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REVIEW 4 major objections 4 minor 83 references

Broadband Search for Axion Dark Matter via Shift Current

T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A Weyl-semimetal shift current could detect QCD axion dark matter in the 10-100 meV mass window.

desk verdict A genuinely new axion detection idea with an elegant background suppression, but the claimed reach depends on a pulsed 10^8 V/m source whose duty cycle is never addressed—so the sensitivity forecast is not yet supported. read the letter →

arxiv 2505.17007 v1 pith:SZX4HZGR submitted 2025-05-22 hep-ph

Dan Kondo , Takahiro Morimoto , Genta Osaki , Thanaporn Sichanugrist This is my paper
classification hep-ph
keywords axiondarkmattershiftcurrentWeylsemimetaldifferencefrequencygenerationnonlinearopticalresponseQCDbulkphotovoltaiceffectdetection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes using the shift current, a nonlinear photocurrent generated in crystals without inversion symmetry, to detect axion dark matter. A static magnetic field converts axions into a feeble electric field, and a strong applied oscillating electric field mixes with it to produce a current at a low difference frequency that is easy to read out. Using the Weyl semimetal TaAs, the authors estimate that QCD axions with masses of roughly 10-100 meV and photon couplings of order $10^{-12}$ to $10^{-11}$ GeV$^{-1}$ could be seen at signal-to-noise ratio one with a 1 T magnet, a $10^8$ V/m drive field, a 1 mK receiver, and 100 days of observation. If correct, this would open a new broad-band laboratory window on axion dark matter without requiring a large resonant cavity.

What carries the argument

The load-bearing object is the shift current: a non-dissipative second-order photocurrent arising from the quantum-geometric shift of electron wave functions during optical transitions in crystals lacking inversion symmetry. The conductivity formula, Eqs. (5) and (11), is built from Berry connections and band energies, and the broadband operation comes from the momentum-space integral that keeps the response finite for many input frequencies. In the proposed detector, the cross term $\sigma^{xzx}_{\rm shift}E_{\rm DM}E_{\rm exp}$ is selected while the symmetry of TaAs forbids the background term $\sigma^{xxx}E_{\rm exp}E_{\rm exp}$, leaving Johnson-Nyquist noise as the main limitation.

What would settle it

Measure the shift-current conductivity $\sigma^{xzx}_{\rm shift}$ of TaAs with two input fields whose frequencies differ by $\Delta\omega\lesssim1$ THz across the 25-350 meV range; if the conductivity is far below the assumed $\sim200\,\mu$A/V$^2$ or the response is not flat in $\Delta\omega$, the SNR=1 curve in Fig. 3 moves to larger $g_{a\gamma\gamma}$ and may no longer cover the QCD axion band.

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Extended reading notes

Core claim

The central claim is that the axion-induced electric field $E_{\rm DM}=g_{a\gamma\gamma}B_0\sqrt{2\rho_{\rm DM}}/m_{\rm DM}$, obtained by applying a static magnetic field $B_0$, can be amplified and down-converted by mixing it with a strong applied field $E_{\rm exp}$ inside a noncentrosymmetric crystal. The shift-current conductivity $\sigma_{\rm shift}$ generates an output current $J=\sigma_{\rm shift}E_{\rm DM}E_{\rm exp}$ at the difference frequency $\Delta\omega = \omega_{\rm exp}-m_{\rm DM}$. Because the shift current is a non-dissipative second-order response whose resonance condition is automatically met by integrating over momentum, the signal remains strong over a broad frequency range; a single setting of $\omega_{\rm exp}$ covers about a 1 THz window. Using the measured shift-current conductivity of TaAs, the paper derives a sensitivity estimate that reaches the QCD axion band in the 10-100 meV mass range.

Load-bearing premise

The reach assumes that an oscillating electric field near $10^8$ V/m can be supplied with pulses at least 100 ps long and with enough duty cycle to accumulate about one day of integration per frequency step; the paper states that such a long-enough pulse is still required.

Editorial extensions

If this is right

  • A single experimental setup with a modest 1 T magnet and a square-centimeter TaAs sample could scan roughly 10-300 meV of axion masses in about 100 days, without the frequency tuning needed in cavity haloscopes.
  • The signal appears at DC to about 1 THz, so readout can use standard low-frequency electronics rather than detectors operating at the axion frequency itself.
  • The background from the drive field is suppressed by crystal symmetry, so the search is limited mainly by thermal noise in the readout circuit.
  • The same difference-frequency mechanism could be applied to other noncentrosymmetric materials, and the paper notes that magnon and phonon shift currents might extend the method to smaller axion masses and to hidden-photon dark matter.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The quoted reach assumes effectively continuous integration; if the $10^8$ V/m field can only be delivered in low-duty-cycle short pulses, the effective observation time drops and the SNR, which scales as $\sqrt{\tau_{\rm scan}}$, would push the sensitivity curve to larger couplings.
  • A direct material check is available: measuring the shift-current conductivity of TaAs with two input fields separated by a small $\Delta\omega$ would test the prediction that the response is flat for $\Delta\omega\ll\omega_{\rm exp}$, which is what makes the 1 THz instantaneous scan window possible.
  • The method could in principle be aimed at other feebly interacting high-frequency fields by choosing crystals whose band gaps match the source frequency, though the practical limitation is finding materials with large, non-dissipative second-order conductivities.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper proposes a new axion dark matter detection scheme based on the shift current, a second-order nonlinear optical response in non-centrosymmetric materials. The axion under a static magnetic field produces an oscillating electric field E_DM; applying a strong oscillating field E_exp at frequencies in the 10–100 meV range generates a shift-current cross-term at the difference frequency, which can be read out at low frequency. Using literature values for the shift conductivity of TaAs, the authors derive a sensitivity estimate (Eqs. (13)–(14), Fig. 3) that claims to reach the QCD axion band for masses 10–100 meV and couplings g_{aγγ} ~ 10^–12 to 10^–11 GeV^–1 with B0 = 1 T, E_exp = 10^8 V/m, T = 1 mK, and 100 days of observation. The appendices contain detailed derivations of the nonlinear response, and the broadband nature of the response is illustrated with a Rice-Mele toy model.

Significance. If the sensitivity estimate were correct, this would open a new solid-state route to axion dark matter detection in a mass range that is challenging for cavity haloscopes. The formal derivation of the shift-current response is detailed and self-consistent, and the idea of using a two-field cross-term to downconvert axion signals is original. The Rice-Mele example usefully demonstrates the broad frequency response. However, the quantitative claim depends on several experimental and electrodynamic assumptions that are not justified in the manuscript, and at least two of these can suppress the signal by many orders of magnitude.

major comments (4)
  1. [Section III, Eqs. (12)–(14)] The sensitivity estimate assumes that the cross-term current J ∝ σ E_DM E_exp integrates coherently over the sample volume, yielding a total current scaling as L_exp^2 and power as L_exp^4. The axion field is spatially uniform over the de Broglie wavelength (~1 cm), but the experimental field at ω_exp ~ 100 meV has a vacuum wavelength of ~12 µm. The product E_DM E_exp therefore acquires a spatial phase e^{i k_exp·r} with period ~12 µm, so for a 1 cm sample the current cancels upon integration unless the sample is a thin film (thickness ≪ 12 µm) in the propagation direction. If such a thin film is intended, the current-collection cross-section is then reduced by a factor of order λ_exp/L_exp relative to the L_exp^2 used in Eq. (12), suppressing the signal power by ~10^-8. The manuscript does not specify a geometry that avoids this cancellation, nor does it discuss phase matching; as written, Eq. (13) appears to overestimate the signal by many orders of magnitude.
  2. [Section IV and Eq. (14)] The SNR calculation assumes the applied field E_exp = 10^8 V/m is available continuously for τscan = 1 day per frequency setting. The manuscript concedes in Section IV that such fields are currently achievable only with short-pulse lasers and that pulses of at least 100 ps are needed for the 10 GHz resolution bandwidth, but it does not identify a source with that pulse duration and a high repetition rate, nor does it evaluate the duty cycle. For a pulsed source with duty cycle D, the time-averaged signal power entering the radiometer equation is reduced by D (for a periodic pulse train whose spectrum overlaps the signal bin), and the required coupling scales as D^{-1/2}. Even for a duty cycle of 10^-5, the reach in g_{aγγ} degrades by a factor of ~300, moving the SNR = 1 contour above the QCD axion band. The paper does not quantify the pulsed-source penalty at all.
  3. [Section II, conductivity assumption] The value σ_xzx = 200 µA/V^2 is taken from single-frequency shift-current measurements in Ref. [47] and is assumed without justification to apply to the two-frequency cross-term σ_xzx(Δω; m_DM, ω_exp) in Eq. (11) over the entire 10–100 meV range. The sensitivity scales as σ^2, so a factor-of-10 error in σ changes the reach by a factor of 10 in g_{aγγ}. The Rice-Mele demonstration in Fig. 1 shows that the conductivity has significant frequency dependence, especially near band edges, so applying a single measured value to the full mass range requires either a frequency-dependent calculation for TaAs or a clear argument for why the approximation is valid.
  4. [Section II, Eq. (4)] The axion-induced electric field E_DM in Eq. (4) is the free-space expression. The manuscript does not address how this field is modified inside the TaAs sample, which is a semimetal with free carriers and a complex dielectric response at THz frequencies. The internal field may be screened or attenuated depending on the conductivity, permittivity, and sample boundary conditions. Since the signal power scales as E_DM^2, an order-of-magnitude reduction in the internal field would shift the reach by a factor of 10 in g_{aγγ}. The authors should model the axion-to-photon conversion in the presence of the detector material or justify why free-space boundary conditions apply.
minor comments (4)
  1. [Section IV] The sentence 'we adopt the ferroelectric material as a sample' is inconsistent with the rest of the paper, which uses TaAs (a Weyl semimetal), and appears to be a leftover from an earlier version.
  2. [Fig. 3 caption] The caption states 'area Lexp × Lexp ∼ 4 × 4 cm2', but the text in Section III uses L_exp = 1 cm; this discrepancy should be resolved, since Eq. (13) depends sensitively on L_exp^4.
  3. [Section II] The symbol σ is used both for the shift-current conductivity and for the signal linewidth σ_sig; this dual use may confuse readers and should be disambiguated.
  4. [Section III] The relationship between the coherent-segment duration τ = 0.1 ns and the total integration time τscan = 1 day in the radiometer equation is not fully explained; a sentence describing how the Fourier-transformed segments are combined would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the sensitivity estimate uses an externally measured shift-current conductivity, a first-principles response derivation, and the standard radiometer equation, with no fitted axion parameters.

full rationale

The paper's claimed derivation chain is self-contained in the relevant sense. The axion-induced electric field E_DM in Eq. (4) follows from the standard axion-photon coupling. The shift-current response in Eq. (5) and the cross-term conductivity in Eq. (11) are derived in Appendices A-C from a coherent-state path integral, without inserting the target axion coupling as an input. The conductivity value sigma_xzx ~ 200 microA/V^2 is taken from the external experimental reference [47], not fitted to the claimed axion sensitivity. The signal power in Eq. (13) and SNR in Eq. (14) are direct applications of the radiometer equation to the product of this measured conductivity, the standard E_DM, and the assumed experimental field E_exp. The QCD axion band in Fig. 3 is used as a comparison target, not as a constraint used to choose parameters. The stated experimental parameters (B0 = 1 T, E_exp = 10^8 V/m, T = 1 mK, tau_scan = 1 day) are assumed operating points, not fitted outputs; the same equations would produce a different reach if these parameters were changed. The paper's own Section IV caveat that 100 ps pulses are still needed to reach the 10 GHz resolution bandwidth is a limitation on experimental feasibility, not a circularity in the derivation. Multiple self-citations by author Morimoto support background formalism and material properties, but the central conductivity input is external and the response formula is rederived in the appendices, so these citations are not load-bearing circularity. The manuscript also contains a wording inconsistency in Section IV ('we adopt the ferroelectric material as a sample'), but this is an editorial error, not a circular derivation step.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central sensitivity estimate depends on several hand-chosen experimental parameters (E_exp, L_exp, T, tau_scan) and on extrapolating a measured single-frequency shift-current conductivity to a two-frequency cross-term. There are no new physical entities introduced. The main body of the calculation is standard nonlinear response theory applied to a known material, so the axiomatic load is carried mostly by optimistic experimental assumptions rather than by new physics postulates.

free parameters (6)
  • E_exp (applied oscillating electric field) = 10^8 V/m
    Hand-chosen as the enhancement field. It sets the signal power scale (P proportional to E_exp^2) and is said to be achievable with short-pulse lasers, but the required 100 ps pulse duration is acknowledged as unresolved in Section IV.
  • sigma_xzx (shift-current conductivity) = 200 microA/V^2
    Taken from Ref. 47 at about 100 meV, but assumed constant for both input frequencies over 25-350 meV. The measured value does not directly constrain the two-frequency DFG cross-term; this is an extrapolation.
  • L_exp (sample size) = 4 cm
    The text initially says O(1) cm; the Fig. 3 sensitivity line uses L_exp = 4 cm (area 4x4 cm^2). Power scales as L^4, so this choice strongly affects the claimed reach.
  • T (noise temperature) = 1 mK
    Imposed as the operating temperature for Johnson-Nyquist noise; standard dilution refrigerator temperature but challenging in a setup with THz fields.
  • tau_scan (integration time per frequency bin) = 1 day
    Sets the SNR via sqrt(tau/Delta f); total 100 days across the scan. Chosen to reach SNR = 1.
  • B0 (static magnetic field) = 1 T
    Converts axions to an electric field; a modest field, but the axion-induced E field scales linearly with B0.
assumptions (5)
  • domain assumption Axion dark matter is a classical coherent oscillating field with amplitude sqrt(2 rho)/m.
    Standard in axion haloscope searches; cited in Ref. 40.
  • domain assumption Shift current is the dominant second-order response; other intrinsic second-order responses vanish for linearly polarized fields under time-reversal symmetry.
    Stated in Section II; assumes TRS and no other contributions.
  • domain assumption The axion-induced electric field E_DM inside the sample equals the free-space value from Eq. (4).
    Implicit in the protocol; boundary conditions and screening are not discussed.
  • ad hoc to paper The measured single-frequency shift-current conductivity applies to the two-frequency cross-term.
    Extrapolated from Ref. 47 to the DFG response; not derived or measured.
  • domain assumption Electron scattering rate gamma is small compared to band energies and frequency differences.
    Used to derive Eqs. (5) and (11); no numerical value specified.

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Cite this review

Pith. "Pith review of Broadband Search for Axion Dark Matter via Shift Current." pith.science (2026). https://pith.science/paper/SZX4HZGR

@misc{pith2026250517007,
  author       = {Pith},
  title        = {Pith review of: Broadband Search for Axion Dark Matter via Shift Current},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SZX4HZGR}},
  note         = {Machine review of arXiv:2505.17007}
}
abstract

We propose a novel method to detect axion dark matter based on a topological phenomenon known as the shift current. We exploit the second-order nonlinearity of the shift current by applying a strong oscillating electric field. This field enhances the axion-induced shift current signal and downconverts its frequency to a more accessible range. The non-dissipative nature of the shift current allows us to achieve broadband detection via difference frequency generation. We demonstrate, using Type-I Weyl semimetal TaAs property, the possibility of probing the parameter space of the QCD axion in the mass range of $\mathcal{O}(10)$ - $\mathcal{O}(100) \ \rm meV$ corresponding to the photon coupling of $g_{a\gamma\gamma}\simeq$ $\mathcal{O}(10^{-12})$ - $\mathcal{O}(10^{-11})~\text{GeV}^{-1}$, respectively.

Figures

Figures reproduced from arXiv: 2505.17007 by the authors.

Figure 1
Figure 1. FIG. 1. The plot of the shift-current conductivity as a func [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The schematic picture of the experimental setup. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Sensitivity to the axion photon coupling [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Band structure of Rice-Mele model. The potential of each site is [PITH_FULL_IMAGE:figures/full_fig_p027_4.png]

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    Notation Let us begin with the second quantized Hamiltonian for electrons. bH0 = X a Z ddk (2π)d εkac† kacka (A1) where {a} is the band label. The integration over k is for the Brillouin zone. εka is the eigen energy and c† ka, ckn are the corresponding creation/annihilation o...

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    Bloch state Assuming periodic boundary condition ( ri → ri + Li), the wave function can be expressed by ψka(r) = eik·ruka(r) (B1) where uka(r) is a periodic function: uka(r) = uka(r + miLi). (B2) It is an eigenfunction of k-dependent Hamiltonian associated with the operator (A...

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    Covariant derivative Let us calculate the expectation value of the position operator br. ⟨Ψ′|br|Ψ⟩ = Z ddr⟨Ψ′|br|r⟩⟨r|Ψ⟩ = X a′,a Z ddr ddk′ (2π)d ddk (2π)d C ∗ k′a′ie−ik′·ru∗ k′a′(r)eik·ruka(r) ∂ ∂k Cka (B5) + X a′,a Z ddr ddk′ (2π)d ddk (2π)d C ∗ k′a′ie−ik′·reik·ru∗ k′a′(r) ...

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    bHA(k, t) = bH0 (k − qA(t))

    Electromagnetic interactions Electromagnetic perturbation is realized by gauge principle replacing k → k − qA(t) where the vector potential A(t) is chosen so that E(t) = −∂tA(t). bHA(k, t) = bH0 (k − qA(t)) . (B17) Using (B3), (B14) and BCH formula: e bA bBe− bA = bB + h bA, b...

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    (C5) We perform Fourier transformation 4 : ξka(τ ) = 1 β X n ξka(ωn)e−iωnτ , ξ ∗ ka(τ ) = 1 β X n ξ∗ ka(ωn)eiωnτ , (C6) where ωn is called Matsubara frequency ( ωn = (2n + 1)π/β)5

    Partition function Consider the path-integral form of partition function: Z = Z ξf =−ξi Dξ∗Dξ e−S (C1) S = Z β 0 dτ X aa′ Z ddk (2π)d δaa′ξ∗ ka(τ ) ∂ξka′(τ ) ∂τ + H0(ξ∗ ka(τ ), ξka′(τ )) + VE(ξ∗ ka(τ ), ξka′(τ )) (C2) H0(ξ∗ ka(τ ), ξka′(τ )) = δaa′ξ∗ ka(τ )εka′ξka′(τ ) (C3) VE...

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    Green function We introduce Green function Gkaa′(τ, τ′) ≡ −⟨Tcka(τ )c† ka′(τ ′)⟩ = −Tr e−β bH cka(τ )c† ka′(τ ′) . (C12) Applying Heisenberg picture cka(τ ) = eτ bH cka(0)e−τ bH , c † ka(τ ) = eτ bH c† ka(0)e−τ bH , Gkaa′(τ, τ′) = − Tr e−β bH eτ bH cka(0)e−τ bH eτ ′ bH c† ka′(...

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    Source fields We introduce source fields {αka(τ ), γka(τ )} for {ξka(τ ), ξ∗ ka(τ )}. Then, the non-perturbative action S0,α,γ is, S0,α,γ = Z β 0 dτ X a Z ddk (2π)d ξ∗ ka(τ ) ∂ξka(τ ) ∂τ + ξ∗ ka(τ )εkaξka(τ ) + αka(τ )ξka(τ ) + ξ∗ ka(τ )γka(τ ) . (C22) We perform Fourier trans...

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    propagator

    The expectation value of the current The expectation value of the output current is, ⟨ bJ µ⟩(τ ) = 1 Z Z Dξ∗Dξ evµ E(τ )e−S , (C32) where bvµ E(τ ) is the velocity operator obtained by the analytic continuation bvµ E(τ ) ≡ bvµ E(t), with bvµ E(t) ≡ ˙br µ = −i[brµ, bH0 + bVE(t)...

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    (C39) We perform the inverse Fourier transformation ⟨ bJ µ⟩(ωn) = R β 0 dτ ⟨ bJ µ⟩(τ )eiωnτ

    The first order The corresponding terms in the product of (C35) and (C36) is, (O(E) terms) = (X aa′ Z ddk (2π)d −δ δγka(τ ) hµ kaa′ δ δαka′(τ ) ) × ( − Z β 0 dτ ′ X bb′ Z ddk′ (2π)d i Z dωn;1e−iωn;1τ ′ e ωn;1 Eα1 (ωn;1) −δ δγk′b(τ ′) hα1 k′bb′ δ δαk′b′(τ ′) ) + (X aa′ Z ddk (2...

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    1 /2” is added on the latter three terms and the position of “[( ω1, α1) ← →(ω2, α2)]

    The second order The corresponding terms in the product of (C35) and (C36) is, (O(E2) terms) = X aa′ Z ddk (2π)d −δ δγka(τ ) hµ kaa′ δ δαka′(τ ) × ( 1 2! Z β 0 dτ ′dτ ′′ X bb′cc′ Z ddk′ (2π)d ddk′′ (2π)d i2 Z dωn;1dωn;2e−i(ωn;1τ ′+ωn;2τ ′′) × e2 ωn;1ωn;2 Eα1 (ωn;1)Eα2 (ωn;2) −...

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    It is obtained from the contribution satisfying a ̸= c

    Shift current Shift current is the γ independent part of the second order response. It is obtained from the contribution satisfying a ̸= c. We assume that γ, ω is sufficiently small compared to the energy scale of the system. Then the resonant contribution (ω1, ω2 ∼ εkab) is, ...

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    Note that velocity operator given by Eq

    Linear order Here, we assume field E(t) = Ee−iωt+γt, where γ is small positive constant, and the factor eγt added for the convergence at t → −∞. Note that velocity operator given by Eq. (D5) depends on electric field as well. Expanding the above equation, we have ⟨vµ(t)⟩(1) = ...

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    Second order Assume field E(t) = E1e−iω1t+γt + E2e−iω2t+γt. Expand the term including two fields and insert complete sets between every operators, similarly as in the case of linear order, we obtain ⟨vµ(t)⟩(2) =⟨vµ I (t)⟩0 − i⟨vµ I (t) Z t −∞ dt1VI (t1)⟩0 − i⟨ Z −∞ t dt1VI (t1...

Pith tools

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