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Lecturer
Stefano Marcantoni stefano.marcantoni@gssi.it
Timetable and workload
Lectures: 16 hours
Course content
Open quantum systems are quantum systems interacting with the external environment (typically another physical system that is much larger and not controllable). Their dynamics is qualitatively different from the one described by the Schrödinger equation, that fails to capture dissipative effects.
In this short course, I will introduce the mathematical framework used to describe the dynamics of open quantum systems. This is based on completely positive maps and Markovian master equations in GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) form. I will discuss the general structure of the latter (GKSL Theorem) and present some simple examples in the finite-dimensional case. Among them, I will focus on the so-called "Davies generator" describing the thermalization of a finite quantum system induced by the interaction with a free Bose field in a thermal state. I will present the basic ideas for its rigorous derivation in the weak-coupling limit (following the modern strategy developed by Marco Merkli). In the last two lectures, I will give a broad overview of current research directions (e.g. structure theorems for non-Markovian dynamics, stochastic unravellings of the master equation, microscopic derivations in different settings, etc.).
People with no previous exposure to quantum mechanics are welcome to attend. The first part of the course will be calibrated depending on the audience, introducing all the relevant ingredients that may be unfamiliar.
Connection with other courses
Bogoliubov Theory for dilute Bose gases