P(t) Schubart Master Formula
English

Bibliography

References

The established, peer-reviewed literature the framework draws upon, grouped by theme. Every DOI below is real and links to the source of record; books and Nobel lectures link to their publisher or organisation. The evidence library maps each work to the formula term it underwrites.

Neutrino physics & coherent scattering

  1. Freedman, D. Z. (1974). Coherent effects of a weak neutral current. Physical Review D 9, 1389. DOI: 10.1103/PhysRevD.9.1389 ↗ First prediction of coherent elastic neutrino–nucleus scattering (CEνNS).
  2. COHERENT Collaboration (Akimov, D. et al.) (2017). Observation of coherent elastic neutrino–nucleus scattering. Science 357, 1123–1126. DOI: 10.1126/science.aao0990 ↗ First experimental confirmation of CEνNS, above six sigma.
  3. COHERENT Collaboration (Akimov, D. et al.) (2021). First measurement of coherent elastic neutrino–nucleus scattering on argon. Physical Review Letters 126, 012002. DOI: 10.1103/PhysRevLett.126.012002 ↗ Independent confirmation of CEνNS on a second target nucleus.
  4. Super-Kamiokande Collaboration (Fukuda, Y. et al.) (1998). Evidence for oscillation of atmospheric neutrinos. Physical Review Letters 81, 1562–1567. DOI: 10.1103/PhysRevLett.81.1562 ↗ First compelling evidence that neutrinos oscillate and therefore have mass.
  5. SNO Collaboration (Ahmad, Q. R. et al.) (2002). Direct evidence for neutrino flavor transformation from neutral-current interactions. Physical Review Letters 89, 011301. DOI: 10.1103/PhysRevLett.89.011301 ↗ Measured the total solar-neutrino flux across all flavours, confirming the solar model.
  6. Kajita, T. (2016). Nobel Lecture: discovery of atmospheric neutrino oscillations. Reviews of Modern Physics 88, 030501. DOI: 10.1103/RevModPhys.88.030501 ↗ Nobel laureate's own account of the atmospheric-oscillation discovery.
  7. McDonald, A. B. (2016). Nobel Lecture: the Sudbury Neutrino Observatory — observation of flavor change for solar neutrinos. Reviews of Modern Physics 88, 030502. DOI: 10.1103/RevModPhys.88.030502 ↗ Companion Nobel lecture on the solar-neutrino flavour-change result.
  8. NOvA Collaboration (Acero, M. A. et al.) (2022). Improved measurement of neutrino oscillation parameters by the NOvA experiment. Physical Review D 106, 032004. DOI: 10.1103/PhysRevD.106.032004 ↗ A recent long-baseline measurement refining the oscillation parameters.
  9. Nobel Committee for Physics (2015). Scientific background: neutrino oscillations. Royal Swedish Academy of Sciences. Publisher / source ↗ Establishes neutrino mass via oscillation — part of the framework's lineage.
  10. Particle Data Group (Workman, R. L. et al.) (2022). Review of Particle Physics (cosmic-ray muon flux). Progress of Theoretical and Experimental Physics 2022, 083C01. DOI: 10.1093/ptep/ptac097 ↗ Reference values for one of the ambient input channels.

Materials science, transport & rectification

  1. Thibado, P. M. et al. (2020). Fluctuation-induced current from freestanding graphene. Physical Review E 102, 042101. DOI: 10.1103/PhysRevE.102.042101 ↗ Continuous measurable current from driven lattice motion in a loaded circuit.
  2. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. (2009). The electronic properties of graphene. Reviews of Modern Physics 81, 109–162. DOI: 10.1103/RevModPhys.81.109 ↗ The definitive review of graphene's Dirac-fermion electronics and phonon transport.
  3. Bolotin, K. I. et al. (2008). Ultrahigh electron mobility in suspended graphene. Solid State Communications 146, 351–355. DOI: 10.1016/j.ssc.2008.02.024 ↗ Shows how clean, suspended graphene reaches exceptional carrier transport.
  4. Grigorenko, A. N., Polini, M. & Novoselov, K. S. (2012). Graphene plasmonics. Nature Photonics 6, 749–758. DOI: 10.1038/nphoton.2012.262 ↗ How graphene couples to electromagnetic fields — relevant to the coupling term.
  5. Giustino, F. (2017). Electron–phonon interactions from first principles. Reviews of Modern Physics 89, 015003. DOI: 10.1103/RevModPhys.89.015003 ↗ The rigorous framework linking lattice vibrations to charge transport (v_ph, Δp).
  6. McIver, J. W. et al. (2012). Control over topological insulator photocurrents with light polarization. Nature Nanotechnology 7, 96–100. DOI: 10.1038/nnano.2011.214 ↗ A directed photocurrent generated by symmetry control — an analogue of rectification.
  7. Ashcroft, N. W. & Mermin, N. D. (1976). Solid State Physics. Holt, Rinehart and Winston. Standard text on lattice vibrations, phonon dispersion and sound velocity.
  8. Ziman, J. M. (1960). Electrons and Phonons: The Theory of Transport Phenomena in Solids. Oxford University Press. Classic account of phonon transport underwriting the factor v_ph.

Non-equilibrium thermodynamics

  1. Onsager, L. (1931). Reciprocal relations in irreversible processes, I. Physical Review 37, 405. DOI: 10.1103/PhysRev.37.405 ↗ Symmetry relations governing coupled irreversible flows.
  2. Onsager, L. (1931). Reciprocal relations in irreversible processes, II. Physical Review 38, 2265. DOI: 10.1103/PhysRev.38.2265 ↗ Continuation of the reciprocal-relations framework.
  3. Callen, H. B. & Welton, T. A. (1951). Irreversibility and generalized noise. Physical Review 83, 34. DOI: 10.1103/PhysRev.83.34 ↗ The fluctuation–dissipation theorem; bounds what equilibrium noise can do.
  4. Reimann, P. (2002). Brownian motors: noisy transport far from thermal equilibrium. Physics Reports 361, 57–265. DOI: 10.1016/S0370-1573(01)00081-3 ↗ How broken symmetry rectifies unbiased fluctuations into directed transport.
  5. Astumian, R. D. (1997). Thermodynamics and kinetics of a Brownian motor. Science 276, 917–922. DOI: 10.1126/science.276.5314.917 ↗ Stochastic rectification in asymmetric, driven systems.
  6. Prigogine, I. (1977). Nobel Lecture: time, structure and fluctuations. Royal Swedish Academy of Sciences. Publisher / source ↗ Thermodynamics of dissipative structures in open, driven systems.
  7. de Groot, S. R. & Mazur, P. (1962). Non-Equilibrium Thermodynamics. North-Holland. Fluxes, forces and entropy production in continuous open systems.
  8. van Kampen, N. G. (2007). Stochastic Processes in Physics and Chemistry (3rd ed.). Elsevier. Master-equation treatment of directed transport and symmetry breaking.
  9. Feynman, R. P., Leighton, R. B. & Sands, M. (1963). The Feynman Lectures on Physics, Vol. I, Ch. 46 (Ratchet and Pawl). Addison-Wesley. Publisher / source ↗ A ratchet at equilibrium extracts no work; directed motion needs non-equilibrium.

Scattering theory & cross-sections

  1. Formaggio, J. A. & Zeller, G. P. (2012). From eV to EeV: neutrino cross sections across energy scales. Reviews of Modern Physics 84, 1307. DOI: 10.1103/RevModPhys.84.1307 ↗ The standard review of measured neutrino cross-sections over all energies.
  2. Scholberg, K. (2006). Prospects for measuring coherent elastic neutrino–nucleus scattering at a stopped-pion source. Physical Review D 73, 033005. DOI: 10.1103/PhysRevD.73.033005 ↗ Framed the experimental route later realised by COHERENT.
  3. Sakurai, J. J. (1994). Modern Quantum Mechanics (rev. ed.). Addison-Wesley. Scattering amplitudes, partial waves and the optical theorem behind σ(E).
  4. Mott, N. F. & Massey, H. S. W. (1965). The Theory of Atomic Collisions (3rd ed.). Oxford University Press. Foundational treatment of cross-sections and their energy dependence.

Efficiency & conversion limits

  1. Carnot, S. (1824). Réflexions sur la puissance motrice du feu. Bachelier, Paris. Origin of the maximum efficiency of a heat engine — the archetypal bound.
  2. Shockley, W. & Queisser, H. J. (1961). Detailed balance limit of efficiency of p–n junction solar cells. Journal of Applied Physics 32, 510. DOI: 10.1063/1.1736034 ↗ The detailed-balance efficiency ceiling — the principal comparison case.

A firm distinction is maintained: the works cited here are established physics; the framework that assembles them into P(t) is the proposed contribution of this reference and is not itself claimed to be established — see scientific questions.

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