Open Quantum Systems

A closed quantum system evolves according to the Schroedinger equation. When the quantum system is “open”, namely in interaction with its own environment, the picture becomes richer and more complicated. The objective of these lectures is to try and understand how an open quantum system behaves. This will shed light on the structure of quantum mechanics and some of its most interesting aspects.


  1. Closed and open quantum systems. Quantum dynamics. Evolution of quantum states. Short, intermediate and long times. Exponential decay. The Fermi Golden Rule.
  2. Quantum field theoretical description. Weisskopf-Wigner approximation. Intermezzo: partial differential equations and propagators.
  3. Intermezzo: Method of characteristics. Propagators and more examples.
  4. The Markov approximation. Memory effects. The Master equation.
  5. The modern approach. Density matrices and superoperators. The Kraus-Sudarshan representation. The Gorini-Kossakowski-Sudarshan-Lindblad structure of the evolution.
  6. Examples. Quantum dissipative systems.
  7. Positivity and complete positivity. The role of entanglement. The structure of the evolution law in quantum mechanics.

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