Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Controlling Schwinger tunneling via engineering of virtual particle phases in vacuum

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper shows that Schwinger pair production can be controlled by engineering electromagnetic potentials that shift the quantum phase of virtual particles, while the strong electric field in the interaction region stays unchanged.

desk verdict A useful three-configuration comparison with a real analytic cross-check, but the 'solely virtual phase' mechanism is overstated and needs an early-time rate analysis to support it. read the letter →

arxiv 2505.02882 v1 pith:5O5ZKCK3 submitted 2025-05-05 quant-ph hep-th

D.D. Su , B.F. Shen , Q.Z. Lv This is my paper · ORCID
classification quant-phhep-th
keywords SchwingerpairproductionvacuumtunnelingAharonov-BohmanaloguevectorpotentialphaseKleinregioncomputationalquantumfieldtheorymomentumspectra
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

This paper claims that the rate of electron-positron pair creation from vacuum, the Schwinger process, can be controlled by electromagnetic potentials rather than only by the electric field strength in the pair-creation region. In their simulations, adding a static vector potential beside or overlapping the strong-field zone changes the total pair-creation rate substantially, from 7251 to about 4260 in the configurations studied, without altering the field at x=0. The effect is traced to a shift of the Klein region and to interference between left- and right-moving pair states, both encoded in the phase of virtual particles. The authors reproduce the numerical energy spectra with an analytical transmission-coefficient model that agrees with the computed rates within 2.65 percent. If correct, the work establishes a vacuum analogue of the Aharonov-Bohm effect, where potentials control tunneling through phase, and suggests a less invasive experimental route to Schwinger pair production.

What carries the argument

The engine of the argument is the mapping from pair-production spectra to the single-particle Dirac transmission coefficient via the Hund formula, $\rho(E,t) = (2t/\pi)T(E)$. For delta-function scalar and vector potentials separated by a distance $L$, matching wave functions across the three spatial regions yields the transmission coefficients in Eqs. (3a)-(3c); in the presence of the vector potential they contain oscillatory terms $\sin(\eta)$ and $\cos(\eta)$ with $\eta = p_{2,\perp}L$, which encode interference between left- and right-going waves in the intermediate region. This object carries the paper's central claim: the phase a virtual particle accumulates between the electric-field barrier and the vector-potential barrier becomes a measurable modulation of the pair-creation rate, so potential engineering controls vacuum tunneling.

What would settle it

Vary the separation L between the electric and vector-potential regions in a full numerical CQFT simulation, entering a regime where multiple reflections between x=0 and x=L are non-negligible; if the production rate no longer follows the sinusoidal $\eta = p_{2,\perp}L$ modulation predicted by Eqs. (3b)-(3c), the phase-control claim holds only within the first-order scattering approximation. Alternatively, in a heavy-ion collision experiment, search for the predicted interference fringes in the pair momentum spectrum and check that they appear only after the return time $t_{\rm inf}$.

Watch

Extended reading notes

Core claim

The central discovery claim is that a static vector potential, placed either outside or overlapping the strong electric field, modifies Schwinger pair production through delocalized phase modulation of virtual particles: the Klein region, defined as the energy-momentum window where the positive and negative Dirac continua overlap, shifts and loses its symmetry, and the total creation rate changes from Gamma_I = 7251 to Gamma_II = 4260 and Gamma_III = 4244 while the local field in the interaction region remains unchanged. The momentum distribution of created electrons develops interference fringes that are absent in the field-only case, and the time-resolved spectra show that the Klein-region shift is instantaneous while the interference grows only after scattered particles return from the vector-potential region. The mechanism is captured analytically by transmission coefficients whose oscillatory terms depend on the phase $\eta = p_{2,\perp}L$ accumulated between the two potential barriers, matching the numerical spectra. The authors conclude that the vector potential influences the Schwinger tunneling process solely through phase, not through field intensity, making it a vacuum analogue of the Aharonov-Bohm effect.

Load-bearing premise

The load-bearing premise is that neglected multiple scattering between the electric-field region and the vector-potential region is genuinely negligible, so the analytical transmission coefficient stays a quantitatively faithful proxy for the full pair-creation rate.

Editorial extensions

If this is right

  • Pair production can be suppressed or enhanced in selected momentum intervals by placing a vector potential at a chosen position, without raising the field strength in the interaction zone.
  • The total yields in Cases II and III are nearly equal, but their optimal longitudinal momenta differ, so momentum-resolved measurements can identify which side of the pair-creation region holds the potential and can be used to save laser energy.
  • Interference fringes appear only after a characteristic return time $t_{\rm inf}$, giving a temporal signature that could distinguish potential-phase effects from field-intensity effects in an experiment.
  • The field configurations are in principle realizable in head-on or grazing heavy-ion collisions, linking the proposal to existing accelerator facilities.

Reading between the lines

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

  • A natural extension the paper leaves open: time-dependent potentials should allow dynamical phase control of pair production, with the accumulated phase acting as a time-varying knob; the static results here are the zeroth-order case.
  • If the effect is truly Aharonov-Bohm-like, the controlling quantity should be the gauge-invariant flux enclosed by virtual-particle trajectories, which would predict robustness to gauge choices and dependence on the loop geometry; the paper does not compute such an invariant.
  • The first-order scattering assumption sets a quantitative limit: at smaller separations or stronger potentials, multiple reflections between x=0 and x=L should produce Fabry-Perot-type resonances that modify the predicted sinusoidal modulation.
  • The same phase-engineering mechanism might extend to other tunneling-dominated vacuum processes, such as dynamically assisted Schwinger production, where potential phase could be combined with temporal driving.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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. This manuscript studies Schwinger pair production in three static field configurations: Case I with only a localized electric field, Case II with a vector-potential step located at x=+L, and Case III with the same vector-potential step located at x=-L, in each case leaving the electric field in the central interaction region unchanged. Using the computational quantum field theory (CQFT) approach, the authors compute particle numbers, momentum-resolved energy spectra, and time- and space-resolved distributions, finding that Case II and Case III reduce the total pair-creation rate by roughly 40% relative to Case I and that the momentum spectra exhibit interference patterns. An analytical model based on single-particle transmission coefficients for delta-function scalar and vector potential steps is developed in Appendix I, and the integrated rates agree with the numerical results within 2.65%. The paper interprets these results as evidence that electromagnetic potentials control Schwinger tunneling through delocalized phase modification of virtual particles, analogous to the Aharonov-Bohm effect.

Significance. If the central claim holds, the paper would establish a conceptually new control mechanism for vacuum pair production: altering the electromagnetic potential configuration while keeping the strong-field interaction region intact would change the pair-creation rate and momentum spectra through quantum phase effects rather than through local field intensity. This would be of considerable interest to the strong-field QED and vacuum-structure communities. The manuscript has concrete strengths: the CQFT numerical results are self-consistent, the analytical transmission model is derived independently of the numerics rather than fitted to them, and the reported 2.65% agreement between analytical and numerical integrated rates is a genuine cross-check. The paper also makes a falsifiable prediction, namely that moving the vector-potential step from x=+L to x=-L changes the momentum-resolved spectrum while keeping the central electric field fixed.

major comments (3)
  1. [Section II, Fig. 4, and Fig. 5] The text in Section II asserts that "the vector potential influences the Schwinger tunneling process solely through the delocalized phase modulation of virtual particles in the vacuum." However, the long-time rates quoted in the text (Gamma_I = 7251, Gamma_II = 4260, Gamma_III = 4244) are extracted up to t = 0.2 a.u., which is long after the positrons in Case II and the electrons in Case III reach the magnetic-field regions at t_inf = 2e-3 a.u. and are scattered there, as shown explicitly in Fig. 4 and Fig. 5. The analytic transmission coefficients in Eqs. (3b) and (3c) also describe a single-particle scattering process that includes real-particle scattering at the vector-potential step. Therefore the observed suppression of the total rate and the interference structure cannot be attributed solely to an instantaneous phase modification of virtual particles unless the contribution from real-particle scattering is quantified. Please report the early-time dN/dt before t_inf, or present a calculation with the magnetic-field step artificially removed, to isolate the phase-only contribution.
  2. [Appendix I B, Eq. (10)] The statement "As the multi-scattering process between x=0 and x=L is negligible, we consider only the first-order reflection and transmission processes" is not consistent with the actual calculation in Eqs. (10). Those equations include both left- and right-going waves in region R2, with amplitudes c1 and c2 and full phase factors exp(+-i p_{2,⊥} L), and the resulting transmission coefficient T_II in Eq. (11) contains sin(eta) and cos(eta) interference terms that are precisely the multiple-reflection interference terms between the two barriers. Please clarify whether multiple scattering between x=0 and x=L is included or neglected, and provide a quantitative estimate of the neglected contribution, for example by comparing with a calculation that treats the two barriers exactly or by estimating the magnitude of the second-order reflection coefficients.
  3. [Section III and Appendix I A] The analytical model approximates the scalar and vector potential steps as delta-function barriers (Wv = Wa = 0), while the numerical simulations use tanh profiles with Wv = Wa = 0.1 lambda_c. The reported 2.65% agreement in integrated rates is encouraging, but the claimed validation of the spectra in Fig. 3(d-f) is weakened by the missing high-energy peaks in Case II (Fig. 3(e)) and by the absence of a systematic comparison over parameter variations such as L, W, and eA0. Please provide a sensitivity analysis or at least quantify how the agreement degrades as the barrier widths are increased, and discuss whether the finite barrier width changes the phase-shift mechanism or only the quantitative details.
minor comments (5)
  1. [Abstract] There is a typographical error: "strong ffelds" should read "strong fields."
  2. [Section II, first paragraph] "It is worth to point out" should be "It is worth pointing out," and later "showes" should be "shows."
  3. [Appendix I, first paragraph] "analyical" should be "analytical."
  4. [References] Reference [54] is incomplete: the book is "An Introduction to Quantum Field Theory" by Michael E. Peskin and Daniel V. Schroeder (Westview Press, 1995); the current entry lists only one author and repeats the title as publisher.
  5. [Section II, Fig. 3 discussion] The text says the high-energy peaks in Fig. 3(e) are not reproduced by the analytical model, but this limitation is not mentioned in the figure caption; adding a note there would make the comparison fairer for the reader.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the analytical transmission coefficients are derived from the Dirac equation and independently cross-checked against CQFT numerics; self-citations are methodological, not load-bearing.

full rationale

The paper's central quantitative comparison is between CQFT numerical spectra/rates and the analytical transmission coefficients derived in Appendix I. The T(E) formulas (8), (11), and (14) are obtained from stationary scattering states and matching conditions; no parameter is fitted to the numerical spectra. The same field parameters are used in both calculations, which is a consistency check rather than a circular prediction. The relation rho(E,t)=2t/pi T(E) is cited to Hund and to prior work including the authors' [63], but the numerical spectra are computed independently by the CQFT method, so the agreement within 2.65% is genuine external corroboration. The 'virtual phase' language is interpretive: the vector potential enters the derivation as a momentum shift p2,parallel = pi,parallel - eA0 and through the phase eta = p2,perp L in the matching conditions; calling this 'phase modulation of virtual particles' does not make the result definitionally equivalent to its inputs. No fitted input is renamed as a prediction, no uniqueness theorem from the authors' prior work is invoked to forbid alternatives, and no self-citation is load-bearing in the sense of being the only support for the central claim. The main vulnerability (whether the phase-only causal attribution is fully separated from post-creation scattering of real pairs at x=+-L) is a correctness or interpretation concern, not circularity.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central claim rests on hand-chosen field amplitudes and widths, on the CQFT method borrowed from prior authors (including self-citations), and on an analytical delta-function scattering model that neglects multiple scattering. No parameter is fitted to the numerical output; the model parameters are the same as the simulation parameters. No new entities are postulated.

free parameters (6)
  • Scalar potential amplitude e phi0 = 2.5 c^2
    Hand-chosen supercritical potential step; sets the Klein region size.
  • Vector potential amplitude eA0 = 0.6 c^2
    Hand-chosen to shift longitudinal momentum and create visible asymmetry.
  • Electric-field width Wv = 0.1 lambda_c
    Hand-chosen width for the tanh scalar potential; finite-width effects are not systematically scanned.
  • Vector-potential width Wa = 0.1 lambda_c
    Hand-chosen width of the magnetic-field region.
  • Separation L = 24.5 lambda_c (xB = +/-L)
    Hand-chosen distance between scalar and vector potentials; controls the phase accumulation p2,perp L.
  • Interaction time for EMD snapshots = 0.036 a.u.
    Chosen observation time for momentum distributions; rates are taken at long time.
assumptions (7)
  • domain assumption Dirac equation with classical external potentials describes virtual-particle dynamics in the vacuum.
    Used throughout the CQFT mode expansion and the analytical scattering model.
  • domain assumption The CQFT framework with time-dependent Bogoliubov coefficients yields exact pair numbers and distributions for the given background.
    Method taken from refs [11,60]; no convergence or validation against independent methods is shown.
  • domain assumption The pair-creation rate can be mapped to the single-particle transmission coefficient via the Hund formula, rho(E,t)=2t/pi T(E).
    Invoked in Section III to connect numerical spectra to analytical transmission coefficients.
  • ad hoc to paper In the analytical model, the scalar and vector potential steps are delta-function barriers (Wv=Wa=0).
    Appendix I sets widths to zero to derive closed-form transmission coefficients; finite-width numerical fields differ.
  • ad hoc to paper Multiple scattering between x=0 and x=L is negligible; only first-order reflection and transmission are retained.
    Explicit assumption in Appendix I section B; no estimate of the neglected multi-scattering amplitude is provided.
  • domain assumption Momentum pz can be set to zero without loss because fields are homogeneous along z.
    Section II; reduces the 3D simulation to independent 1D channels.
  • domain assumption The Klein-region shift is an instantaneous vacuum-phase effect independent of particle propagation.
    This is the paper's mechanistic interpretation in Section IV and Appendix II; it is not independently measured.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Controlling Schwinger tunneling via engineering of virtual particle phases in vacuum." pith.science (2026). https://pith.science/paper/5O5ZKCK3

@misc{pith2026250502882,
  author       = {Pith},
  title        = {Pith review of: Controlling Schwinger tunneling via engineering of virtual particle phases in vacuum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5O5ZKCK3}},
  note         = {Machine review of arXiv:2505.02882}
}
read the original abstract

An investigation into Schwinger pair production mechanisms is presented, demonstrating that vacuum tunneling processes can be effectively controlled through electromagnetic potential modulation while maintaining the strong ffelds in the interaction region. This challenges the conventional paradigm that attributes exclusive governance of Schwinger processes to localized ffeld intensities. Through comprehensive analysis of particle number, momentum spectra, and spatial distribution of created pairs, we establish that the observed modulation effects originate from electromagnetic potential - induced modiffcations to the quantum phase structure of virtual particles. This phenomenon reveals a profound connection between Schwinger tunneling dynamics and the geometric phase properties of the quantum vacuum state - a vacuum analogue to the Aharonov-Bohm effect in charged particle systems. This discovery not only advances our understanding of electromagnetic interactions in quantum vacuum but also opens up new experimental opportunities for realizing Schwinger tunneling processes with existing facilities.

Figures

Figures reproduced from arXiv: 2505.02882 by the authors.

Figure 1
Figure 1. Up row: Sketch of the electromagnetic fields for di [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The particle number as a function of time for the created [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. The time evolution of the spatial distribution [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: The energy spectrum of the created electrons for the most [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: The energy spectrum of the created electrons for the most [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: The energy spectrum of the created electrons for the most [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Holographic Schwinger effect with Translational Symmetry Breaking

    hep-th 2025-10 conditional novelty 4.0 of 10

    In a holographic model with broken translational symmetry, chemical potential and magnetic fields lower the Schwinger pair-production barrier, while the disorder parameter raises it near and above the critical field.

Reference graph

Works this paper leans on

63 extracted references · 62 canonical work pages · cited by 1 Pith paper

  1. [1]

    Mark Srednicki, Chaper 16 and 29 in Quantum field theory (Cambridge University Press, 2007)

    work page 2007

  2. [2]

    1 (Cambridge university press, 1995)

    Steven Weinberg, Chapter 10 in The quantum theory of fields, V ol. 1 (Cambridge university press, 1995)

    work page 1995

  3. [3]

    New developments in the casimir effect,

    Michael Bordag, Umar Mohideen, and Vladimir M Mostepa- nenko, “New developments in the casimir effect,” Physics reports 353, 1–205 (2001)

    work page 2001

  4. [4]

    Peter W Milonni,The quantum vacuum: an introduction to quantum electrodynamics (Academic press, 2013). 9

    work page 2013

  5. [5]

    Probing the quantum vacuum with an artificial atom in front of a mirror,

    I-C Hoi, A Frisk Kockum, L Tornberg, A Pourkabirian, G Jo- hansson, Per Delsing, and CM Wilson, “Probing the quantum vacuum with an artificial atom in front of a mirror,” Nature Physics 11, 1045–1049 (2015)

    work page 2015

  6. [6]

    Casimir self- interaction energy density of quantum electrodynamic fields,

    Alexandre Tkatchenko and Dmitry V . Fedorov, “Casimir self- interaction energy density of quantum electrodynamic fields,” Phys. Rev. Lett. 130, 041601 (2023)

    work page 2023

  7. [7]

    On the attraction between two perfectly conducting plates,

    H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. Akad. Wet. Amsterdam51, 793–795 (1948)

    work page 1948

  8. [8]

    Hadronic vacuum polarization and the lamb shift,

    J. L. Friar, J. Martorell, and D. W. L. Sprung, “Hadronic vacuum polarization and the lamb shift,” Phys. Rev. A 59, 4061–4063 (1999)

    work page 1999

Show all 63 references
  1. [9]

    Real-time observation of instanta- neous ac stark shift of a vacuum using a zeptosecond laser pulse,

    Dandan Su and Miao Jiang, “Real-time observation of instanta- neous ac stark shift of a vacuum using a zeptosecond laser pulse,” Chinese Physics Letters 41, 014201 (2024)

    2024

  2. [10]

    E. S. Fradkin, D. M. Gitman, S. M. Shvartsman, and D. M. Gitman, Quantum electrodynamics: with unstable vacuum (Springer, 1991)

    1991

  3. [11]

    Quantum electrodynamics of strong fields,

    Walter Greiner, “Quantum electrodynamics of strong fields,” in Hadrons and Heavy Ions: Proceedings of the Summer School Held at the University of Cape Town January 16–27, 1984 (Springer, 2005) pp. 95–226

    1984

  4. [12]

    Nonlinear collective effects in photon-photon and photon-plasma interactions,

    Mattias Marklund and Padma K. Shukla, “Nonlinear collective effects in photon-photon and photon-plasma interactions,” Rev. Mod. Phys. 78, 591–640 (2006)

    2006

  5. [13]

    Extremely high-intensity laser interactions with fundamental format quantum systems,

    A Di Piazza, C Müller, KZ Hatsagortsyan, and C H Keitel, “Extremely high-intensity laser interactions with fundamental format quantum systems,” Reviews of Modern Physics84, 1177– 1228 (2012)

    2012

  6. [14]

    Advances in qed with intense background fields,

    A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, “Advances in qed with intense background fields,” Physics Reports 1010, 1–138 (2023)

    2023

  7. [15]

    On gauge invariance and vacuum polariza- tion,

    Julian Schwinger, “On gauge invariance and vacuum polariza- tion,” Phys. Rev.82, 664–679 (1951)

    1951

  8. [16]

    Holographic schwinger effect and the geometry of entanglement,

    Julian Sonner, “Holographic schwinger effect and the geometry of entanglement,” Phys. Rev. Lett.111, 211603 (2013)

    2013

  9. [17]

    Holographic schwinger effect,

    Gordon W. Semenoff and Konstantin Zarembo, “Holographic schwinger effect,” Phys. Rev. Lett.107, 171601 (2011)

    2011

  10. [18]

    Schwinger mechanism revis- ited,

    François Gelis and Naoto Tanji, “Schwinger mechanism revis- ited,” Progress in Particle and Nuclear Physics 87, 1–49 (2016)

    2016

  11. [19]

    Critical schwinger pair production,

    Holger Gies and Greger Torgrimsson, “Critical schwinger pair production,” Phys. Rev. Lett.116, 090406 (2016)

    2016

  12. [20]

    Real-time nonperturbative dynamics of jet production in schwinger model: Quantum entanglement and vacuum modification,

    Adrien Florio, David Frenklakh, Kazuki Ikeda, Dmitri Kharzeev, Vladimir Korepin, Shuzhe Shi, and Kwangmin Yu, “Real-time nonperturbative dynamics of jet production in schwinger model: Quantum entanglement and vacuum modification,” Phys. Rev. Lett. 131, 021902 (2023)

    2023

  13. [21]

    Gravitational pair production and black hole evaporation,

    Michael F. Wondrak, Walter D. van Suijlekom, and Heino Fal- cke, “Gravitational pair production and black hole evaporation,” Phys. Rev. Lett. 130, 221502 (2023)

    2023

  14. [22]

    Moedal search in the cms beam pipe for magnetic monopoles produced via the schwinger effect,

    B. Acharya, J. Alexandre, S. C. Behera, P. Benes, B. Bergmann, S. Bertolucci, A. Bevan, R. Brancaccio, H. Branzas, P. Burian, M. Campbell, S. Cecchini, Y . M. Cho, M. de Montigny, A. De Roeck, J. R. Ellis, M. Fairbairn, D. Felea, M. Frank, O. Gould, J. Hays, A. M. Hirt, D. L.-...

    2024

  15. [23]

    Magnetic control of the pair creation in spatially lo- calized supercritical fields,

    Q. Su, W. Su, Q. Z. Lv, M. Jiang, X. Lu, Z. M. Sheng, and R. Grobe, “Magnetic control of the pair creation in spatially lo- calized supercritical fields,” Phys. Rev. Lett.109, 253202 (2012)

    2012

  16. [24]

    Finite-size effect in the schwinger particle-production mechanism,

    Ren-Chuan Wang and Cheuk-Yin Wong, “Finite-size effect in the schwinger particle-production mechanism,” Phys. Rev. D38, 348–359 (1988)

    1988

  17. [25]

    Finite-size e ffects in pair production by an external field,

    Cécile Martin and D. Vautherin, “Finite-size e ffects in pair production by an external field,” Phys. Rev. D 38, 3593–3595 (1988)

    1988

  18. [26]

    Probing nonpertur- bative qed with optimally focused laser pulses,

    A. Gonoskov, I. Gonoskov, C. Harvey, A. Ilderton, A. Kim, M. Marklund, G. Mourou, and A. Sergeev, “Probing nonpertur- bative qed with optimally focused laser pulses,” Phys. Rev. Lett. 111, 060404 (2013)

    2013

  19. [27]

    Real- time dynamics of string breaking,

    Florian Hebenstreit, Jürgen Berges, and Daniil Gelfand, “Real- time dynamics of string breaking,” Physical review letters 111, 201601 (2013)

    2013

  20. [28]

    Schwinger effect and back- reaction in de sitter spacetime,

    Clément Stahl and She-Sheng Xue, “Schwinger effect and back- reaction in de sitter spacetime,” Physics Letters B 760, 288–292 (2016)

    2016

  21. [29]

    Pair production due to an electric field in 1+ 1 dimensions and the validity of the semiclassical approxi- mation,

    Silvia Pla, Ian M Newsome, Robert S Link, Paul R Anderson, and Jose Navarro-Salas, “Pair production due to an electric field in 1+ 1 dimensions and the validity of the semiclassical approxi- mation,” Physical Review D 103, 105003 (2021)

    2021

  22. [30]

    Backreaction e ffect and plasma oscillation in pair production for rapidly oscillating electric fields,

    RZ Jiang, C Gong, ZL Li, and YJ Li, “Backreaction e ffect and plasma oscillation in pair production for rapidly oscillating electric fields,” Physical Review D 108, 076015 (2023)

    2023

  23. [31]

    Numerical studies of back reaction effects in an analog model of cosmological pre- heating,

    Salvatore Butera and Iacopo Carusotto, “Numerical studies of back reaction effects in an analog model of cosmological pre- heating,” Phys. Rev. Lett.130, 241501 (2023)

    2023

  24. [32]

    Dynamically assisted schwinger mechanism,

    Ralf Schützhold, Holger Gies, and Gerald Dunne, “Dynamically assisted schwinger mechanism,” Phys. Rev. Lett.101, 130404 (2008)

    2008

  25. [33]

    Spatially assisted schwinger mechanism and magnetic catalysis,

    Patrick Copinger and Kenji Fukushima, “Spatially assisted schwinger mechanism and magnetic catalysis,” Phys. Rev. Lett. 117, 081603 (2016)

    2016

  26. [34]

    Franz-keldysh effect in strong-field qed,

    Hidetoshi Taya, “Franz-keldysh effect in strong-field qed,” Phys. Rev. D 99, 056006 (2019)

    2019

  27. [35]

    Dynamically assisted tunneling in the floquet picture,

    Daniil Ryndyk, Christian Kohlfürst, Friedemann Queisser, and Ralf Schützhold, “Dynamically assisted tunneling in the floquet picture,” Phys. Rev. Res.6, 023056 (2024)

    2024

  28. [36]

    Light intensification towards the schwinger limit,

    Sergei V Bulanov, Timur Esirkepov, and Toshiki Tajima, “Light intensification towards the schwinger limit,” Physical review letters 91, 085001 (2003)

    2003

  29. [37]

    Schwinger limit attain- ability with extreme power lasers,

    Stepan S Bulanov, Timur Zh Esirkepov, Alexander GR Thomas, James K Koga, and Sergei V Bulanov, “Schwinger limit attain- ability with extreme power lasers,” Physical review letters105, 220407 (2010)

    2010

  30. [38]

    Re- alization of laser intensity over 1023w/cm2,

    Jin Woo Yoon, Yeong Gyu Kim, Il Woo Choi, Jae Hee Sung, Hwang Woon Lee, Seong Ku Lee, and Chang Hee Nam, “Re- alization of laser intensity over 1023w/cm2,” Optica 8, 630–635 (2021)

    2021

  31. [39]

    Pair production in laser fields oscillating in space and time,

    Matthias Ruf, Guido R. Mocken, Carsten Müller, Karen Z. Hat- sagortsyan, and Christoph H. Keitel, “Pair production in laser fields oscillating in space and time,” Phys. Rev. Lett.102, 080402 (2009)

    2009

  32. [40]

    Barrier control in tunneling e+−e− photoproduction,

    A. Di Piazza, E. Lötstedt, A. I. Milstein, and C. H. Keitel, “Barrier control in tunneling e+−e− photoproduction,” Phys. Rev. Lett. 103, 170403 (2009)

    2009

  33. [41]

    Multiple colliding electromagnetic pulses: A way to lower the threshold of e+e− pair production from vacuum,

    S. S. Bulanov, V . D. Mur, N. B. Narozhny, J. Nees, and V . S. Popov, “Multiple colliding electromagnetic pulses: A way to lower the threshold of e+e− pair production from vacuum,” Phys. Rev. Lett. 104, 220404 (2010). 10

    2010

  34. [42]

    Pair production by a constant external field,

    AI Nikishov, “Pair production by a constant external field,” Sov. Phys. JETP 30, 660 (1970)

    1970

  35. [43]

    Probing vacuum polarization effects with high- intensity lasers,

    Felix Karbstein, “Probing vacuum polarization effects with high- intensity lasers,” Particles 3, 39–61 (2020)

    2020

  36. [44]

    Ramsey fringes and time-domain multiple-slit interference from vacuum,

    Eric Akkermans and Gerald V . Dunne, “Ramsey fringes and time-domain multiple-slit interference from vacuum,” Phys. Rev. Lett. 108, 030401 (2012)

    2012

  37. [45]

    Enhanced schwinger pair production in many-centre systems,

    François Fillion-Gourdeau, Emmanuel Lorin, and André D Bandrauk, “Enhanced schwinger pair production in many-centre systems,” Journal of Physics B: Atomic, Molecular and Optical Physics 46, 175002 (2013)

    2013

  38. [46]

    Resonantly enhanced pair production in a simple diatomic model,

    Fran çois Fillion-Gourdeau, Emmanuel Lorin, and André D. Bandrauk, “Resonantly enhanced pair production in a simple diatomic model,” Phys. Rev. Lett.110, 013002 (2013)

    2013

  39. [47]

    Spatially dependent electron-positron pair creation rate,

    Q. Z. Lv, J. Unger, Y . T. Li, Q. Su, and R. Grobe, “Spatially dependent electron-positron pair creation rate,” Europhysics Letters 116, 40003 (2016)

    2016

  40. [48]

    Geometric phase from aharonov-bohm to pancharatnam-berry and beyond,

    Eliahu Cohen, Hugo Larocque, Frederic Bouchard, Farshad Nejadsattari, and Ebrahim Karimi, “Geometric phase from aharonov-bohm to pancharatnam-berry and beyond,” Nature Reviews Physics (2019)

    2019

  41. [49]

    The electromagnetic vacuum field as an essential hidden ingredient of the quantum- mechanical ontology,

    Ana Maria Cetto and Luis de la Peña, “The electromagnetic vacuum field as an essential hidden ingredient of the quantum- mechanical ontology,” Entropy 24, 1717 (2022)

    2022

  42. [50]

    Significance of electromagnetic potentials in the quantum theory,

    Y . Aharonov and D. Bohm, “Significance of electromagnetic potentials in the quantum theory,” Phys. Rev. 115, 485–491 (1959)

    1959

  43. [51]

    Shift of an electron interference pattern by enclosed magnetic flux,

    R. G. Chambers, “Shift of an electron interference pattern by enclosed magnetic flux,” Phys. Rev. Lett.5, 3–5 (1960)

    1960

  44. [52]

    Role of potentials in the aharonov-bohm effect,

    Lev Vaidman, “Role of potentials in the aharonov-bohm effect,” Physical Review A—Atomic, Molecular, and Optical Physics 86, 040101 (2012)

    2012

  45. [53]

    Broken symmetries and the masses of gauge bosons,

    Peter W. Higgs, “Broken symmetries and the masses of gauge bosons,” Phys. Rev. Lett.13, 508–509 (1964)

    1964

  46. [54]

    Peskin, An Introduction to Quantum Field Theory (An Introduction to Quantum Field Theory, 2006)

    Michael E. Peskin, An Introduction to Quantum Field Theory (An Introduction to Quantum Field Theory, 2006)

    2006

  47. [55]

    Electron-positron pair production in the aharonov-bohm poten- tial,

    Vladimir D. Skarzhinsky, Jürgen Audretsch, and Ulf Jasper, “Electron-positron pair production in the aharonov-bohm poten- tial,” Phys. Rev. D53, 2190–2200 (1996)

    1996

  48. [56]

    Dynamically assisted schwinger mechanism and chirality production in parallel electromagnetic field,

    Hidetoshi Taya, “Dynamically assisted schwinger mechanism and chirality production in parallel electromagnetic field,” Phys. Rev. Res. 2, 023257 (2020)

    2020

  49. [57]

    Pair production in temporally and spatially oscillating fields,

    Ivan A. Aleksandrov and Christian Kohlfürst, “Pair production in temporally and spatially oscillating fields,” Phys. Rev. D 101, 096009 (2020)

    2020

  50. [58]

    Effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron- positron pair production,

    Christian Kohlfürst, “Effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron- positron pair production,” Phys. Rev. D101, 096003 (2020)

    2020

  51. [59]

    Materieerzeugung im anschaulichen und im gequan- telten wellenbild der materie,

    F. Hund, “Materieerzeugung im anschaulichen und im gequan- telten wellenbild der materie,” Zeitschrift für Physik 117, 1–17 (1941)

    1941

  52. [60]

    Time- and space-resolved selective multipair creation,

    Q. Z. Lv and Heiko Bauke, “Time- and space-resolved selective multipair creation,” Phys. Rev. D96, 056017 (2017)

    2017

  53. [61]

    Pairwise mode entanglement in schwinger production of particle-antiparticle pairs in an electric field,

    Yujie Li, Yue Dai, and Yu Shi, “Pairwise mode entanglement in schwinger production of particle-antiparticle pairs in an electric field,” Phys. Rev. D95, 036006 (2017)

    2017

  54. [62]

    Manipulation of the vacuum to control its field-induced decay,

    Q. Z. Lv, Q. Su, and R. Grobe, “Manipulation of the vacuum to control its field-induced decay,” Phys. Rev. Lett.121, 183606 (2018)

    2018

  55. [63]

    Suppression of pair creation due to a steady magnetic field,

    W. Su, M. Jiang, Z. Q. Lv, Y . J. Li, Z. M. Sheng, R. Grobe, and Q. Su, “Suppression of pair creation due to a steady magnetic field,” Phys. Rev. A86, 013422 (2012)

    2012

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.