Title : Developments and applications of the optical equivalence theorem
The optical equivalence theorem is analyzed and developped for almost-infinte-valued-operator eigenstates. Pertinent expansions are presented after the calculation of new formalisms for the Optical equivalence theorem. New extensions for the Optical equivalence principle are formulated, and applied to different types of quantum systems, semiclassical systems and optical systems.
The optical equivalent for operators , with weighted density matrix and the spectral component f on compact support is defined in the projector operator. The definition of the first-approximation correction orders is demonstrated to depend on the definition of the parameters qualifying the definitions of the weighting-support-control function. The investigation is apt for systems constituted of intense, non-monochromatic laser fields. The power spectrum of the operators is this way decomposed as a sequence obtained after the majorization of the operators after those of the weighting function. The power spectrum is therefore not needed to be expressed as a sequence (of majorizations), where such majorization do not apply to pure states. The control of the spectral analysis is proposed, to distinguish among the several contributions. Calculations are performed for the most extreme case the long-time limit of the error estimations. Applications are proposed for cold dynamics ensembles, cold atomic trapped ions, temperature experiments for protein folding in molecular dynamics; jump processes between states; quantums epration of multispatial Gauss-Markoffmodels; uncertainty estimations in metrology, decoherence and dissipation, noisy metrology beyond the standard quantum limit.