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Complex Hamiltonians extend the traditional Hermitian formalism to accommodate Physical Systems that may not be isolated or have Gain and loss parameters, such as those used in Quantum Optics and Open Quantum Systems. They play a crucial role in the study of PT-symmetric systems, where the Hamiltonian respects Parity-time symmetry, leading to Real energy spectra and Unique phase transitions even in Non-Hermitian scenarios.
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