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    Area of Science:

    • Quantum Mechanics
    • Condensed Matter Physics
    • Quantum Optics

    Background:

    • Linear response theory typically formulates susceptibility in the Schrödinger picture.
    • Existing theories often neglect non-Markovian effects in open or Floquet quantum systems.

    Purpose of the Study:

    • To develop a new method for deriving exact susceptibility in non-Markovian Floquet systems.
    • To incorporate environmental influences and analyze Floquet energy spectra.

    Main Methods:

    • Introduction of Heisenberg operators to derive exact susceptibility.
    • Analysis of the susceptibility's connection to the Floquet energy spectrum of the system plus environment.

    Main Results:

    • An exact susceptibility for non-Markovian Floquet systems is derived.
    • The susceptibility reveals connections to the Floquet energy spectrum.
    • Floquet bound states within the first Brillouin zone are identifiable from the susceptibility.

    Conclusions:

    • The new method accurately captures environmental influences on Floquet systems.
    • The derived susceptibility provides insights into Floquet energy spectra and bound states.
    • Potential applications in quantum engineering for open systems with modulated periodic evolution.