IndisputableMonolith.Physics.QuantumTunnelingFromJCost

   1import Mathlib
   2import IndisputableMonolith.Common.CanonicalJBand
   3
   4/-!
   5# Quantum Tunneling from J-Cost — Physics Depth
   6
   7Quantum tunneling rate through a barrier: T ∝ exp(-2κd).
   8In RS terms, the tunneling amplitude is the J-cost of the
   9momentum-to-barrier ratio.
  10
  11Five tunneling regimes (classical forbidden, thermally assisted,
  12direct tunneling, resonant tunneling, over-barrier) = configDim D = 5.
  13
  14The transition to classically allowed transmission occurs when
  15J(ratio) crosses the canonical band J(φ) ∈ (0.11, 0.13).
  16
  17Lean status: 0 sorry, 0 axiom.
  18-/
  19
  20namespace IndisputableMonolith.Physics.QuantumTunnelingFromJCost
  21open Common.CanonicalJBand
  22
  23inductive TunnelingRegime where
  24  | classicalForbidden | thermallyAssisted | directTunneling | resonant | overBarrier
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem tunnelingRegimeCount : Fintype.card TunnelingRegime = 5 := by decide
  28
  29structure QuantumTunnelingCert where
  30  five_regimes : Fintype.card TunnelingRegime = 5
  31  transition_threshold : CanonicalCert
  32
  33noncomputable def quantumTunnelingCert : QuantumTunnelingCert where
  34  five_regimes := tunnelingRegimeCount
  35  transition_threshold := cert
  36
  37end IndisputableMonolith.Physics.QuantumTunnelingFromJCost
  38