MasterNanosciences, nanotechnologies

These lectures will provide the mathematical formalism, concepts and tools required to model quantum open systems (quantum systems coupled to a dissipative environment), and address the main physical questions raised in their description. A particular attention will be paid to the notions of entropy and Gibbs states, of bi-partite systems and (de-)coherence and of Markovian evolution and Lindblad operators. 
 

Chapter 1: Tool box and basics

* Mathematical framework, Functional Calculus for matrices

* Quantum formalism, Density matrices, Pure states, Gibbs states

* Von Neumann entropy, relative entropy and their properties

* Quantum trajectories, two-time measurement protocols

Chapter 2: Bi-partite systems 

* By-partite systems, tensor products, partial traces

* Purifications, Schmidt decomposition, Entropy (in-)equalities

* Subadditivity of entropy and Landauer's bound

Chapter 3: Dynamics

* Markovian approximation of Quantum Dynamics

* CPTP maps and Markovian semi-groups

* Lindblad generators and their properties

* Entropy production
 

Prerequisites:

Quantum Mechanics M1 

Statistical physics M1

References:

Exploring the quantum (Haroche & Raimond, Cambridge University Press)

Quantum measurement and control (Wiseman & Milburn, Cambridge University Press)

Quantum computation (Online lectures by John Preskill)