Advanced Quantum Mechanics-S3

Advanced Quantum Mechanics

Contact: Pr. Alberto Verga or Pr. Alejandro Perez


I- Path Integrals: The path integral representation of quantum mechanics (History, relation with the Schrödinger representation, advantages relation to the classical theory), the phase space path integral, the configuration space path integral, duality with statistical mechanics (Brownian motion, Wick rotation), stationary phase approximation, Gaussian integrals (bosonic and fermionic), The heat kernel expansion, Examples (free particle, the harmonic oscillator, the particle in a uniform magnetic field, the particle in a circle, the particle in a box), the Aharonov-Bohm effect. Tunneling and instantons.

II- Quantum information: entanglement and entropy; open systems, master equation, decoherence; chaos, random matrices, dynamical localization.



B. Schumacher and M. Westmoreland, Quantum Process, Systems and Information, Cambridge 2010
Haake, Quantum Chaos, Springer 2010.