### Abstract

Abstract The goal of these lecture notes is to illustrate connections between two

widely used, but often separately adopted approaches to deal with quantum systems

out of equilibrium, namely quantum master equations and nonequilibrium Green's

functions. For the paradigmatic case of the Anderson impurity model out of equilib-

rium we elaborate on these connections and map its description from one approach

to the other. At the end of this chapter, we will show how the "best of the two worlds"

can be combined to obtain a highly accurate solution of this model, which resolves

the nonequilibrium Kondo physics down to temperatures well below the Kondo scale.

As a training course, these lectures devote a large portion to an introduction to the

Lindblad quantum master equation based on standard treatments, as well as methods

to solve this equation. For nonequilibrium Green's functions, which are discussed

in the first part of the course, we only provide a summary of the most important

aspects necessary to address the topics of the present chapter. The relevant aspects

of these two topics are presented in a self-contained manner so that a background in

equilibrium many-body physics is sufficient to follow these notes.

widely used, but often separately adopted approaches to deal with quantum systems

out of equilibrium, namely quantum master equations and nonequilibrium Green's

functions. For the paradigmatic case of the Anderson impurity model out of equilib-

rium we elaborate on these connections and map its description from one approach

to the other. At the end of this chapter, we will show how the "best of the two worlds"

can be combined to obtain a highly accurate solution of this model, which resolves

the nonequilibrium Kondo physics down to temperatures well below the Kondo scale.

As a training course, these lectures devote a large portion to an introduction to the

Lindblad quantum master equation based on standard treatments, as well as methods

to solve this equation. For nonequilibrium Green's functions, which are discussed

in the first part of the course, we only provide a summary of the most important

aspects necessary to address the topics of the present chapter. The relevant aspects

of these two topics are presented in a self-contained manner so that a background in

equilibrium many-body physics is sufficient to follow these notes.

Original language | English |
---|---|

Title of host publication | Out-of-Equilibrium Physics of Correlated Electron Systems |

Editors | Roberta Citro, Ferdinando Mancini |

Place of Publication | Cham, Switzerland |

Publisher | Springer International Publishing AG |

Chapter | 4 |

Pages | 121-188 |

Number of pages | 68 |

Volume | 191 |

ISBN (Electronic) | 978-3-319-94956-7 |

ISBN (Print) | 978-3-319-94955-0 |

DOIs | |

Publication status | Published - 2018 |

### Publication series

Name | Springer Series in Solid-State Sciences |
---|---|

Publisher | Springer International Publishing |

### Fingerprint

### Fields of Expertise

- Advanced Materials Science

### Cite this

Arrigoni, E., & Dorda, A. (2018). Master Equations Versus Keldysh Green's Functions for Correlated Quantum Systems Out of Equilibrium. In R. Citro, & F. Mancini (Eds.),

*Out-of-Equilibrium Physics of Correlated Electron Systems*(Vol. 191, pp. 121-188). (Springer Series in Solid-State Sciences). Cham, Switzerland: Springer International Publishing AG . https://doi.org/10.1007/978-3-319-94956-7_1