LiouvilleEquation

LiouvilleEquation[sys, h]
gives the evolution equations for the density matrix describing atomic system sys under the action of the Hamiltonian h.
LiouvilleEquation[sys, h, rel]
gives the evolution equations for the system subject to the relaxation matrix rel.
LiouvilleEquation[sys, h, rel, rep]
gives the evolution equations for the system subject to the repopulation matrix rep.
  • The atomic system sys is specified as a list of AtomicState objects.
  • LiouvilleEquation takes the same options as DensityMatrix, with the default value for each being Automatic, indicating that the corresponding default value for DensityMatrix is used.
  • With TimeDependenceTrue specified directly for LiouvilleEquation or as the default value for DensityMatrix, the evolution equations are ordinary differential equations in time.
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The Hamiltonian for a two-level atomic system subject to a static electric field:
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The evolution equations:
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The matrix for transit relaxation at a rate :
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The evolution equations with relaxation taken into account:
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The matrix for transit repopulation at a rate :
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The evolution equations with repopulation taken into account:
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