I’d like to advertise the video of my 5th lecture on the theory of quantum noise and decoherence, which is now available. Here I introduce coherent states and displacement/Weyl operators:

An open science weblog focussed on quantum information theory, condensed matter physics, and mathematical physics

I’d like to advertise the video of my 5th lecture on the theory of quantum noise and decoherence, which is now available. Here I introduce coherent states and displacement/Weyl operators:

I’d like to share with you the video of lecture 4 of my course on the theory of quantum noise and decoherence in which I introduce coherent states and displacement/Weyl operators.

As always, if you want to see more of this kind of thing then please like this video; if you think it sucked then do go ahead and dislike it. And if you want to stay up to date with more content like this then please don’t hesitate to subscribe.

Today I’d like to share the video of lecture 3 of my course on the theory of quantum noise and decoherence in which I continue the discussion of dynamics, both closed and open, in quantum mechanics. Additionally, the description of many particle systems via Fock space is introduced.

As always, if you want to see more of this kind of thing then please like this video; if you think it sucked then do go ahead and dislike it. And if you want to stay up to date with more content like this then please don’t hesitate to subscribe.

This semester, as part of the research training group “Quantum mechanical noise in complex systems“, I am giving a course on the theory of quantum noise and decoherence. This course is intended for both theorists and experimentalists alike who have at least some familiarity with basic textbook quantum mechanics. The main objective is to introduce the Lindblad equation, its derivation, solution, and important examples. I am recording the lectures and will post them here soon after they are completed. Today I’d like to share Lecture 1

in which I give a review of quantum mechanics according to the “Hannover rules” :)

The course will be “not without mathematical rigour”, however, the main emphasis will be on physical examples.

If you want to see more of this kind of thing then please like this video; if you think it sucked then do go ahead and dislike it. And if you want to stay up to date with more content like this then please don’t hesitate to subscribe.

**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.

**1. Lecture 11: the time-dependent variational principle and mean-field theory **

In this and the following lectures we are going to apply the *time-dependent variation principle* (TDVP) to the variational classes we have met previously, namely, product states for quantum spin systems, mean-field states for bosons and fermions, and matrix product states.

The pdf version of these notes can be found here. Read the rest of this entry »

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.