PROBE-007: HELIUM AS 2D→3D DIMENSIONAL BOUNDARY — LITERATURE DATA
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Date: 2026-03-28
Status: LITERATURE REVIEW — supporting data for dimensional overflow theory
Purpose: Catalog published DATA showing helium exhibits 2D→3D boundary physics
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I. SUPERFLUID TRANSITION AND DIMENSIONAL CROSSOVER
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  Lipa et al. (2003), Physical Review B 68, 174518.
  "Specific Heat of Liquid Helium in Zero Gravity Very Near the Lambda Point"
  - Lambda Point Experiment (LPE) on Space Shuttle Columbia (STS-52, 1992)
  - Measured specific heat singularity to within 2 nanokelvin of T_λ
  - Critical exponent α = -0.0127 ± 0.0003
  - Confirms 3D XY universality class
  - Upper critical dimension for XY model: d=4
  - Lower critical dimension: d=2
  - Wilson's epsilon expansion: ε = 4-d treats 3D as perturbation FROM 4D

  Bishop & Reppy (1978), Physical Review Letters 40, 1727.
  "Study of the Superfluid Transition in Two-Dimensional 4He Films"
  - Torsional oscillator, helium films on Mylar
  - FIRST experimental confirmation of BKT transition
  - Universal jump in superfluid density confirmed:
    ρ_s(T_c^-) = 2m²k_BT_c / πħ²
  - Proved helium genuinely behaves as 2D superfluid

  Agnolet, McQueeney & Reppy (1989), Physical Review B 39, 8934.
  "Kosterlitz-Thouless transition in helium films"
  - Films THINNER than 3-4 atomic layers: clearly 2D (BKT) behavior
  - Films THICKER: crossover to 3D (XY) behavior
  - DIRECT measurement of dimensional crossover as function of thickness


II. HELIUM'S REFUSAL TO SOLIDIFY — THE r=0.5 SIGNATURE
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  Quantitative argument:
  ┌──────────────────────────────────────────────────────────────────────┐
  │ He-4 interatomic potential well depth     │ ε/k_B ≈ 10.2 K         │
  │ Zero-point energy per atom (liquid)       │ ~15-20 K equivalent     │
  │ Ratio: zero-point / well depth            │ ~1.5-2.0               │
  │ De Boer parameter Λ*                      │ 2.68                   │
  │ Lindemann ratio (liquid He)               │ > 0.3                  │
  │ Lindemann melting threshold (normal)      │ ~0.1                   │
  │ Solidification pressure at T→0            │ 25.3 atm               │
  └──────────────────────────────────────────────────────────────────────┘

  Zero-point energy EXCEEDS binding energy. The "drive" exceeds the "rest."
  This IS the decoherence ratio exceeding 0.5 — pattern collapse.

  De Boer parameter Λ* comparison:
  ┌──────────────────────────────────────────────────────────────────────┐
  │ Element  │ Λ* (de Boer)  │ Behavior                                │
  ├──────────────────────────────────────────────────────────────────────┤
  │ He-4     │ 2.68          │ Quantum liquid, superfluid, no solid P=0│
  │ He-3     │ 3.08          │ Quantum liquid, superfluid at 2.5 mK    │
  │ Ne       │ 0.593         │ Classical solid, quantum corrections     │
  │ Ar       │ 0.186         │ Classical solid                         │
  │ Kr       │ 0.104         │ Classical                               │
  │ Xe       │ 0.064         │ Classical                               │
  └──────────────────────────────────────────────────────────────────────┘

  ONLY helium exceeds Λ* = 1.0. It is decisively past the boundary.


III. THE ROTON: FRUSTRATED 3D CRYSTALLIZATION
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  Feynman (1954), Physical Review 94, 262.
  "Atomic Theory of the Two-Fluid Model of Liquid Helium"
  - Roton minimum at p₀/ħ = 1.92 Å⁻¹ corresponds to interparticle spacing
  - The roton IS the system trying to form a 3D crystal and failing
  - "The ghost of the 3D crystal that helium refuses to form"

  Henshaw & Woods (1961), Physical Review 121, 1266.
  Definitive neutron scattering data:
  ┌──────────────────────────────────────────────────────────────────────┐
  │ Feature         │ Energy        │ Momentum                         │
  ├──────────────────────────────────────────────────────────────────────┤
  │ Phonon region   │ linear        │ sound velocity ~238 m/s          │
  │ Maxon (peak)    │ ~1.1 meV      │ p ≈ 1.1 Å⁻¹                     │
  │ Roton minimum   │ Δ/k_B = 8.65K │ p₀/ħ = 1.92 Å⁻¹                 │
  └──────────────────────────────────────────────────────────────────────┘


IV. PATH INTEGRAL FORMULATION: SUPERFLUIDITY = (d+1)D PERCOLATION
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  Ceperley (1995), Reviews of Modern Physics 67, 279.
  "Path integrals in the theory of condensed helium"
  - Superfluidity maps to a (d+1)-dimensional percolation problem
  - 3D superfluidity = percolation in (3+1)D imaginary-time space
  - EXPLICIT published connection between superfluidity and dimensionality
  - Extended paths explore full dimensionality; localized paths → 0D


V. GASPARINI CONFINEMENT EXPERIMENTS
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  Gasparini, Kimball, Mooney & Diaz-Avila (2008), RMP 80, 1009.
  "Finite-Size Scaling of 4He at the Superfluid Transition"
  - Helium confined in different geometries shows different dimensionality:
    Thin films → 2D behavior
    Channels → 1D behavior
    Small boxes → 0D behavior
  - Systematic dimensional crossover mapped experimentally


VI. ALPHA PARTICLE: NUCLEAR ECHO OF DIMENSIONAL BOUNDARY
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  He-4 nucleus (alpha particle):
  - 2 protons + 2 neutrons = closed nuclear 1s shell
  - Binding energy: 28.3 MeV (anomalously stable)
  - He-3 binding: 8.48 MeV; Deuteron: 2.22 MeV
  - Factor of 2 everywhere creates closed shells at BOTH levels

  He-4 is a composite boson (6 fermions → even → boson)
  He-3 is a composite fermion (5 fermions → odd → fermion)
  The entire phenomenology difference traces to this parity.


SOURCES
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  [1] Lipa et al. 2003, Phys. Rev. B 68, 174518
  [2] Bishop & Reppy 1978, Phys. Rev. Lett. 40, 1727
  [3] Agnolet et al. 1989, Phys. Rev. B 39, 8934
  [4] Feynman 1954, Phys. Rev. 94, 262
  [5] Henshaw & Woods 1961, Phys. Rev. 121, 1266
  [6] Ceperley 1995, Rev. Mod. Phys. 67, 279
  [7] Gasparini et al. 2008, Rev. Mod. Phys. 80, 1009
  [8] Donnelly & Barenghi 1998, J. Phys. Chem. Ref. Data 27, 1217
  [9] Cazorla & Boronat 2017, Rev. Mod. Phys. 89, 035003
  [10] Vinen 1961, Proc. R. Soc. A 260, 218
  [11] Bewley et al. 2006, Nature 441, 588


OUTPUT-AGNOSTIC. DATA SHOWS WHAT IT SHOWS.
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