Correlation Phenomena in Solid State Physics:
Open Quantum Systems


Content of the lecture

Introduction and motivation

Further material from WS 2021/22 can be found in the cloud (see teach center)

Password restricted content:

Further material from previous years: In the three classes 1.10.2019 to 15.10.2019 we addressed the density matrix: pag. 10-34 of
the handwritten vietri-lecturenotes.pdf
These also have a printed version with more text: vietri-proceedings.pdf which can be downloaded here as well. It has been printed in Springer as a book chapter

Following classes:
kraus operators and lindblad equation (22.10)

notes on decoherence and qubits (22.10-29.10)

On 29.10 we also discussed the general time evolution of the density matrix due to the Lindblad equation and expansion in eigenvectors, vietri-lecturenotes.pdf pag 39-42

notes on equations of motion and bosonic cavity 2019-11-05

driven cavity 2019-11-05

notes on bloch equation 2019-11-05 (partly)

On 2019-11-12 we concluded the Bloch equation and we started with the microscopic derivation of the Lindblad equation vietri-lecturenotes.pdf pagg. 45-59

On 2019-11-19 we concluded the microscopic derivation. vietri-lecturenotes.pdf pagg. 60-72

On 2019-12-03 we discussed the derivation of a fermionic reservoir vietri-lecturenotes.pdf pagg. 72-80
On 2019-12-10 we summarized the fermionic model summarized the fermionic model and did some exercises on a single-site version (calculation of current, etc.) We started an exercise with a two-site model

On 2020-01-07 we discussed the solution of the Two site model with dissipation and started the quantum regression theorem vietri-lecturenotes.pdf pagg. 99-108

On 2020-01-14 we concluded the quantum regression theorem (vietri-lecturenotes.pdf pagg. 99-108) and used to compute correlation functions correlation functions with the equations of motion method We applied it to the cavity in a thermal bath problem

On 2020-01-21 We finished the exercise on correlation functions for the bosonic cavity
We discussed the quantum regression theorem for fermions (vietri-lecturenotes.pdf pag. 107-..) and applied it to the calculation of correlation and Green's functions (including Fourier transformation) for a single-site fermionic model

On 2020-01-28 we discussed the stochastic Schrodinger equation (also called Quantum Jumps) approach

Further material from previous years:


open-af.pdf (afisher)


pauli-master-and-highbias.pdf: Pauli-Master equation


quantum regression theoem




direct link Super fermion representation (A. A. Dzhioev and D. S. Kosov 2011)

Lecture Notes of the XX Training Course in the Physics of Strongly Correlated Systems

Vietri sul Mare, Oct 2016