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structure definition def or abbrev

DiscreteEvolution

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formal statement (Lean)

 122structure DiscreteEvolution (N : ℕ) where
 123  hamiltonian : Fin N → Fin N → ℝ
 124  symmetric : ∀ i j, hamiltonian i j = hamiltonian j i
 125
 126/-- Apply one step of discrete evolution to deviations (linearized). -/
 127def DiscreteEvolution.step (ev : DiscreteEvolution N) (ψ : DeviationHilbert N) :
 128    DeviationHilbert N :=

proof body

Definition body.

 129  fun i => ψ i - Complex.I * (Finset.univ.sum fun j => (ev.hamiltonian i j : ℂ) * ψ j)
 130
 131/-- The diagonal Hamiltonian: H_ii = 1 (from J''(1) = 1 calibration). -/

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