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REVIEW 4 major objections 4 minor 41 references

Adiabaticity violation under arbitrarily slow evolution

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

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Pith's one-line read Pausing a Landau-Zener sweep lets a quantum state switch energy levels even though average evolution is five times slower.

desk verdict A competent coherent-control experiment with an unsupported headline claim: the 'arbitrarily slow' violation is an artifact of comparing average speed while keeping the sweep speed finite. read the letter →

arxiv 2506.02681 v1 pith:QMWCILJO submitted 2025-06-03 quant-ph physics.optics

Oubo You , Zhaoqi Jiang , Jinhui Shi , Qing Dai , Chunying Guan , Shuang Zhang This is my paper
classification quant-phphysics.optics
keywords adiabatictheoremLandau-Zenerprocessinstantaneoustransitionprobabilityaccumulationcross-Berryconnectionphasedifferencemanipulationspoofsurfaceplasmonpolaritonwaveguide
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 seeks to show that the quantum adiabatic theorem's promise—stay in the instantaneous eigenstate if the evolution is slow, gapped, and resonance-free—does not cover every slow-looking schedule. By inserting pauses into a Landau-Zener sweep, the authors make a photonic two-level system end on the opposite energy level even though its average parameter speed is five times smaller than a conventional adiabatic sweep. They attribute the effect to the instantaneous transition probability and its time integral, and show that pausing at the right moments redirects population rather than suppressing transitions. If correct, this means slow average speed alone does not guarantee adiabaticity, with direct implications for quantum computing schedules, topological pumps, and waveguide mode converters.

What carries the argument

The central object is the instantaneous transition probability $P_n(t)=2i\sum_{m\neq n} c_m(t)c_n^*(t)A_{nm}(t)$, with $A_{nm}=i\langle n(t)|m'(t)\rangle$ the cross-Berry connection, together with its time integral, the instantaneous transition accumulation (ITA). Equation (1) is the identity that carries the argument: the rate of change of an eigenstate's population is the real part of a product of the evolving state amplitudes and the geometric connection, so adiabaticity is a matter of whether this real part integrates to zero, not merely whether the coupling is small. Pausing sets $A_{nm}=0$ while the phase of $c_m c_n^*$ advances, which lets an experimenter keep $\mathrm{Re}(P_n)$ nonnegative and force one-way population transfer along a fixed parameter path.

What would settle it

Compare the paused protocol with a smooth sweep of the same total duration and endpoints: if, as total time grows, the smooth sweep always returns to the initial eigenstate while the paused protocol can still flip levels, then the effect is tied to the discontinuous-in-scaled-time schedule rather than to a failure of adiabatic following for genuinely slow smooth evolution.

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Extended reading notes

Core claim

For a two-level Landau-Zener Hamiltonian $H_{LZ}(t)=V\sigma_x+\lambda(t)\sigma_z$, the paper writes the rate of change of an instantaneous eigenstate's population as $d|c_n|^2/dt=\mathrm{Re}(2i\sum_{m\neq n} c_m c_n^* A_{nm})$, where $A_{nm}=i\langle n|m'\rangle$ is the cross-Berry connection. It argues that the sign of this real part, not the conventional small ratio $|\langle n|m'\rangle/(E_n-E_m)|$, controls whether population is lost, and that the accumulated integral (ITA) is what vanishes in adiabatic evolution. The phase difference manipulation method pauses the Hamiltonian whenever the real part would turn negative; during the pause the cross-Berry connection is zero while the amplitude product $c_m c_n^*$ keeps rotating, so the next ramp resumes with the transition rate positive. The designed protocol leaves the state on the lower energy branch despite a fivefold smaller average speed, and the level switch is reproduced in full-wave simulations and microwave measurements on coupled spoof surface plasmon polariton waveguides.

Load-bearing premise

The argument depends on treating a sweep that is slow only on average, because the Hamiltonian is held fixed during long pauses, as covered by the adiabatic theorem's 'sufficiently slow' guarantee, whereas the theorem requires the rate of change to be small and smooth at every instant.

Editorial extensions

If this is right

  • The conventional adiabatic criterion $|\langle n|m'\rangle/(E_n-E_m)|\ll 1$ is not sufficient by itself; the phase history of the amplitude product $c_m c_n^*$ determines whether individual transitions accumulate or cancel.
  • Adiabatic quantum computing schedules that include idle or paused periods can lose ground-state fidelity even when their average speed is extremely low.
  • Topological pumps and waveguide mode converters that rely on adiabatic following can be disrupted by adding pauses along the same parameter path.
  • The ITP/ITA decomposition turns non-adiabatic control into a phase-engineering problem: one can induce or suppress transitions without changing the path, including the shortcut-like cases the supplementary information reports.

Reading between the lines

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

  • Beyond the paper: if the phase-rotation mechanism is correct, the same pause recipe should generalize to multi-level sweeps by controlling each pair's ITP independently; this is a testable extension the paper does not report.
  • Beyond the paper: the protocol implies that 'slow' should be judged by uniform smallness of the instantaneous rate of change along a smooth schedule, not by average speed; slow-by-dwelling schedules occupy a regime the standard adiabatic theorem was never formulated to cover.
  • Beyond the paper: each pause acts as a free phase rotation between ramp segments, so the final transition probability may be expressible as a product of ramp transition matrices and phase gates, a closed-form description the paper leaves implicit.
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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 claims that the quantum adiabatic theorem can be violated in arbitrarily slow, resonance-free processes. It introduces two quantities, ITP and ITA, defined through the exact rate of population change of instantaneous eigenstates, and proposes a 'phase difference manipulation' (PDM) scheme in which a Landau-Zener sweep is interrupted by pauses designed to keep the real part of the transition rate non-negative. The authors report a spoof-surface-plasmon waveguide experiment in which a paused Landau-Zener sweep produces a final state on the opposite energy level, despite an average sweep speed five times smaller than that of a conventional adiabatic sweep. They conclude that the adiabatic theorem is incomplete and that ITA/ITP provide a more fundamental framework for adiabatic evolution.

Significance. If the central claim were correct, it would contradict the Born-Fock theorem and would have broad implications for adiabatic quantum computing and topological pumps. The exact population-rate identity in Eq. (1) and the experimental mode switching in a finite-time Landau-Zener process appear credible. However, the manuscript does not support the advertised conclusion: the protocol never approaches the adiabatic slow limit, the ITA criterion is a tautology, and the PDM schedule is constructed from the exact solution it claims to predict. The experimental control (long adiabatic sample) shows only that inserting pauses into a sweep changes the final population at fixed finite speed, not that adiabaticity fails in the slow limit. The significance claim is therefore not established.

major comments (4)
  1. [Abstract; Fig. 1b] The central claim that adiabaticity can be violated at arbitrarily slow evolution is not supported by the presented protocol. In Fig. 1b the instantaneous sweep speed remains alpha = 0.2 during every parameter-changing segment; the pauses only dilute the total time and reduce the average speed. The adiabatic theorem's slow limit is defined by a uniform vanishing of dH/dt as the total evolution time goes to infinity, or by a fixed smooth H(s) with T going to infinity. Here, increasing the total time by prolonging pauses does not reduce dH/dt on the sweep segments, and in the scaled-time variable the sweep segments shrink while H develops discontinuities in derivative, and in the limit of infinitely long pauses actual discontinuities, at the pause boundaries. All population transfer between instantaneous eigenstates occurs during the finite-speed sweep segments, so the experiment is a finite-time control demonstration and not a counterexample to the Born-Fock theorem.
  2. [Eq. (1); 'Instantaneous transition and its manipulation'] The ITA criterion is tautological. Equation (1) states d|c_n|^2/dt = Re(P_n), and ITA is defined as the integral of Re(P_n); therefore Re(A_n) = |c_n(t_f)|^2 - |c_n(t_i)|^2 exactly. The statement that adiabaticity holds when Re(A_n) is approximately zero is equivalent to saying the population of band n is unchanged when its total change is zero. No independent approximation for Re(P_n) in terms of the Hamiltonian and its derivatives is derived in the main text; without such an approximation the framework provides no predictive content beyond the exact Schrodinger equation. The traditional criterion can be derived from Eq. (1), but that does not make ITA a new physical principle.
  3. [PDM method, Fig. 2a] The PDM scheduling rule is circular as a method for controlling adiabaticity. The proposed rule is to pause the Hamiltonian when Re(P_n) is about to become negative, but P_n(t) = 2i sum over m of c_m c_n^* A_nm depends on the instantaneous amplitudes c_m(t) and c_n(t); knowing when to pause therefore requires knowing the exact solution of the time-dependent Schrodinger equation that the method is supposed to predict. The paper does not provide a closed-form or Hamiltonian-only criterion for choosing the pause points. Thus the method reconstructs the exact dynamics rather than explaining it.
  4. [Fig. 3e,f] The experimental comparison also undermines the 'fivefold slower' language. The stretched adiabatic sample in Fig. 3e,f has the same total evolution length as the counter-adiabatic sample but a uniform sweep speed of 0.04, and it remains adiabatic. This control demonstrates that the switching in Fig. 3c,d is caused by the non-smooth pause structure at a fixed instantaneous speed, not by a slower overall evolution. It is therefore not evidence for adiabaticity violation in arbitrarily slow processes.
minor comments (4)
  1. [Eq. (1)] The text says 'to the first order in a Taylor series' but then uses the result as an exact identity; please clarify that the derivative formula is exact and that no small-delta-t approximation is being made.
  2. [Supplementary Information] The paper repeatedly refers to SI sections I-VI, but the SI was not included with the manuscript, so the derivations of the traditional criterion and the additional examples could not be checked.
  3. [Data availability] The data availability statement says data are available 'by contacting corresponding authors'; this is not a data-availability statement and should be replaced with a repository or a specific description of the data and code.
  4. [Abstract and Introduction] The words 'revolutionary' and 'counter-intuitive' overstate the novelty; please temper the language to match the actual claims of the manuscript.

Circularity Check

3 steps flagged · score 8.0 of 10

The new ITA/ITP criterion restates the definition of population change, the PDM schedule enforces the sign of that change by construction, and 'arbitrarily slow' is achieved by adding zero-effect pauses, so the central claim is forced by definition rather than by the adiabatic theorem.

  1. self definitional [Instantaneous transition and its manipulation; Eq. (1) and following paragraph]
    "ITA, the integral of ITP along the entire evolution process, whose real part Re(An) = Re (∫ Pn dt), quantifies the population deviation of the nth band. Adiabaticity holds when Re(An) ≈ 0 for all bands."

    By Eq. (1), d|cn|^2/dt = Re(Pn), so Re(An) = Re(∫ Pn dt) = |cn(tf)|^2 − |cn(ti)|^2 by the fundamental theorem of calculus. The paper first defines adiabatic evolution as |cn(tf)|^2 ≈ |cn(ti)|^2, then 'derives' that adiabaticity holds when Re(An) ≈ 0. The latter is just the former with the population difference renamed ITA. Thus ITA is not independent evidence for or an explanation of adiabaticity; it is the target quantity itself.

  2. self definitional [Instantaneous transition and its manipulation; PDM method description]
    "To prevent this, we propose pausing the time variation of the Hamiltonian when Pn approaches the negative half plane. During this pause, the cross-Berry connection becomes zero, setting Pn = 0, and halting population loss from the nth band. Meanwhile, cm(t)cn*(t) continues to rotate. After a half cycle, defined by the circular frequency Δω = ωn − ωm, the Hamiltonian’s time variation resumes, ensuring Re(Pn) remains non-negative and population accumulates (Re(An) > 0)."

    In Eq. (1), Re(Pn) is the instantaneous rate d|cn|^2/dt. The PDM protocol is defined as pausing whenever Re(Pn) would become negative and resuming after a half cycle so that Re(Pn) stays non-negative. Therefore the statement 'population accumulates (Re(An)>0)' is true by construction: the schedule was selected to make the derivative non-negative. Reporting the resulting monotonic transfer as a discovered 'adiabaticity violation' presents the imposed control signal as an independent prediction. The exact Schrödinger equation guarantees the result; no unforeseen content is added.

1 more flagged steps
  1. self definitional [Breaking adiabaticity in slow LZ process; Fig. 1b and following paragraph]
    "In this modified process, the maximum instantaneous speed, given by the slopes of the yellow segments in Fig. 1b, remains 0.2 while the average speed, λ̅′ = 0.04, is significantly lower than the standard adiabatic LZ process. This violates the traditional adiabatic theorem, which predicts better adiabaticity at lower speeds."

    The schedule is called fivefold slower because pauses are inserted while the sweep segments still run at λ′=0.2. During a pause dH/dt=0, so from Eq. (1) the cross-Berry connection vanishes and d|cn|^2/dt = Re(Pn) = 0; populations are frozen. Lengthening pauses therefore makes the average speed arbitrarily small without changing any population transfer. 'Adiabaticity is violated at arbitrarily slow evolution' is then true only under the paper's average-speed definition, not in the adiabatic theorem's limit of uniformly vanishing instantaneous rate; the contradiction is manufactured by defining 'slow' to include flat intervals that do no dynamical work.

full rationale

The central derivation chain is definitional rather than predictive. Eq. (1) is an exact identity for the instantaneous-basis population derivative, so ITA is simply the total population change and the criterion 'adiabaticity holds when Re(An)≈0' restates the definition of adiabaticity given two sentences earlier. The PDM method then uses Eq. (1) as a control signal, pausing to prevent Re(Pn) from becoming negative; the resulting monotonic population transfer is imposed by construction, not discovered. The 'arbitrarily slow' claim is likewise built from pauses that have zero transition rate and leave final populations unchanged, while the active sweep segments remain at the original finite speed; comparing average speeds makes the slowness an artifact of definition. No load-bearing self-citations or fitted data are involved, and the waveguide experiment and full-wave simulations are genuine and self-consistent, which prevents a score of 10. The circularity is in the interpretation: the new framework and the central counterintuitive conclusion are forced by the paper's own definitions rather than by any independent derivation.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The central derivation relies only on the Schrodinger equation; Eq. (1) is exact. The paper adds no new axioms beyond the two-level model and the mapping of waveguide propagation distance to time. The pause schedule and sweep parameters are chosen to produce the effect, and the ITA/ITP framework is a restatement of exact population dynamics rather than an independent theory.

free parameters (4)
  • Sweep speed alpha = 0.2
    Chosen maximum instantaneous sweep speed; the comparison process runs at this speed. The adiabatic limit would require alpha to go to zero, which is not taken.
  • Pause schedule = Segments selected so Re(P_-+) >= 0
    Pause positions and durations are chosen to keep the real part of the transition rate non-negative; this schedule is the control input that forces the level switch.
  • Effective coupling Delta beta = 0.0713 mm^-1
    Extracted from CST full-wave simulation of the waveguide geometry, not from an independent experiment.
  • Landau-Zener sweep range = -1.5 to 1.5
    Truncated sweep chosen for numerical and experimental practicality instead of the ideal +/- infinity.
assumptions (5)
  • standard math Schrodinger equation with hbar = 1
    Used to derive Eq. (1), the exact population dynamics.
  • domain assumption Two-level Landau-Zener Hamiltonian H = V sigma_x + lambda sigma_z
    Assumed to describe the two coupled waveguide modes.
  • domain assumption Paraxial approximation maps propagation distance z to time t
    Used to design the sSPP waveguide system; not exact for all geometries.
  • domain assumption Effective Hamiltonian parameters extracted from full-wave simulation are faithful
    Used to convert theory to sample geometry; relies on simulation fidelity rather than independent measurement.
  • standard math Smoothness and uniform rate reduction required by the adiabatic theorem
    The paper compares against the theorem but does not maintain its hypotheses; the paused Hamiltonian is non-smooth in the adiabatic limit.
invented entities (2)
  • ITA (Instantaneous Transition Accumulation)
    purpose: Claimed new parameter to quantify adiabaticity; defined as the integral of Re(P_n).
    Defined such that it is exactly the population change, so it has no independent predictive handle.
  • ITP (Instantaneous Transition Probability)
    purpose: Claimed new parameter; defined as the real part of 2 i sum c_m c_n^* A_nm.
    An exact expression for d|c_n|^2/dt; no separate physical content beyond the Schrodinger equation.

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Cite this review

Pith. "Pith review of Adiabaticity violation under arbitrarily slow evolution." pith.science (2026). https://pith.science/paper/QMWCILJO

@misc{pith2026250602681,
  author       = {Pith},
  title        = {Pith review of: Adiabaticity violation under arbitrarily slow evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QMWCILJO}},
  note         = {Machine review of arXiv:2506.02681}
}
read the original abstract

The quantum adiabatic theorem, a cornerstone of quantum mechanics, asserts that a gapped quantum system remains in its instantaneous eigenstate during sufficiently slow evolution, provided no resonances occur. Here we challenge this principle and show that adiabaticity can be violated even in arbitrarily slow processes. We introduce two new parameters, Instantaneous Transition Accumulation (ITA) and Instantaneous Transition Probability (ITP), to redefine the framework of adiabatic evolution. These parameters, grounded in cross-Berry connections and eigenstate amplitudes, reveal the dynamic and geometric factors governing adiabaticity. Using a new Phase Difference Manipulation (PDM) method, we control ITP and ITA to induce adiabaticity violation in a Landau-Zener (LZ) process. We experimentally demonstrate this counterintuitive phenomenon in a photonic waveguide system, where a slow LZ process defies adiabaticity, switching energy levels despite a fivefold slower evolution speed than a conventional adiabatic process. This discovery reshapes our understanding of quantum evolution and holds potential for quantum computing, topological physics, and photonic technologies.

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Works this paper leans on

41 extracted references · 37 canonical work pages

  1. [1]

    Born and V

    M. Born and V. Fock, Zeitschrift für Physik 51, 165 (1928)

    work page 1928

  2. [2]

    N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Annu Rev Phys Chem 52, 763 (2001)

    work page 2001

  3. [3]

    K. P. Marzlin and B. C. Sanders, Phys Rev Lett 93, 160408 (2004)

    work page 2004

  4. [4]

    J. Du, L. Hu, Y. Wang, J. Wu, M. Zhao, and D. Suter, Phys Rev Lett 101, 060403 (2008)

    work page 2008

  5. [5]

    M. H. Amin, Phys Rev Lett 102, 220401 (2009)

    work page 2009

  6. [6]

    Wang and M

    Z.-Y. Wang and M. B. Plenio, Physical Review A 93, 052107 (2016)

    work page 2016

  7. [7]

    J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics (Cambridge University Press, Cambridge, 2020), 3 edn

    work page 2020

  8. [8]

    D. M. Tong, Phys Rev Lett 104, 120401 (2010)

    work page 2010

Show all 41 references
  1. [9]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, arXiv:quant (2000)

    2000

  2. [10]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science 292, 472 (2001)

    2001

  3. [11]

    Roland and N

    J. Roland and N. J. Cerf, Physical Review A 65, 042308 (2002)

    2002

  4. [12]

    M. W. Johnson et al., Nature 473, 194 (2011)

    2011

  5. [13]

    T. F. Ronnow, Z. H. Wang, J. Job, S. Boixo, S. V. Isakov, D. Wecker, J. M. Martinis, D. A. Lidar, and M. Troyer, Science 345, 420 (2014)

    2014

  6. [14]

    Wilczek and A

    F. Wilczek and A. Zee, Physical Review Letters 52, 2111 (1984)

    1984

  7. [15]

    M. V. Berry, Proce edings of the Royal Society of London. A. Mathematical and Physical Sciences 392, 45 (1997)

    1997

  8. [16]

    M. Z. Hasan and C. L. Kane, Reviews of Modern Physics 82, 3045 (2010)

    2010

  9. [17]

    Xiao, M.-C

    D. Xiao, M.-C. Chang, and Q. Niu, Reviews of Modern Physics 82, 1959 (2010)

    2010

  10. [18]

    Alexandradinata, X

    A. Alexandradinata, X. Dai, and B. A. Bernevig, Phys Rev B 89, 155114 (2014)

    2014

  11. [19]

    Masuda, K

    S. Masuda, K. Nakamura, and A. del Campo, Phys Rev Lett 113, 063003 (2014)

    2014

  12. [20]

    H. I. Lu, M. Schemmer, L. M. Aycock, D. Genkina, S. Sugawa, and I. B. Spielman, Phys Rev Lett 116, 200402 (2016)

    2016

  13. [21]

    Hänsel, P

    W. Hänsel, P. Hommelhoff, T. W. Hänsch, and J. Reichel, Nature 413, 498 (2001)

    2001

  14. [22]

    D. J. Thouless, Phys Rev B 27, 6083 (1983)

    1983

  15. [23]

    H. Q. Zhou, S. Young Cho, and R. H. McKenzie, Phys Rev Lett 91, 186803 (2003)

    2003

  16. [24]

    Y. E. Kraus, Y. Lahini, Z. Ringel, M. Verbin, and O. Zilberberg, Phys Rev Lett 109, 106402 (2012)

    2012

  17. [25]

    L. Wang, M. Troyer, and X. Dai, Phys Rev Lett 111, 026802 (2013)

    2013

  18. [26]

    Taddia, E

    L. Taddia, E. Cornfeld, D. Rossini, L. Mazza, E. Sela, and R. Fazio, Phys Rev Lett 118, 230402 (2017)

    2017

  19. [27]

    Zilberberg, S

    O. Zilberberg, S. Huang, J. Guglielmon, M. Wang, K. P. Chen, Y. E. Kraus, and M. C. Rechtsman, Nature 553, 59 (2018)

    2018

  20. [28]

    Jurgensen, S

    M. Jurgensen, S. Mukherjee, and M. C. Rechtsman, Nature 596, 63 (2021)

    2021

  21. [29]

    O. You, S. Liang, B. Xie, W. Gao, W. Ye, J. Zhu, and S. Zhang, Phys Rev Lett 128, 244302 (2022)

    2022

  22. [30]

    Sun, X.-L

    Y.-K. Sun, X.-L. Zhang, F. Yu, Z.-N. Tian, Q.-D. Chen, and H.-B. Sun, Nature Physics 18, 1080 (2022)

    2022

  23. [31]

    Song et al., Sci Adv 10, eadn5028 (2024)

    W. Song et al., Sci Adv 10, eadn5028 (2024)

    2024

  24. [32]

    X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guery-Odelin, and J. G. Muga, Phys Rev Lett 104, 063002 (2010)

    2010

  25. [33]

    X. Chen, E. Torrontegui, and J. G. Muga, Physical Review A 83, 062116 (2011)

    2011

  26. [34]

    X. Chen, E. Torrontegui, D. Stefanatos, J.-S. Li, and J. G. Muga, Physical Review A 84, 043415 (2011)

    2011

  27. [35]

    M. V. Berry, Journal of Physics A: Mathematical and Theoretical 42, 365303 (2009)

    2009

  28. [36]

    M. G. Bason et al., Nature Physics 8, 147 (2011)

    2011

  29. [37]

    Martínez-Garaot, A

    S. Martínez-Garaot, A. Ruschhaupt, J. Gillet, T. Busch, and J. G. Muga, Physical Review A 92, 043406 (2015)

    2015

  30. [38]

    Guéry-Odelin, A

    D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, Reviews of Modern Physics 91, 045001 (2019)

    2019

  31. [39]

    del Campo and K

    A. del Campo and K. Kim, New Journal of Physics 21, 050201 (2019)

    2019

  32. [40]

    A. K. Taras, A. Tuniz, M. A. Bajwa, V. Ng, J. M. Dawes, C. G. Poulton, and C. M. De Sterke, Advances in Physics: X 6, 1894978 (2021)

    2021

  33. [41]

    Zener, Proceedings of the Royal Society of Lon don

    C. Zener, Proceedings of the Royal Society of Lon don. Series A, Containing Papers of a Mathematical and Physical Character 137, 696 (1932). Fig. 1 Adiabaticity violation in LZ process. a, Schematic of adiabatic LZ process with average evolution speed 𝜆̅′ = 0.2 which is indica...

    1932

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Reviewed August 7, 2026 · model on record in the stance chip above.