## Syllabus

### Topics

Part A: Introduction

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

Part B: Dissipative quantum mechanics

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

Part C: Applications

- AES treatment of Josephson junctions, quasi-particles
- P(E)-Theory, Coulomb blockade in shunted junctions, incoherent Cooper-Pair tunneling
- AES formalism for magnetic systems: derivation of stochastic Landau-Lifshitz-Gilbert equation, spin torque transfer in magnetic tunnel junctions
- Extra advanced subjects (time permitting): for example RG for spin-boson and/or for Bose-Kondo Model

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