In lecture 9 we continued reading the papers on matrix product states that we began in lectures 7 and 8.

**1. Lecture 10: the time-dependent variational principle **

In this lecture we will discuss the *time-dependent variation principle* (TDVP), which is a powerful method to simulate the nonequilibrium dynamics of a general quantum system while remaining within a given variational class. The TDVP is due, as far as I’m aware, to Dirac. Additionally, describing the TDVP isn’t especially difficult, so it is rather surprising that this elegant method it hasn’t made into standard textbooks. The general framework of the time-dependent variational principle can be found in [P. Kramer and M. Saraceno, *Geometry of the Time-Dependent Variational Principle in Quantum Mechanics* (Springer-Verlag, Berlin) (1981)].

These notes can be found in pdf format here.

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