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In this paper we study the time evolution of an observable in the interactingfermion systems driven out of equilibrium. We present a method for solving theHeisenberg equations of motion by constructing excitation operators which aredefined as the operators A satisfying [H,A]=\lambda A. It is demonstrated howan excitation operator and its excitation energy \lambda can be calculated. Byan appropriate supposition of the form of A we turn the problem into the one ofdiagonalizing a series of matrices whose dimension depends linearly on the sizeof the system. We perform this method to calculate the evolution of thecreation operator in a toy model Hamiltonian which is inspired by the Hubbardmodel and the nonequilibrium current through the single impurity Andersonmodel. This method is beyond the traditional perturbation theory inKeldysh-Green's function formalism, because the excitation energy \lambda ismodified by the interaction and it will appear in the exponent in the functionof time.

Solving real time evolution problems by constructing excitation operators