Three Questions for Any System with Nonlinear Charge Transfer Across a Gap
What the Nature Photonics 2026 experiment shows about the engineering discipline of measurement — and where the comparison with VENDOR.Max ends.
VENDOR.Max is an Armstrong-type nonlinear electrodynamic oscillator operating in a controlled discharge-resonant regime. The architecture is classified in the patent record under IPC H03K 3/537 — generation of pulses by means of a storage element discharged through the load via a spark gap. This is a recognized engineering category with a long history in the pulsed-power literature.
In July 2026, Nature Photonics published a study by a group from the University of Regensburg and the Max Planck Institute, “Tracking electrons at the space-time limit” (Maier et al., DOI: 10.1038/s41566-026-01932-0) — an experiment on controlling electron transfer across the vacuum gap of a scanning tunneling microscope with attosecond temporal resolution. This article examines what the two systems — incommensurable in scale and mechanism — are nonetheless equally obliged to answer, and how.
Both systems — an attosecond tunneling experiment and a controlled discharge-resonant oscillator — must answer the same three engineering questions: whether the gap is a source or a switch, how the measured signal is proven not to be an artifact, and how a single event connects to a continuously measured quantity. In both, the gap is a nonlinear switching element, not a source; source, losses, and storage are determined only at the complete device boundary via Pin,boundary = Pcustomer + Plosses + dEstored/dt.
The Maier et al. experiment is not evidence for the VENDOR.Max energy balance and is not used as such. What the two works share is neither mechanism nor scale — it is discipline: boundary energy accounting, event-to-average arithmetic, sensitivity of nonlinear systems to field shape, and metrology engineered against artifacts. The shared element is the method of proof, not the physics.
Two systems, one accounting discipline
The scales of the two systems are incommensurable. Attosecond transients versus a sub-microsecond regime period. A picoampere measurement signal versus macroscopic power delivery. Atomically localized transfer versus continuous delivery to a load. A quantum mechanism versus classical electrodynamics.
And yet, at the most general level, both problems can be stated identically: field-controlled charge transfer across an inter-electrode gap. That is enough to oblige both systems to answer the same three engineering questions. What is interesting is not that the answers are similar. What is interesting is that the discipline of obtaining those answers is built on the same principles: define the source, rule out the artifact, and connect a single event to an aggregate measured quantity.
Question 1. Is the gap an energy source or a switch?
This is the first question any qualified reviewer asks of any system with a discharge or tunneling gap: where does the energy come from?
The Regensburg group’s answer is unambiguous. The transfer is initiated and controlled by the applied optical field; the vacuum gap does not act as an independent energy source — it nonlinearly controls the transfer. The system’s response to the field is sharply nonlinear: to illustrate the sensitivity to pulse shape, the authors use simplified response models with higher-order terms in the field. It is precisely the nonlinearity that makes the gap a controllable element — but not a source.
The VENDOR.Max answer is the same in structure and is fixed in our canonical energy balance. The switching gap is publicly treated as a nonlinear switching element: the sharp increase in conductivity during switching is a conductivity effect, not a creation of energy. The gap determines the timing and the temporal shape of the transfer of energy already accounted for within the regime, but it does not add a separate source to the energy balance. The energy inputs, losses, stored-energy change, and customer power are determined only through measurement at the complete device boundary:
This is exactly the engineering role of a nonlinear switching element. In the 2023 patent analytical framework (the ES2950176 family), the Townsend form of carrier multiplication is used to explain the sharp rise in conductivity: the carrier density grows along the gap as n(x) = n0·eαx, and the multiplication factor is MT = eαd. These expressions belong to the patent level of description and are not presented as an independently confirmed microscopic model of the current sealed vacuum switching assembly: the engineering implementation has advanced beyond the 2023 patent baseline, and the public description of the current implementation remains at the levels of switching behavior, work done by the field, and boundary energy accounting.
The growth in carrier number raises the effective conductivity of the gap and promotes the formation of a short-lived conducting state; the temporal structure of the event is determined by the joint dynamics of the field and the coupled circuit. The directed motion of charges constitutes an electric current, and this current participates in shaping the electromagnetic field of the primary resonant circuit. Carrier multiplication, however, is not energy multiplication. The carriers’ energy is supplied by the work of the electric field; increasing their number changes the conductivity and the temporal structure of the transfer, but introduces no additional energy source. Carrier number and event energy are different physical quantities: the total energy of the event is determined by the accounted energy state of the coupled system and the work done by the field over the course of the event.
Two functions must therefore be distinguished. The nonlinear gap forms the switching event and controls the manner in which energy is transferred. Compensation of the regime’s losses is provided by a regulated internal feedback path, and stability is assessed over a representative time window: the average returned power must compensate the average regime losses and, where necessary, restore the internal energy reserve. The feedback remains an internal flow inside the complete device boundary and is not a separate input in the boundary equation. Nonlinearity controls the manner of energy transfer, not its origin. Engineering has known this principle for over a century — since Armstrong’s regenerative circuit and the van der Pol oscillator: regenerative feedback transfers energy from an accounted internal path into the oscillatory regime, while the system nonlinearity limits amplitude growth and establishes a stable limit cycle.
The nonlinear gap is a regulator of the flow of field energy, not its source. A system that claims otherwise has its accounting wrong. A system that states this explicitly passes the reviewer’s first filter.
Question 2. How do you prove the measured signal is not an artifact?
This is the central methodological problem of both studies, and here the parallel is most instructive.
For the Regensburg group, the useful signal is a phase-dependent component of the tunneling current at the picoampere level. A parasitic thermal effect from fluctuations in laser power can exceed this signal by many orders of magnitude: even microwatt-level modulations of the incident power produce a noticeable thermal modulation of the current. The authors state directly that the thermal artifact is synchronized with the power modulation and is therefore easily confused with the signal being sought.
Their solution has two layers. The first is suppression of the disturbance itself: the relative stability of the laser power is held to better than 10−4. The second — and this is the key — is the architecture of the measurement: the useful component is isolated by fast modulation of the phase of the optical carrier relative to the envelope (carrier-envelope phase, CEP) and by synchronous detection at a fixed frequency, while the average power in the scheme is by construction independent of the scanned parameter. The protocol is built so that thermal power modulation cannot reproduce the phase signature of the sought current: the signal and the principal thermal artifact are separated by distinct modulation signatures at the level of the experimental protocol itself, before any subsequent data processing. Separately, when mapping the atom, the authors switch to constant-height mode to exclude cross-coupling through the microscope’s feedback loop — again, artifact exclusion by protocol design, not by post-processing.
In VENDOR.Max, the same discipline is implemented at the level of measurement-interface definition. The startup port is a separate, physically disconnectable interface. After the regime is initiated, this port is disconnected. The startup circuit must therefore be accounted for separately and cannot be conflated with the sustained operational regime. The completeness of the energy balance, however, is established not by the single fact of startup-port disconnection, but by synchronized metrology of all physical channels of the complete device boundary — the subject of an independent boundary-measurement protocol, the next stage of validation.
Uniting the Nature Photonics laboratory and the TRL 5–6 engineering bench: the credibility of a measurement is secured by a protocol in which the principal competing interpretations are constrained or excluded by protocol design rather than removed retrospectively through data processing. Precisely this principle — independent metrology at the complete device boundary — is the central thesis of our validation program.
Question 3. How do you connect a single event to a continuously measured quantity?
Both systems are event-based. In both, the immediate physical process is a short, discrete charge-transfer event, while the measured and practically meaningful quantity is a continuous averaged flow.
In the Regensburg experiment, a single charge-transfer transient is shorter than one femtosecond. The continuously measured current arises as the product of the charge transferred per pulse and the laser repetition rate of 80 MHz. The authors apply this bridge explicitly: the calculated charge transfer per event, multiplied by the repetition rate, matches the measured average current, and it is this correspondence that connects their simulation to the experiment.
In VENDOR.Max, the same numerical bridge connects the event level to the regime level. At the aggregate level, the average customer power is obtained by summing the energy delivered through the customer interface by all valid events within the measurement window and dividing by the duration of that window. For a stationary event sequence, this reduces to:
where f is the effective event rate, not merely a nominal oscillator frequency.
If the contributions of individual channels are determined independently, the same quantity can be represented as the sum of their contributions: Pcustomer,avg = Σ Ecustomer,event,j × fj (summed over j from 1 to Nch), and, for equal channel event rates and energies, Pcustomer,avg = Ecustomer,event,ch × fch × Nch, where fch is the per-channel event rate and the suffix ch denotes the event energy of a single channel. The publicly described VENDOR.Max architecture includes three parallel discharge channels with overlapping but shifted spectra (patent claim 5); the regime’s operating frequency lies in the megahertz range, so the continuous power is composed of millions of events per second.
This also raises a natural engineering question: why does the architecture use several parallel discharge channels? A single switching channel contributes a sequence of discrete, short-duration events. In a multichannel architecture, the aggregate regime is formed by the combined contributions of several channels rather than by one event sequence alone. Patent claim 5 describes three parallel discharge channels with overlapping but shifted spectra; at the public level, this establishes spectral diversification of the excitation, but does not by itself establish a particular temporal interleaving pattern between individual switching events.
Where channel timing and event energies are independently measured, a multichannel arrangement may distribute the aggregate event contribution across the available switching cells and shape the temporal and spectral structure presented to the coupled resonant system. Whether this reduces per-cell stress, fills gaps between events, or increases regime stability is an empirical architecture-level question to be established by event-resolved and phase-resolved measurements. The number of channels does not alter the balance at the complete device boundary: it changes how the accounted energy transfer is distributed among events and channels, not the amount of energy available to the system.
This is comparable to the Maier et al. experiment only at the most general methodological level: multiple controlled contributions can be combined to synthesize a waveform that cannot be inferred from average power alone. It is not a claim that the two systems share the same superposition mechanism, microscopic physics, or temporal dynamics.
It is important to be clear about what this formula is and what it is not. It is the arithmetic of repeating events — a numerical scale check with which future event-resolved metrology is obliged to agree. It does not define the energy source and does not replace the boundary balance: the source and the balance are established separately and only at the complete device boundary. If the event-level energetics and the averaged power fail to agree arithmetically, the system has been described incorrectly; reconciling these levels by independent measurements is part of the validation program.
Two engineering principles the experiment makes tangible
Behind the three accounting questions in the Regensburg study, two principles of pulsed-power engineering come into view — valid for nonlinear event-based systems as a class, regardless of scale and mechanism.
At practically constant average power, charge transfer changes radically depending on the temporal superposition of the fields. The regime is defined by shape, asymmetry, and phase structure — not by averaged quantities.
The most intense transfer was the least localized. For regulated nonlinear systems, what is optimized is a combination — stability, localization, repeatability, useful response — not the peak of a single parameter.
Principle 1 in the experiment
A key detail: the spectra of the two laser pulses do not overlap, so as their mutual delay is varied, the total average power at the sample remains practically constant — the authors verify this by direct measurement. And at this constant average power, the charge transfer changes radically: it is maximal when the resultant field forms a single asymmetric cycle with a dominant half-period, and it drops sharply when the same energy is distributed over a multi-cycle waveform with two comparable envelope maxima.
In other words, two configurations with practically unchanged average power and unchanged energies of the constituent pulses yield fundamentally different responses as a consequence of the different temporal superposition of the fields. This is a general engineering principle for the analysis of nonlinear pulsed systems: root-mean-square and averaged quantities are by themselves insufficient to define the regime; the regime is defined by the temporal shape, the asymmetry, and the phase structure of the field at the nonlinear element. This is exactly why the VENDOR.Max regime is described as controlled discharge-resonant — a category of shape and phase, not a category of average amplitude.
Principle 2 in the experiment
The second illustrative result: at the highest pulse energy, the transfer was the most intense but the least spatially localized — the characteristic decay length was about 8.7 Å. As the pulse energy was reduced, the electron wave packet became spatially more compact — down to roughly 3.8 Å. In this experiment, the optimal point for spatiotemporal localization did not coincide with the maximum transfer amplitude.
For regulated nonlinear systems this is a fundamental lesson: what is optimized is not the peak value of a single parameter but a combination — stability, event localization, repeatability, and useful response. In the VENDOR.Max architecture, this corresponds to supervisory regime control: the task of the control loop is to hold the system within the regime’s operating window, not to drive any single parameter to a maximum. We cite this result as a class-level engineering principle, without claiming that the same microscopic effect operates in VENDOR.Max.
Where the analogy ends
This section is mandatory, and it matters more than the ones before it.
The Regensburg study is a quantum experiment. Electrons tunnel through a barrier; the regime is characterized by a Keldysh parameter of order unity; the timescales are such that the rate of barrier modulation becomes comparable to the response time of the electrons themselves, and the response ceases to be instantaneous. This is attosecond-domain physics, and its conclusions belong to that domain.
VENDOR.Max is described entirely within classical Maxwell–Lorentz electrodynamics. We do not borrow the attosecond tunneling mechanism, do not rely on it, and do not introduce on its basis any delayed electron response or memory functions into the description of our system. There is no new physics in the VENDOR.Max architecture — there is an engineering composition of known classical effects into a regulated topology with supervisory regime control, protected by a patent family (ES2950176B2 granted; WO2024209235A1 PCT; EP/US/CN/IN national phases under examination).
What the two works share is neither mechanism nor scale. What they share is discipline: boundary energy accounting, event-to-average arithmetic, the sensitivity of nonlinear systems to field shape, and metrology engineered against artifacts.
What this means for an investor
Measurement credibility is established by designing the protocol so that the principal known artifacts cannot reproduce the defining signature of the target signal. This is the discipline used to prove the existence of signals that, without a dedicated protocol, can be hidden beneath artifacts exceeding them by several orders of magnitude. The methodological standard
When we say that the VENDOR.Max independent validation program is being designed around metrology of the complete device boundary, separate accounting of the physically disconnectable startup port and of all remaining channels of the complete device boundary, and a numerical bridge from event dynamics to continuous power — we are describing the methodological discipline accepted in modern experimental physics.
The difference lies not only in the scale of the signal but in the status of the evidence. The Maier et al. study is a published fundamental experiment with open methodology, peer review, and published data. VENDOR.Max is at TRL 5–6: an internal operational record has been formed, while independent verification of the complete device boundary remains the next validation milestone. The similarity lies not in the equality of the evidentiary base but in the principle of its construction: separating signal from artifact by protocol design, and connecting local event dynamics to a continuously measured aggregate quantity. It is this principle that we adopt as our standard — and it is by this principle that we invite the next stage of validation to be judged.
Direct answers
Does the Nature Photonics paper confirm the operation of VENDOR.Max?
No. The Maier et al. experiment investigates quantum photon-assisted tunneling on attosecond scales; VENDOR.Max is a classical electrodynamic system with a regime period of about 408 ns. The paper is not evidence for the VENDOR.Max energy balance and is not used as such. What the two works share is methodological discipline: boundary accounting of the source, exclusion of artifacts by design, and event-to-average arithmetic.
Why can the discharge gap not be an energy source?
Because it is a nonlinear switching element. In both the Nature Photonics experiment and the VENDOR.Max architecture, the gap controls the timing and shape of the transfer of energy already accounted for in the system, but adds no source of its own. The sharp increase in conductivity during switching is a conductivity effect, not a creation of energy. The source, the losses, and the stored energy are determined only through measurement at the complete device boundary.
What is the “event → average power” bridge and what does it prove?
It is the standard arithmetic of pulsed systems: the average quantity equals the contribution of a single event multiplied by the repetition rate. In Maier et al., the calculated charge per pulse, multiplied by 80 MHz, matches the measured average current. For VENDOR.Max, the analogous aggregate expression Pcustomer,avg = ⟨Ecustomer,event⟩ × f is a numerical scale check with which event-level metrology is obliged to agree. The bridge does not prove the energy source; it verifies the internal consistency of the description.
Does VENDOR.Max use quantum tunneling or attosecond effects?
No. The architecture is described within classical Maxwell–Lorentz electrodynamics; its operating timescales are eight to nine orders of magnitude slower than attosecond transients. Neither the Keldysh parameter, nor delayed electron response, nor memory functions from the quantum experiment are transferred to VENDOR.Max. No new physics is claimed.
What in VENDOR.Max is already documented, and what remains to be confirmed?
Documented internally (TRL 5–6): regime stability under continuous load, including a 532-hour continuous segment, and a one-time startup pulse of approximately 0.015 Wh followed by physical disconnection of the startup port. Ahead: independent metrology of all physical channels of the complete device boundary under an accredited protocol — the next validation milestone. Until it is completed, internal results are not presented as independently confirmed.
Why is average power insufficient to describe a nonlinear regime?
Because a nonlinear element responds to the instantaneous configuration of the field, not to its average value. The Maier et al. experiment demonstrates this directly: at practically constant average power, the charge transfer changes radically depending on the temporal superposition of the pulses. For nonlinear pulsed systems as a class, root-mean-square and averaged quantities are by themselves insufficient; the regime is defined by the shape, asymmetry, and phase structure of the field — hence the category “controlled discharge-resonant regime,” a category of shape and phase.
How does carrier multiplication help sustain the regime if it creates no energy?
In the 2023 patent analytical framework, the Townsend form of carrier multiplication explains the sharp rise in the conductivity of the switching gap; it does not describe a confirmed mechanism of the current sealed vacuum switching assembly. The rise in conductivity makes it possible to form a short current pulse and excite the electromagnetic field of the resonant circuit. Carrier multiplication, however, does not increase the energy of the event: the carriers’ energy comes from the work of the electric field. The regime’s losses are compensated not by carrier multiplication but by a regulated feedback path — over a representative time window, the average returned power compensates the average regime losses. Multiplication assists the gap’s transition into a conducting state; regulated feedback returns the energy needed to compensate the losses.
People also ask
Adjacent questions frequently asked in connection with discharge gaps, pulsed measurement, and boundary energy accounting.
References
A list for further reading, ordered in five layers: the primary source and reviews of field-driven electronics [1]–[4]; field control of charge transfer across inter-electrode gaps [5]–[11]; nonlinear response and regime parameters [12]–[15]; classical foundations of regenerative oscillators and nonlinear dynamics [16]–[17]; and metrology and artifact protection [18]–[19]. It includes peer-reviewed contemporary publications and historical primary sources; together they provide the scientific context of the class “field-controlled charge transfer across a gap” and the methodology of pulsed measurements. None of the entries constitutes confirmation of the specific VENDOR.Max architecture.
- Maier, S. et al. (2026). “Tracking electrons at the space-time limit.” Nature Photonics. The experiment under discussion; published open access under the CC BY 4.0 license. DOI: 10.1038/s41566-026-01932-0
- Krausz, F., Ivanov, M. (2009). “Attosecond physics.” Reviews of Modern Physics, 81, 163–234. The foundational review of attosecond science.
- Borsch, M. et al. (2023). “Lightwave electronics in condensed matter.” Nature Reviews Materials, 8, 668–687. A review of light-field control of electrons in solids.
- Heide, C. et al. (2024). “Petahertz electronics.” Nature Reviews Physics, 6, 648–662. A review of ultimately fast field-driven electronics.
- Cocker, T. L. et al. (2013). “An ultrafast terahertz scanning tunnelling microscope.” Nature Photonics, 7, 620–625. An early realization of laser-driven terahertz tunneling microscopy.
- Cocker, T. L. et al. (2016). “Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging.” Nature, 539, 263–267.
- Ludwig, M. et al. (2020). “Sub-femtosecond electron transport in a nanoscale gap.” Nature Physics, 16, 341–345. Sub-femtosecond transport in a nanoscale gap.
- Krüger, M., Schenk, M., Hommelhoff, P. (2011). “Attosecond control of electrons emitted from a nanoscale metal tip.” Nature, 475, 78–81. Phase control of emission from a metal tip.
- Kim, H. Y. et al. (2023). “Attosecond field emission.” Nature, 613, 662–666.
- Garg, M., Kern, K. (2020). “Attosecond coherent manipulation of electrons in tunneling microscopy.” Science, 367, 411–415.
- Schiffrin, A. et al. (2013). “Optical-field-induced current in dielectrics.” Nature, 493, 70–74. Field-induced currents in dielectrics.
- Keldysh, L. V. (1965). “Ionization in the field of a strong electromagnetic wave.” Soviet Physics JETP, 20, 1307–1314. The primary source of the Keldysh parameter separating the multiphoton and field regimes.
- Zheltikov, A. M. et al. (2016). “Keldysh parameter, photoionization adiabaticity, and the tunneling time.” Physical Review A, 94, 043412.
- Vorobeichik, I., Lefebvre, R., Moiseyev, N. (1998). “Field-induced barrier transparency.” Europhysics Letters, 41, 111–116. Dynamic barrier transparency in an alternating field.
- Eckle, P. et al. (2008). “Attosecond ionization and tunneling delay time measurements in helium.” Science, 322, 1525–1529.
- Armstrong, E. H. (1915). “Some recent developments in the audion receiver.” Proceedings of the IRE, 3, 215–247. The primary source of the regenerative (Armstrong) circuit, the classification anchor of the VENDOR.Max architecture.
- van der Pol, B. (1926). “On relaxation-oscillations.” The London, Edinburgh, and Dublin Philosophical Magazine, 2, 978–992. A classic of the theory of nonlinear self-oscillating systems.
- Scofield, J. H. (1994). “Frequency-domain description of a lock-in amplifier.” American Journal of Physics, 62, 129–133. The methodological basis of synchronous detection.
- Keathley, P. D. et al. (2019). “Vanishing carrier-envelope-phase-sensitive response in optical-field photoemission from plasmonic nanoantennas.” Nature Physics, 15, 1128–1133. An example of rigorous verification in which an expected phase-sensitive signal is correctly recognized as absent: the discipline of the null result.
VENDOR.Energy is being developed by MICRO DIGITAL ELECTRONICS CORP S.R.L. (Bucharest, Romania). Patent canon: PCT WO2024209235; ES2950176 granted by OEPM (Spain); EP, US, CN, and IN national/regional examination tracks active. EUIPO Trademark Reg No. 019220462. Technology readiness: TRL 5–6. Nothing in this article constitutes an investment offer, a certified performance claim, or a representation that boundary closure has been independently verified. The paper by Maier et al. is cited as independent scientific context for the measurement discipline of field-controlled charge transfer, not as evidence for any specific device.