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

Source: [How to interpret the spectral density of the Keldysh nonequilibrium Green's function](<https://www.sota2.com/research/paper/68fa2d601e209131ce858a9c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:13:00.724Z

Authors: K.J. Pototzky, E.K.U. Gross

Published: 2014-05-23T08:06:30.000Z

## Abstract

This paper is devoted to the study and interpretation of the spectral function $\\mathbf{A}(\\omega, T)$ 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1405.5984>)

[PDF](<https://arxiv.org/pdf/1405.5984.pdf>)