A Deep Truth

• Verlet integrator replaces the true Liouville propagator by an approximate one

• We can make these equal by saying the approximate propagator is obtained as the propagator of an approximate Liouville operator

• or

• This corresponds to some unknown Hamiltonian

  • and this Hamiltonian is conserved by the Verlet propagator
  • the Verlet algorithm will not likely give rise to drift in the true Hamiltonian, since this “shadow” Hamiltonian is conserved

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