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Non-equilibrium Green's function formalism and the problem of bound states

Abhishek Dhar·Diptiman Sen
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Abstract

The non-equilibrium Green's function formalism for infinitely extended reservoirs coupled to a finite system can be derived by solving the equations of motion for a tight-binding Hamiltonian. While this approach gives the correct density for the continuum states, we find that it does not lead, in the absence of any additional mechanisms for equilibration, to a unique expression for the density matrix of any bound states which may be present. Introducing some auxiliary reservoirs which are very weakly coupled to the system leads to a density matrix which is unique in the equilibrium situation, but which depends on the details of the auxiliary reservoirs in the non-equilibrium case.

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Abhishek Dhar, Diptiman Sen. 2006-03-02. Non-equilibrium Green's function formalism and the problem of bound states. https://doi.org/10.1103/physrevb.73.085119

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