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arxiv: 2604.27489 · v1 · submitted 2026-04-30 · ❄️ cond-mat.quant-gas · hep-th

Recognition: unknown

Anomalous tunneling as a low-energy theorem for Nambu-Goldstone modes

Daichi Kagamihara, Keisuke Fujii, Masaru Hongo

Pith reviewed 2026-05-07 09:46 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas hep-th
keywords anomalous tunnelingNambu-Goldstone modeslow-energy theoremeffective field theorysuperfluid phononsmagnonsspontaneous symmetry breakingtransmission coefficient
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The pith

Anomalous tunneling of Nambu-Goldstone modes through barriers is a universal low-energy theorem required by symmetry alone.

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

The paper establishes that anomalous tunneling, in which transmission approaches unity as particle energy tends to zero, occurs for Nambu-Goldstone modes as a direct consequence of symmetry and scaling. It uses a low-energy effective field theory to treat scattering off external potentials that vary in space, showing that potentials preserving the broken symmetry become irrelevant at long wavelengths and produce perfect transmission. In contrast, symmetry-breaking perturbations remain relevant and destroy the effect. A reader would care because this accounts for the phenomenon in superfluids and magnets using only general principles, without reference to microscopic details. The result applies to any system with spontaneous symmetry breaking at sufficiently low energies.

Core claim

Anomalous tunneling of Nambu-Goldstone modes is a universal low-energy theorem dictated solely by symmetry and scaling. In the effective field theory, symmetry-preserving localized potentials are irrelevant in the long-wavelength limit and therefore produce perfect transmission, whereas symmetry-breaking perturbations are relevant and suppress transmission, eliminating anomalous tunneling. The same distinction holds for superfluid phonons and magnons.

What carries the argument

Low-energy effective field theory for Nambu-Goldstone modes with spatially dependent coefficients, where external potentials are classified strictly as symmetry-preserving or symmetry-breaking.

If this is right

  • Superfluid phonons exhibit perfect transmission through any symmetry-preserving localized barrier at sufficiently low energy.
  • Magnons show no anomalous tunneling when the potential breaks the relevant spin symmetry.
  • The transmission behavior at long wavelengths depends only on the symmetry classification of the potential, independent of its detailed shape or microscopic origin.
  • The theorem holds in any system with spontaneous symmetry breaking once the energy is low enough for the effective theory to apply.

Where Pith is reading between the lines

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

  • The result suggests that low-energy scattering calculations in broken-symmetry phases can be simplified by retaining only the symmetry properties of the potential.
  • Similar low-energy theorems may exist for other Goldstone modes in relativistic or non-relativistic field theories.
  • Experiments in ultracold atomic gases could directly test the predicted difference between symmetry-preserving and symmetry-breaking barriers by tuning the potential form.

Load-bearing premise

The low-energy effective field theory remains valid for scattering and external potentials can be classified as strictly symmetry-preserving or symmetry-breaking with no additional relevant operators at long wavelengths.

What would settle it

Measure the zero-energy transmission coefficient for phonons in a superfluid through a localized barrier that preserves the U(1) symmetry and check whether it reaches exactly unity, then repeat with a symmetry-breaking perturbation and check whether transmission drops below unity.

Figures

Figures reproduced from arXiv: 2604.27489 by Daichi Kagamihara, Keisuke Fujii, Masaru Hongo.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of our result. At low en view at source ↗
read the original abstract

Anomalous tunneling refers to the phenomenon in which the transmission coefficient through a potential barrier approaches unity as the energy of an incident particle or quasiparticle tends to zero. This counterintuitive effect has been reported in systems exhibiting spontaneous symmetry breaking (SSB), such as superfluids, yet the general conditions for its occurrence remain unclear. In this Letter, we establish that anomalous tunneling of Nambu-Goldstone (NG) modes is a universal low-energy theorem dictated solely by symmetry and scaling, using a low-energy effective field theory (EFT) framework. We formulate the scattering of NG modes by external potentials in terms of spatially dependent EFT coefficients and demonstrate that symmetry-preserving localized potentials are irrelevant in the long-wavelength limit, leading to perfect transmission. In contrast, symmetry-breaking perturbations are relevant and suppress transmission, resulting in the absence of anomalous tunneling. We illustrate this universal behavior with explicit examples of superfluid phonons and magnons.

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 paper claims that anomalous tunneling of Nambu-Goldstone (NG) modes—where the transmission coefficient through a localized potential approaches unity as incident energy tends to zero—is a universal low-energy theorem dictated solely by symmetry and scaling. Using a low-energy EFT with spatially dependent coefficients, it classifies external potentials as symmetry-preserving (irrelevant at long wavelengths, yielding perfect transmission) or symmetry-breaking (relevant, suppressing transmission), and illustrates the result with superfluid phonons and magnons.

Significance. If the central EFT argument holds, the result supplies a model-independent explanation for anomalous tunneling observed in SSB systems, unifying phenomena across superfluids and magnets under standard symmetry principles without additional assumptions. The formulation in terms of spatially dependent EFT coefficients is a clear strength, as it directly ties the effect to irrelevance of operators rather than microscopic details.

major comments (2)
  1. The central claim that symmetry-preserving localized potentials are irrelevant operators (leading to unit transmission as k→0) requires explicit power-counting in the EFT. The manuscript must demonstrate that the finite length scale introduced by the potential does not generate relevant higher-derivative or non-local operators that survive in the long-wavelength limit; without this scaling analysis, the low-energy theorem rests on an unverified assumption about EFT validity for scattering.
  2. The formulation of NG-mode scattering via spatially dependent EFT coefficients (the step that converts the potential into a position-dependent mass or velocity term) is load-bearing but presented at a high level. An explicit derivation of the transmission amplitude from the resulting wave equation, including the leading-order behavior as energy →0 and an estimate of corrections from higher-order terms in the EFT expansion, is needed to confirm that symmetry-preserving cases indeed reduce to free propagation.
minor comments (1)
  1. The abstract states that the result is illustrated with 'explicit examples' of phonons and magnons; the main text should specify whether these are analytic solutions of the EFT equations, numerical integrations, or comparisons to microscopic models, and include error estimates from neglected operators.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We agree that strengthening the explicit power-counting and derivations will improve clarity, and we outline the revisions below.

read point-by-point responses

  1. Referee: The central claim that symmetry-preserving localized potentials are irrelevant operators (leading to unit transmission as k→0) requires explicit power-counting in the EFT. The manuscript must demonstrate that the finite length scale introduced by the potential does not generate relevant higher-derivative or non-local operators that survive in the long-wavelength limit; without this scaling analysis, the low-energy theorem rests on an unverified assumption about EFT validity for scattering.

    Authors: We agree that an explicit power-counting analysis will make the argument more rigorous. In the revised manuscript, we will add a dedicated subsection performing the scaling analysis in the appropriate (1+1)-dimensional spacetime for the scattering problem. The localized potential modifies the leading EFT coefficients over a finite range a. Symmetry-preserving perturbations correspond to shifts in operators with non-negative scaling dimension that are irrelevant at long wavelengths because their scattering matrix elements vanish as k→0. Position dependence generates higher-derivative corrections that carry additional positive powers of derivatives and are suppressed by (ka)^n with n≥2. Non-local operators are not generated at leading order, as the potential is a local modification; any non-locality from integrating out gapped modes contributes only to already-included higher-order local terms in the EFT expansion. This confirms the leading infrared behavior is free propagation with unit transmission. revision: yes

  2. Referee: The formulation of NG-mode scattering via spatially dependent EFT coefficients (the step that converts the potential into a position-dependent mass or velocity term) is load-bearing but presented at a high level. An explicit derivation of the transmission amplitude from the resulting wave equation, including the leading-order behavior as energy →0 and an estimate of corrections from higher-order terms in the EFT expansion, is needed to confirm that symmetry-preserving cases indeed reduce to free propagation.

    Authors: We acknowledge the presentation was concise and will expand it in the revision. The spatially dependent coefficients follow directly from the microscopic coupling of the external potential to the order parameter, yielding a position-dependent velocity or stiffness in the quadratic action for the NG field. For symmetry-preserving cases the wave equation is a Sturm-Liouville form (e.g., ∂_x [v(x)^2 ∂_x θ] + ω^2 θ = 0) with v(x)→v_∞ at infinity. We will derive the transmission amplitude explicitly by integrating across the localized region and matching to asymptotic plane-wave solutions, obtaining T(ω)=1 + O(ω^2) at leading order. Corrections from higher-order EFT operators (e.g., quartic derivatives) scale as O((ka)^2) and vanish as k→0. The symmetry-breaking case will be contrasted, yielding |T|∼k. This explicit calculation will be included as an extended section or appendix. revision: yes

Circularity Check

0 steps flagged

No circularity: result follows from standard EFT symmetry and scaling arguments

full rationale

The paper derives anomalous tunneling of NG modes as a low-energy theorem by formulating scattering in a spatially dependent EFT, classifying potentials as symmetry-preserving (irrelevant) or symmetry-breaking (relevant) operators, and applying standard power-counting to show perfect transmission at zero energy for the former. This chain relies on general EFT principles and scaling without fitting parameters to data, without renaming known results as new theorems, and without load-bearing self-citations that reduce the central claim to prior unverified assertions by the same authors. The derivation is self-contained against external EFT benchmarks and does not reduce any prediction to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard assumptions of low-energy EFT for NG modes (derivative expansion, symmetry constraints) and the classification of external potentials as localized and either symmetry-preserving or breaking. No free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Low-energy effective field theory for Nambu-Goldstone modes is controlled by symmetry and scaling dimensions.
    Invoked to argue that symmetry-preserving potentials are irrelevant operators in the long-wavelength limit.
  • domain assumption External potentials can be strictly classified as symmetry-preserving or symmetry-breaking without generating additional relevant operators.
    Used to separate cases that exhibit or lack anomalous tunneling.

pith-pipeline@v0.9.0 · 5469 in / 1305 out tokens · 41101 ms · 2026-05-07T09:46:17.557713+00:00 · methodology

discussion (0)

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