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Solving real time evolution problems by constructing excitation operators
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In this paper we study the time evolution of an observable in the interacting fermion systems driven out of equilibrium. We present a method for solving the Heisenberg equations of motion by constructing excitation operators which are defined as the operators satisfying . It is demonstrated how an excitation operator and its excitation energy λ can be calculated. By an appropriate supposition of the form of we turn the problem into the one of diagonalizing a series of matrices whose dimension depends linearly on the size of the system. We perform this method to calculate the evolution of the creation operator in a toy model Hamiltonian which is inspired by the Hubbard model and the nonequilibrium current through the single impurity Anderson model. This method is beyond the traditional perturbation theory in Keldysh-Green's function formalism, because the excitation energy λ is modified by the interaction and it will appear in the exponent in the function of time.
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