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    Area of Science:

    • Quantum mechanics
    • Quantum optics
    • Theoretical physics

    Background:

    • Analyzing Markovian dynamics of coupled quantum systems is complex.
    • Existing methods often involve intricate quantum jump superoperators.
    • A simplified approach is needed for broader applicability.

    Purpose of the Study:

    • To develop a novel method for analyzing the Markovian dynamics of coupled harmonic oscillators.
    • To reformulate the Lindblad master equation into a von Neumann-like equation.
    • To enable the study of quantum systems in a fully quantum domain.

    Main Methods:

    • Utilizing a Schrödinger equation with an effective non-Hermitian Hamiltonian.
    • Employing non-unitary transformations involving superoperators.
    • Applying an additional non-unitary transformation for Hamiltonian diagonalization.

    Main Results:

    • Successfully removed quantum jump superoperators.
    • Rewrote the Lindblad master equation into a von Neumann-like equation.
    • Obtained the evolution of input states via a diagonalized effective non-Hermitian Hamiltonian.

    Conclusions:

    • The proposed method effectively analyzes Markovian dynamics of coupled harmonic oscillators.
    • This technique can be generalized to systems with an arbitrary number of interacting fields.
    • The approach provides a pathway for studying quantum state evolution in a fully quantum domain.