Functional renormalization group for nonequilibrium transport through mesoscopic systems


Lecture details

The lecture will be given by Dr. Jakobs.


At the 'Institut für Theorie der Statistischen Physik', the functional renormalization group is frequently used to compute charge or spin currents through quantum dots and wires. In a suitable formulation based on Keldysh formalism, it allows to study nonequilibrium situations with bias voltage or temperature differences.
A significant first part of the lecture is devoted to Keldysh formalism for nonequilibrium Green functions and to corresponding generating functionals. Then it will be discussed how open quantum systems can be described in Keldysh formalism. The lecture then treats the RG flow equations for the 1-particle irreducible vertex functions and presents some example application.

Learning goal:

The lecture and exercises shall enable the students to
- perform computations with and manipulations of expressions involving Keldysh Green functions,
- specify and relate different classes of Green and vertex functions and their generating functionals,
- derive and interpret a current formula in Keldysh formalism for a simple model for quantum transport,
- derive the flow equations for the 1-partice irreducible vertex functions of such a model and apply standard truncations.

Recommended requirements:

The prerequisites are usually covered in lectures on quantum theory of condensed matter:
- A solid understanding of second quantization is required.
- Some acquaintance with many-body Green functions and diagrammatic expansion, e.g. in Matsubara formalism, is helpful.
- Knowing about coherent many-particle states and Grassmann numbers is beneficial.

Time Room Start/Finish
Wed. 8.30am - 10am 4263 (26C/401) 09.10.2019 - 29.01.2020
Wed. 10.30am - 12pm 4263 (26C/401) 09.10.2019 - 29.01.2020