!!! Änderung !!!

Donnerstags findet die Vorlesung um 14:00 Uhr im Lehmann HS statt.

On Thursdays the lecture takes place at 14:00 in the Lehmann Lecture Hall.

Syllabus

This course is aimed at advanced physics students interested in application of field-theoretical methods to the problems of macroscopic quantum coherence and quantum dissipative systems. During the course we will study the path integral technique, starting from a simple quantum mechanical version for one particle and advancing to the many-body field-theoretical version for bosons and fermions. We will also introduce the Keldysh formalism – the technique, which allows describing non-equilibrium systems in real time. These two main techniques (path integral and Keldysh formalism) will be used to analyze relatively simple, “zero dimensional” systems, e.g. tunnel (Josephson) junctions. 

Part A: Introduction

Here the main concepts and systems will be introduced on a simple level (no path integrals, no Keldysh technique)

1) Tunnel junctions, Coulomb blockade, single-electron-transistor
2) Johnson-Nyquist noise vs. shot noise
3) Josephson junctions, macroscopic quantum tunneling, macroscopic quantum coherence and Josephson qubits

Part B: Dissipative quantum mechanics

In this part the path integral and the Keldysh techniques will be introduced gradually along with the concepts of dissipation in quantum mechanics, effective action, quasi-classical Langevin dynamics etc.

1) Spin-Boson model, Golden Rule rates
2) Bloch-Redfield master equation, Lindblad equation, T1 and T2 relaxation times, Lamb shift (renormalization vs. dissipation)
3) Feynman-Vernon (Caldeira-Legget) description of dissipation of a quantum particle  
4) Caldeira-Leggett model in imaginary time, instantons, suppression of macroscopic quantum tunneling
5) Caldeira-Leggett model in real time, quasi-classical Langevin equations, Keldysh formalism
6) Ambegaokar-Eckern-Schön (AES) formalism for tunnel junctions: imaginary time, real time (Keldysh), shot noise

Part C: Applications

Here we will use the techniques developed in the previous parts in order to describe dissipative phenomena in superconducting and magnetic systems.

1) AES treatment of Josephson junctions, quasi-particles
2) P(E)-Theory, Coulomb blockade in shunted junctions, incoherent Cooper-Pair tunneling
3) AES formalism for magnetic systems: derivation of stochastic Landau-Lifshitz-Gilbert equation, spin torque transfer in magnetic tunnel junctions.