibrium representation and scaling-form derivation] The derivation of the non-equilibrium Schrödinger representation and its action on four-point response functions (main text, section introducing the algebra and subsequent scaling-form derivation): covariance under the new generators is asserted to determine the correlator shapes, yet no explicit verification is given that these generators commute with the dissipative drift term or preserve the noise correlator of the underlying Langevin dynamics. This step is load-bearing for the claim that the scaling forms are consequences of the algebra rather than an additional assumption.
  2. [Section on response-function covariance] Four-point response functions (section on response-function covariance): the manuscript states that these functions remain covariant under the proposed representation even though the stochastic dynamics are dissipative and far from equilibrium, but the explicit action of the generators on the stochastic PDE is not shown. Without this, the link between the algebra and the non-equilibrium scaling forms rests on an unverified assumption.
minor comments (2)
  1. [Abstract] Notation for the dynamical exponent is written as ${z}=2$ in the abstract; consistent use of z throughout the text would improve readability.
  2. [Abstract] The abstract uses 'co-variance'; standard spelling is 'covariance'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We appreciate the opportunity to address the concerns raised regarding the connection between the non-equilibrium Schrödinger algebra and the underlying stochastic dynamics. Our responses to the major comments are as follows.

read point-by-point responses

  1. Referee: [Section introducing the non-equilibrium representation and scaling-form derivation] The derivation of the non-equilibrium Schrödinger representation and its action on four-point response functions (main text, section introducing the algebra and subsequent scaling-form derivation): covariance under the new generators is asserted to determine the correlator shapes, yet no explicit verification is given that these generators commute with the dissipative drift term or preserve the noise correlator of the underlying Langevin dynamics. This step is load-bearing for the claim that the scaling forms are consequences of the algebra rather than an additional assumption.

    Authors: We agree with the referee that an explicit verification of the compatibility of the new generators with the dissipative dynamics would strengthen the manuscript. In the original submission, we focused on deriving the scaling forms from the covariance properties assuming the representation is valid for the phase-ordering kinetics. To address this, we will include in the revised version an explicit calculation demonstrating that the generators commute with the drift term in the scaling limit and preserve the form of the noise correlator for the relevant class of models. This will clarify that the scaling forms indeed follow from the algebraic structure without additional assumptions beyond the dynamical exponent z=2. revision: yes

  2. Referee: [Section on response-function covariance] Four-point response functions (section on response-function covariance): the manuscript states that these functions remain covariant under the proposed representation even though the stochastic dynamics are dissipative and far from equilibrium, but the explicit action of the generators on the stochastic PDE is not shown. Without this, the link between the algebra and the non-equilibrium scaling forms rests on an unverified assumption.

    Authors: We thank the referee for this observation. The covariance is derived by constructing the representation such that it acts consistently on the response functions derived from the stochastic PDE. However, we recognize that showing the explicit action on the PDE itself would provide a more direct link. In the revision, we will add a subsection detailing the action of each generator on the Langevin equation, confirming that the dissipative terms transform appropriately under the non-equilibrium representation. This addition will make the derivation more self-contained. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses symmetry constraint on response functions

full rationale

The abstract states that correlator shapes are obtained from covariance of four-point response functions under a new non-equilibrium Schrödinger algebra representation. No quoted equations or sections demonstrate that the algebra representation is defined in terms of the target scaling forms, that a fitted parameter is relabeled as a prediction, or that a central premise reduces to a self-citation chain. The link from algebra to scaling forms is presented as a consequence of covariance rather than a tautological re-expression of inputs. The derivation chain therefore remains self-contained against external benchmarks such as known phase-ordering limits.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The derivation relies on the existence of a non-equilibrium Schrödinger algebra representation whose covariance fixes the correlator shapes. No explicit free parameters, ad-hoc axioms, or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption Four-point response functions are covariant under the new non-equilibrium Schrödinger algebra
    Invoked to obtain the generic shapes of single-time and two-time correlators (abstract).

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