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Open Quantum Systems and Quantum Thermodynamics

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,

perturbation theory).

(V) Quantum thermal machines (quantum thermodynamic cycles, basics of quantum heat engines,

recent developments).