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外文期刊>Physical review, B. Condensed matter and materials physics
>Erratum: Inhomogeneous spectral moment sum rules for the retarded Green function and selfenergy of strongly correlated electrons or ultracold fermionic atoms in optical lattices Phys. Rev. B 80, 115119 (2009)
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Erratum: Inhomogeneous spectral moment sum rules for the retarded Green function and selfenergy of strongly correlated electrons or ultracold fermionic atoms in optical lattices Phys. Rev. B 80, 115119 (2009)
We have found a mistake in derivation of the nonequilibrium generalization of the expressions for the nonhomogeneous moments for the Green's function and the self-energy. Namely, in the derivation of these moments for the nonequilibrium case when there is explicit time dependence of the Hamiltonian in the Schrodinger representation, H_S=H_S(T), the second and higher time derivatives of an operator in the Heisenberg representation i~nd~nOH/dT~n cannot be simply substituted by the corresponding multiple commutator of the operator with the Hamiltonian L~n0_H=...O_H,H_H(T),H_H(T)..H_H(T). In this case, additional terms proportional to explicit time derivatives of H_S(T) have to be added. Indeed, while the first derivative of an operator can be substituted by a commutator with H_H(T): idO_H/dT=O_H,H_H(T), beginning with the second time derivative, one finds additional terms. For instance, the second derivative satisfies i~2dO_H/dT2=idO_H/dT,H_H(T) +O_H , idH_H(T)/T= L~20_H + O_H ,iH_H(T)/T, where the partial time derivative in the last term is equal to U~+(T)H_S(T)/TU(T), and U(T) is the time evolution operator from the initial time to time T(all partial derivatives of the Hamiltonian are written as a unitary transformation with respect to the evolution operator of the corresponding partial derivative of the Hamiltonian in the Schrodinger representation). Following this procedure, it is easy to obtain the expressions for the higher time derivatives of the operators, which will also contain additional terms. These additional terms will result in additional terms in the expressions for the nonequilibrium spectral moments for the retarded Green's function and the self-energy, beginning from the third and the first order, respectively. It is possible to show that the sum of the additional terms equals zero in the case of the second Green's function moment, independent of the form of the Hamiltonian.'
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