Theoretical Methods for Open Quantum System Dynamics
March 12th, 2019 LOÏC HENRIET / MARIONA MORENO-CARDONER Theoretical Quantum-Nano Photonics
ICFO-The Institute of Photonic Sciences

A large part of modern experimental platforms operate in an out-of-equilibrium context, and are subject to drive and dissipation. As such, the theoretical description of their dynamics can be challenging. In this course, we present a set of methods that allow to compute the dynamics of open quantum systems.

First, we will focus on environment-induced quantum dissipation. In the case of quadratic interaction between the system of interest and its environment, we will show how to derive an exact master equation describing the dynamics of the system density matrix by using a path-integral formalism. This formalism, which is related to Keldysh path integral/non-equilibrium Green functions techniques, fully takes into account non-Markovian effects due to the interaction with the bath and can be widely used in a variety of contexts to describe bosonic or fermionic systems. We will discuss several examples where the use of such formalism allows to identify and describe original bath-induced physical effects.

   In a separate lecture, we will introduce in detail the quantum trajectories technique, and discuss its physical interpretation and implementation. This technique involves rewriting the master equation as a stochastic average over many individual trajectories, which are evolved in time numerically as pure states. The main advantage is that it allows to reduce the size of the propagated object from N^2 to N, being N the size of the Hilbert space. Despite the penalty of having to sample over many trajectories, this remains still more efficient computationally. 

Theory Lectures, March 12, 19, 26; 2019, 10:15. Blue Lecture Room