Title: Theory of Open Quantum Systems and Quantum Thermodynamics
Convenor: Kay Brandner (Nottingham)
Commitment: 10 lectures x 1 hour, 2 lectures / week
Dates: Wednesday and Friday, 12:00-13:00
Start: 26 May 2021
End: 25 June 2021
(Dates and times can be discussed upon request.)
Assessment: Exercise sheet at the end of the module
Module Details: The aim of this module is to provide general theoretical tools to describe the
dynamics of open quantum systems. We develop a systematic approach to quantum master
equations, which are widely used in quantum optics, quantum opto-mechanics, cold-atom and solidstate
physics. We further show how these master equations can be derived from phenomenological
arguments and microscopic models, discuss their range of validity, their consistency with the laws of
thermodynamics and methods to solve them. In the last part of this module, we apply these methods
to quantum thermal machines and discuss recent developments in this area. The module is primarily
designed for post-graduate students working in theoretical condensed matter physics, but is open to
everybody who is interested in the theory of open quantum systems and quantum thermodynamics.
Solid background knowledge on quantum mechanics, statistical and thermal physics will be helpful to
follow this module.
Specific topics include:
(I) Mathematical basics of the theory of open quantum systems (dynamical maps, complete positivity,
GKSL (Lindblad) equations).
(II) Thermodynamics of open quantum systems (detailed balance, the first and the second law,
thermodynamic consistency of quantum master equations).
(III) Microscopic derivations of quantum master equations (Nakajima-Zwanzig formalism, weakcoupling
theory for free and driven systems).
(IV) Methods to solve quantum master equations (exact methods, hierarchies of equations of motion,
(V) Quantum thermal machines (quantum thermodynamic cycles, basics of quantum heat engines,