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REVIEW 3 major objections 5 minor 96 references

Sticking coefficient for atoms impinging on a metallic surfaces, and the x-ray photoemission by metals

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read This paper claims that the adiabatic theorem fails for a gapless Fermi gas beyond a critical localized-potential strength, and that the same electron-gas physics produces oscillatory XPS and a 0.3 eV sticking peak for hydrogen on copper.

desk verdict A thesis with one solid photoemission result, one interesting but under-supported adiabaticity claim, and one suggestive sticking calculation; referee-worthy but needs revision before the gapless-breakdown claim is published. read the letter →

arxiv 2412.14839 v1 pith:NNMMZA4U submitted 2024-12-19 cond-mat.mtrl-sci physics.atom-ph

Gustavo Diniz This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.atom-ph
keywords stickingcoefficientx-rayphotoemissionAndersonorthogonalitycatastropheadiabatictheoremnumericalrenormalizationgroupboundstatehydrogen-coppercollisionDoniach-Sunjicpowerlaw
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 sets out to unify three out-of-equilibrium electron-gas problems: x-ray photoemission from metals, the response of a Fermi gas to a slowly growing localized potential, and the collision of a neutral hydrogen atom with a copper surface. Its central claim is that the conventional adiabatic criterion, which says slow ramps are adiabatic, is wrong for a gapless electron gas: what matters is the number of energy scales involved in screening, with a universal formula giving the ground-state survival probability and a critical potential beyond which adiabatic evolution is impossible. In the same framework, the paper explains the time-dependent photoemission rate as interference between two decay channels, and computes a sticking coefficient that peaks near 0.3 eV, in semi-quantitative agreement with experiment. A sympathetic reader would care because the results give testable predictions for XPS satellite peaks and for when non-adiabatic effects in atom-surface collisions cannot be ignored.

What carries the argument

The central object is the instantaneous many-body eigenbasis of the time-dependent Hamiltonian, together with the derivative coupling $\langle\varphi_n|\partial_t|\varphi_m\rangle$ that drives transitions between instantaneous eigenstates. For a continuous ramp this coupling connects only states differing by one particle-hole pair, which reduces the many-body Schrödinger equation to the closed set of equations (4.9); numerical solution of that set collapses onto the universal law (4.10), from which the adiabatic threshold and the critical potential follow. In the photoemission problem the same basis is split into 'plugged' states, with the bound level occupied and decaying by the Doniach-Sunjic power law, and 'unplugged' states, with the bound level empty and decaying by the Nozières-De Dominicis power law; their phase difference is what produces the predicted oscillations.

What would settle it

Rerun the eNRG calculation with two-particle-hole excitations included for parameter sets on the adiabatic boundary of Fig. 23; if the boundary shifts substantially, the single-pair truncation and the critical potential are falsified, and a time-resolved XPS scan looking for the $|\epsilon_B|/\hbar$ oscillation would test the photoemission interference claim.

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Extended reading notes

Core claim

For an electron gas subject to a localized potential ramped linearly from zero to $\bar K$ over time $T$, the probability that the system remains in the instantaneous ground state is $|c_0(T)|^2 = (4.4\hbar/(\Delta\varepsilon T))^{-(\delta/\pi)^2(1+(\delta/\pi)^2)}$, where $\delta$ is the scattering phase shift and $\Delta\varepsilon$ the single-particle level spacing. Adiabaticity is therefore controlled by the combination $\Delta\varepsilon T/\hbar$ and by the potential strength, not by the ramp rate $\bar K/T$ as the Quantum Adiabatic Criterion would have it. The adiabatic region is bounded by $\rho|\bar K| \leq \eta (\log(4.4\hbar/(\Delta\varepsilon T)))^{-1/2}$, and in the continuum limit there is a critical potential $\rho|\bar K_c| = \eta/\sqrt{4.4}$ beyond which no ramp time $T \leq \hbar/\Delta\varepsilon$ yields adiabatic evolution, a violation of the naive adiabatic theorem in a gapless system. The same bound-state physics, in which a strong core-hole potential creates a level below the band, makes the photoemission fidelity oscillate at frequency $|\epsilon_B|/\hbar$ as two power-law decay channels interfere, and the collision calculation yields a sticking coefficient peaked near 0.3 eV.

Load-bearing premise

The adiabaticity criterion assumes that during a slow ramp the electron gas never needs more than one particle-hole pair at a time; if multiple pairs contribute significantly near the threshold, the universal formula and the critical potential do not follow.

Editorial extensions

If this is right

  • X-ray photoemission spectra of simple metals should show a satellite peak displaced from the main threshold by the bound-state energy $|\epsilon_B|$, decaying with the Nozières-De Dominicis exponent.
  • Time-domain photoemission measurements should display oscillations at frequency $|\epsilon_B|/\hbar$ whose amplitude decays faster than the average current.
  • The Quantum Adiabatic Criterion is unreliable for gapless fermionic systems; adiabaticity estimates should be replaced by the threshold $\rho|\bar K| \leq \eta (\log(4.4\hbar/(\Delta\varepsilon T)))^{-1/2}$.
  • For a strictly gapless band, no slow ramp can adiabatically turn on a localized potential stronger than $\rho|\bar K_c| = \eta/\sqrt{4.4}$, whereas a finite gap restores adiabaticity for sufficiently long ramp times.
  • The H-Cu sticking coefficient is controlled by a tradeoff between growing non-adiabatic energy loss and traversal time through the interaction region, peaking near 0.3 eV.

Reading between the lines

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

  • If the bound-state interference picture is correct, time-resolved XPS on any simple metal with a strong core-hole potential should see the predicted $|\epsilon_B|/\hbar$ oscillations, offering a direct test outside the collision context.
  • The critical-potential result suggests that gapless many-body systems beyond the single-particle picture, such as interacting metals near quantum critical points, may also fail to follow slow ramps once a local perturbation exceeds a threshold.
  • The universal prefactor 4.4 is fitted to a single-particle-hole calculation; a calculation that includes two-particle-hole excitations could shift the threshold and the critical potential, so the quantitative value should be treated with caution.
  • The spinless H-Cu model could be extended to include spin degrees of freedom and phonon channels; the semi-quantitative agreement with experiment suggests those extensions would refine, not overturn, the peak near 0.3 eV.
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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

3 major / 5 minor

Summary. The manuscript, based on the author's doctoral thesis, studies three out-of-equilibrium electron-gas problems. Chapter 3 treats x-ray photoemission from a metal after a sudden core-hole potential, deriving analytical expressions for the fidelity and spectral function that include excitations out of the bound state; it predicts oscillations in the time-domain fidelity with frequency |ε_B|/ℏ and a satellite peak obeying the Nozières–De Dominicis power law, supported by direct diagonalization and eNRG. Chapter 4 studies a Fermi gas with a linearly ramped local potential and claims that adiabaticity is controlled by the number of participating energy scales rather than by the ramp rate, leading to Eq. (4.10), the threshold Eq. (4.13), and a critical potential Eq. (4.15). Chapter 7 applies NRG and Crank-Nicolson to H-Cu collisions and computes a sticking coefficient with a maximum near 0.3 eV, in semi-quantitative agreement with experiment.

Significance. The photoemission part is the strongest: the bound-state/unplugged-state decomposition yields explicit, falsifiable predictions—oscillations at |ε_B|/ℏ whose amplitude decays faster than the Doniach-Sunjic envelope—and these are checked against direct diagonalization and eNRG. The eNRG/block-diagonal methodology is a practical computational contribution. The adiabaticity claim, if correct, is conceptually important because it challenges the Quantum Adiabatic Criterion in gapless systems. However, the central quantitative conclusions in §4 rest on a fitted prefactor and an extrapolation, and the critical-value formula contains an algebraic inconsistency. The sticking-coefficient model is less analytically developed but includes a transparent numerical treatment and a semi-quantitative comparison with experiment.

major comments (3)
  1. [§4.2, Eqs. (4.13) and (4.15)] Setting T=Tm=ℏ/Δε in Eq. (4.13) yields ρ|K| ≤ η (ln 4.4)^{-1/2} ≈ 0.675 η, not η/√4.4 ≈ 0.477 η. Eq. (4.15) therefore does not follow algebraically from Eq. (4.13). Since the critical amplitude is a central claim of the chapter, the manuscript must either correct Eq. (4.15) and the associated text (including the statement 'ρ| ¯K|≤ η√4.4' in §4.2) or identify the missing approximation that changes ln 4.4 into 4.4. This is not a peripheral typo: the existence and value of Kc are used to argue for violation of the adiabatic theorem in the gapless limit.
  2. [§4, Eq. (4.10) and Fig. 21] The constant 4.4 in Eq. (4.10) is introduced by rescaling the horizontal axis in Fig. 21 so that the numerical solution of the truncated system Eq. (4.9) collapses onto a single curve; it is therefore a fit to the very equations used to generate |c0(T)|^2. The exponents are derived in Appendix F, but the prefactor is not. Because Eq. (4.15) inherits this prefactor, the quantitative critical potential ρ|Kc|=η/√4.4 is not a parameter-free prediction. The manuscript should present the determination of 4.4 as an empirical constant, estimate its uncertainty or sensitivity, or derive it analytically.
  3. [§4.2, Figs. 22–23 and text after Eq. (4.13)] The eNRG comparison validates Eq. (4.9) down to |c0|^2≈0.6 for two finite gaps (Δε=1/210 and 1/843), while the adiabatic threshold η=0.1 corresponds to |c0|^2≈0.99, a different corner of parameter space. The sentence 'We expect therefore this expression to hold as Δε→0' is an extrapolation beyond the tested regime: as Δε→0 the number of low-energy single-particle levels diverges, and the validity of the single-pair truncation at the threshold is not established. A direct eNRG run at a smaller gap (e.g., Δε∼1/3000 with appropriate λ and N) targeting the threshold region (T close to Tm, |c0|^2≈0.99) would substantially strengthen the claim. Without it, the critical-Kc conclusion rests on the least-tested ingredient of the model.
minor comments (5)
  1. [Global] The manuscript has numerous typos and grammatical errors, including 'INTRODCUTION' in the Contents, 'beown plots' in §4.2, and 'sticking coefficient for atoms impinging on a metallic surfaces' in the title; a careful language edit is needed.
  2. [Eqs. (3.13)–(3.14)] The numerical constants 600 and 1.25 in Eq. (3.13) are introduced without derivation in the main text; Appendix B should state explicitly whether they are fitted or derived from an asymptotic expansion.
  3. [Fig. 39 caption] The caption says both the solid and dashed lines are computed by Eq. (2.8); one of them should refer to the constant-δ approximation or another distinct expression.
  4. [Eq. (2.8)] The notation 'atan' should be replaced by 'arctan' or 'tan^{-1}', and the sign convention for the phase shift δ should be stated once and used consistently.
  5. [References] Several parameter values in §7 are attributed to DFT calculations without complete citations; please add full references for the DFT-derived values of V0, zim, D, and the Cu surface parameters.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (4.10) is an empirical fit to the truncated dynamics, but the adiabatic threshold Eq. (4.13) is independently benchmarked against eNRG; fitted prefactors do not make the derivation circular.

full rationale

I find no load-bearing step in which a claimed prediction reduces by construction to its inputs. The quasi-adiabatic equations (4.9) are derived from the truncated Schrödinger equation coupled to an explicitly stated one-particle-hole assumption; the exponent in Eq. (4.10) is analytically motivated in Appendix F, while the prefactor 4.4 is inferred from the numerical solution of Eq. (4.9), as the Fig. 21 caption states: 'The black solid line shows that Eq. (4.10) fits the numerical data virtually perfectly.' This is model calibration, not circularity, because the resulting threshold Eq. (4.13) is then tested against independent eNRG data in Fig. 23, where the paper reports 'The curves and circles are in excellent agreement.' The eNRG comparison is a separate numerical method, not the same truncated equations used to produce the 4.4 prefactor. The gapless-limit extrapolation ('We expect therefore this expression to hold as Δε→0') is an unverified limit, and I note that Eq. (4.15) appears algebraically inconsistent with Eq. (4.13) at T = Tm (natural log would give η/√(ln 4.4), not η/√4.4); these are quantitative and extrapolation concerns, not circular reductions. No self-citation chain is used to forbid alternative interpretations, and no known result is merely renamed as a new derivation. The photoemission prefactors (600, 1.25) are likewise fitted constants in expressions for projections, but the oscillation frequency, the exponents, and the Doniach-Sunjic/Nozières-De Dominicis structure are derived and checked against direct diagonalization and eNRG. The central results therefore have independent numerical support despite their fitted prefactors.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central claims rest on several modeling simplifications: flat band, constant phase shift, single-particle-hole truncation, diagonal dominance, spinless collision model, and a finite NRG chain. The fitted prefactors in the analytical formulas introduce additional external input.

free parameters (3)
  • prefactor 4.4 in Eq. (4.10) = 4.4
    Fitted to the numerical solution of the truncated single-particle-hole equations (Fig. 21) to make the scaling collapse. It enters the adiabatic threshold (Eq. 4.13) and the critical potential (Eq. 4.15).
  • constant 600 in Eq. (3.13) = 600
    Appears in the prefactor of the ground-state projection ⟨φ0|φ0⟩ and is adjusted to match direct diagonalization data; affects the magnitude of the plugged-state contribution.
  • coefficient 1.25 in Eq. (3.13) exponent = 1.25
    Empirical correction to the exponent of the projection, fitted to numerical results.
assumptions (7)
  • domain assumption Flat band with constant density of states for the conduction band in the analytical treatment
    Used in Chapter 3 and 4 to derive phase shift, bound state energy, and fidelity formulas; the tight-binding numerics later show deviations at short times (Sec. 3.5).
  • domain assumption Energy-independent phase shift δ
    Invoked in deriving Eqs. (3.28)-(3.38) and the Doniach-Sunjic exponent; the authors note it is reliable only near the Fermi level (Sec. 3.3).
  • domain assumption Single-particle-hole truncation of the dynamics (Eq. 4.9)
    Justified for continuous W(t) by the smallness of Δδ/π terms, but it is an approximation that fails when many pairs are excited; the criterion (4.13) depends on it.
  • ad hoc to paper Diagonal dominance in Slater determinants (Eqs. 3.28-3.29)
    Used to approximate all many-body overlaps from single-particle overlaps; acknowledged by the authors as unreliable for high-energy states.
  • ad hoc to paper Spinless model for the atom-surface collision
    The abstract states 'Using a spinless model'; the full Hamiltonian (7.5) includes spin for the atom but the band is treated spinless; this simplification is not justified in detail.
  • domain assumption NRG discretization with finite Λ and Ñ sets an infrared cutoff via Δε T = ℏ
    Used to truncate the Wilson chain (Sec. 7); the choice Λ=8, Ñ=5 yields only six band levels, which limits the non-adiabatic processes.
  • domain assumption Heisenberg uncertainty relation Δε T = ℏ identifies the time scale
    Used to connect the gap to the observation time, leading to the critical Kc condition.

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Pith. "Pith review of Sticking coefficient for atoms impinging on a metallic surfaces, and the x-ray photoemission by metals." pith.science (2026). https://pith.science/paper/NNMMZA4U

@misc{pith2026241214839,
  author       = {Pith},
  title        = {Pith review of: Sticking coefficient for atoms impinging on a metallic surfaces, and the x-ray photoemission by metals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NNMMZA4U}},
  note         = {Machine review of arXiv:2412.14839}
}
read the original abstract

Out-of-equilibrium electron-gas systems exhibit rich physics, which we explore through three problems. First, we study photoemission from metals, traditionally analyzed in the frequency domain. Unexpectedly, the photoemission rate oscillates at high frequencies as it decays, with the oscillation amplitude decaying faster than the average current. Analytical and numerical results reveal this behavior arises from interference between two excitation processes: one decaying via the Doniach-Sunjic power law and the other following the faster Nozi\`eres-De Dominicis law. XPS experiments targeting this feature could identify its frequency-domain counterpart. Second, we examine adiabaticity in an electron gas subject to a localized potential ramping up at a constant rate. Analytical and numerical findings map the parameter space where the system behaves adiabatically. Contrary to the Quantum Adiabatic Criterion, which links adiabaticity to slow ramp-up rates, we show that the number of energy scales involved in screening the potential dictates non-adiabaticity. Lastly, we investigate the collision of a neutral hydrogen atom with a copper surface. Electron transfer ionizes the H atom, activating an image-charge potential that pulls the ion toward the surface. Using a spinless model, we numerically track the atomic wave packets evolution and compute the sticking coefficient, the probability the atom remains near the surface. The coefficient peaks near 300 meV, balancing non-adiabatic contributions, which increase with energy, and the traversal time through the interaction region. Numerical results align semi-quantitatively with experimental data.

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.