Solving real time evolution problems by constructing excitation operators
arXiv:1009.0576 · doi:10.1063/1.3701702
Abstract
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 A satisfying [H,A]=λA. It is demonstrated how an excitation operator and its excitation energy λcan be calculated. By an appropriate supposition of the form of A 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 λis modified by the interaction and it will appear in the exponent in the function of time.
8 pages
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