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arXiv · 1405.5984

How to interpret the spectral density of the Keldysh nonequilibrium Green's function

K. J. Pototzky·E. K. U. Gross
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Abstract

This paper is devoted to the study and interpretation of the spectral function $\mathbf{A}(ω, T)$ of the Keldysh nonequilibrium Green's function. The spatial diagonal of the spectral function is often interpreted as a time-dependent local density of states. We show that this object can take negative values implying that a simple probability interpretation as a time-dependent density of states is not possible. The same issue also occurs for the Wigner function $P(x,p)$ where it is solved by taking the uncertainty principle into account. We follow the same path and incorporate the time-energy uncertainty relation to define a convoluted spectral function that allows for a probability interpretation. The usefulness of this quantity as a interpretative tool is demonstrated by visualizing the charge dynamics in a quantum dot coupled to superconducting leads.

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K. J. Pototzky, E. K. U. Gross. 2014-05-23. How to interpret the spectral density of the Keldysh nonequilibrium Green's function. https://arxiv.org/abs/1405.5984

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