**1. Lecture 12: the time-dependent variational principle for dissipative dynamics **

The time-dependent variational principle of Dirac is a powerful method to simulate the real and imaginary time dynamics of strongly correlated quantum systems. The original formulation has, as far as I can tell, only been formulated in the case of pure states. The generalisation to quantum systems undergoing dissipative dynamics is nontrivial and appears not to have been attempted. Here we describe a natural generalisation.

The pdf version can be found here.