IndisputableMonolith.QFT.DynamicCasimirRecognition

   1import Mathlib
   2import IndisputableMonolith.QFT.CasimirPhiCorrections
   3
   4/-!
   5# Dynamic Casimir Recognition
   6
   7The dynamic Casimir effect is the time-dependent boundary case: changing the
   8admissible mode inventory can convert boundary work into real photons.  This
   9module proves only structural statements.  Device-level φ-locked schedules
  10remain hypotheses until connected to circuit data.
  11-/
  12
  13namespace IndisputableMonolith
  14namespace QFT
  15namespace DynamicCasimirRecognition
  16
  17open CasimirPhiCorrections
  18
  19noncomputable section
  20
  21/-- A time-dependent boundary modulation. -/
  22structure BoundaryModulation where
  23  amplitude : ℝ
  24  rate : ℝ
  25  carrierFrequency : ℝ
  26
  27/-- Structural photon-production functional for a boundary modulation.  It is
  28quadratic in amplitude and rate, as expected for a parametric boundary drive. -/
  29noncomputable def photonProductionFunctional (M : BoundaryModulation) : ℝ :=
  30  M.amplitude ^ 2 * M.rate ^ 2
  31
  32/-- Static boundary: zero modulation amplitude gives no dynamic photon-production
  33term in this structural model. -/
  34theorem static_boundary_no_dynamic_photons
  35    (M : BoundaryModulation) (hamp : M.amplitude = 0) :
  36    photonProductionFunctional M = 0 := by
  37  unfold photonProductionFunctional
  38  rw [hamp]
  39  ring
  40
  41/-- A nonzero boundary modulation with nonzero rate can feed the photon-production
  42functional. -/
  43theorem nonzero_modulation_positive_functional
  44    (M : BoundaryModulation)
  45    (hamp : M.amplitude ≠ 0) (hrate : M.rate ≠ 0) :
  46    0 < photonProductionFunctional M := by
  47  unfold photonProductionFunctional
  48  exact mul_pos (sq_pos_of_ne_zero hamp) (sq_pos_of_ne_zero hrate)
  49
  50/-- A φ-locked dynamic Casimir schedule is a hypothesis-level package. -/
  51structure PhiLockedDynamicSchedule where
  52  modulation : BoundaryModulation
  53  phi_locked : Prop
  54  superconducting_circuit_realization : Prop
  55  falsifier : Prop
  56
  57/-- Certificate for theorem-level dynamic Casimir structure. -/
  58structure DynamicCasimirCert where
  59  static_zero :
  60    ∀ M : BoundaryModulation,
  61      M.amplitude = 0 → photonProductionFunctional M = 0
  62  nonzero_modulation_positive :
  63    ∀ M : BoundaryModulation,
  64      M.amplitude ≠ 0 → M.rate ≠ 0 → 0 < photonProductionFunctional M
  65
  66/-- The dynamic Casimir structural certificate. -/
  67def dynamicCasimirCert : DynamicCasimirCert where
  68  static_zero := static_boundary_no_dynamic_photons
  69  nonzero_modulation_positive := nonzero_modulation_positive_functional
  70
  71end
  72
  73end DynamicCasimirRecognition
  74end QFT
  75end IndisputableMonolith
  76