Abstract
We present a generalized version of the Feynman-Vernon-Hellwarth geometric representation and a biorthogonal density matrix formalism for the description of the non-Hermitian Schrödinger equation. The theory is applied to the study of complex geometric quantum phases in dissipative systems. It is shown that the complex Aharonov-Anandan (AA) geometric phase is related to the complex solid angle enclosed by a complex Bloch vector trajectory S(t). General analytic formulas are presented for the complex AA phase for a driven dissipative two-level system undergoing multiphoton Rabi floppings.
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