Andrew J. Millis (Columbia University)

Non-equilibrium impurity models and quantum phase transitions (12 h)

Lecture 1

Introduction: classification of non-equilibrium problems and physical examples. Electron transfer in chemistry; pump-probe spectroscopies in condensed matter physics; trapped atomic gasses as example of continuously pumped systems; molecular conductors, quantum dots and dc steady state nonequilibrium. Overview of theoretical approaches.

Lecture 2

Impurity Models at Equilibrium I: Review of non-interacting impurity models: scattering theory, phase shifts, and resonant level model from functional integral formalism.

Lecture 3

Interacting Impurity models at equilibrium I: the X-Ray edge, singular integral equations, orthogonality catastrophe.

Lecture 4

Interacting Impurity models at equilibrium II: from mean field theory to the Kondo Problem; relation to Coulomb Blockade and molecular devices.

Lecture 5

Interacting impurity models at equilibrium III: renormalization group in impurity models from the Caldeira-Leggett localization/delocalization fixed point to the two channel Kondo problem.

Lecture 6

Non-equilibrium impurity models I: basic concepts including elementary calculations of current and conductance quantization; dephasing and decoherence. Schwinger-Keldysh two contour path integral.

Lecture 7

Non-equilibrium impurity models II: from complex phase shifts to non-equilibrium instantons, with application to single molecule devices and the nonequilibrium Kondo problem and some remarks on numerical approaches.

Lecture 8

Effective field theories and renormalization group in non-equilibrium problems. Semiclassical dynamics. Quantum Phase Transitions.