Today I put online a major update of my pair of papers on the variational method for quantum field theory (short here, long here). The idea is still to use the same class of variational wave functions (relativistic continuous matrix product states) to find the ground state of (so far bosonic) quantum field theories in 1+1 dimensions. The novelty comes from the algorithm I now use to compute expectation values, that has a cost only proportional to $D^3$ where $D$ is the bond dimension. Using backpropagation techniques, the cost of computing the gradient of observables with respect to the parameters is also only $D^3$. This is basically the same asymptotic scaling as standard continuous matrix product states.

There are 2 recent preprints on tensor networks I found interesting.

The first is Collective Monte Carlo updates through tensor network renormalization (arxiv:2104.13264) by Miguel Frias-Perez, Michael Marien, David Perez Garcia, Mari Carmen Banuls and Sofyan Iblisdir. I am certainly a bit biased because two authors come from our group at MPQ, and I heard about the result twice in seminars, but I think it is a genuinely new and interesting use of tensor networks. The main idea is to reduce the rejection rate of Markov Chain Monte Carlo (MCMC) by crudely estimating the probability distribution to be sampled from with tensor network renormalization. This combines the advantage of the Monte Carlo method (it is exact asymptotically, but slow especially for frustrated systems) with the advantage of tensor renormalization (it is very fast for approximations).

A bit more than a month ago, I put on arxiv two preprints (short and long) that summarize my recent work on applying the variational method in relativistic quantum field theory. I am happy that they were (so far) well received, and I got the chance to present the corresponding results in a few seminars already. The last two, at the University of Helsinki and EPFL, were recorded. I had a better microphone at EPFL, and expanded more on tensor networks, so I embed the video below (or direct link here).

The preprint on subcritical reactors I had written about two months ago has finally appeared on arxiv. Apparently it was “on hold” for that long because the primary category (applied physics) was not the right one, and the moderators thought “instrumentation and detectors” was better. Honestly, I am not sure they are right, given how theoretical the paper is, but I am just glad the paper appeared (I would have just preferred it to be faster).

I have found a neat nuclear physics problem, and have written a draft of article about it. Below I explain how I came to be interested in this problem, give some context most physicists may not be familiar with, and explain the result briefly.

A while back, I took a small part in the organization of the French public debate on radioactive waste management. My work was not very technical, but got me interested in the rich physics involved. The debate itself didn’t allow me to do real research on the subject: it was certainly not what was asked from me, and there was already so much to learn about the practical details.

Before I finally go on holidays, I put on arxiv an essay on quantum jumps, in fact rather on collapse models, that I initially submitted to the FQXI essay contest.

In this essay/paper, I just make a simple point which I have made orally for years at conferences. Every time, people looked quite surprised and so I thought it made sense to write it down.

The argument is simple enough that I can try to reproduce it here. Collapse models are stochastic non-linear modifications of the Schrödinger equation. The modification is meant to solve the measurement problem. The measurement problem is the fact that in ordinary quantum mechanics, what happens in measurement situations is postulated rather than derived from the dynamics. This is a real problem (contrary to what some may say), the dynamics should say what can be measured and how, it makes no sense to have an independent axiom (and it could bring contradictions). Decoherence explains why the measurement problem does not bring contradictions for all practical purposes, but again contrary to what some may say, it certainly does not solve the measurement problem. So the measurement problem is a real problem and collapse models provide a solution that works.

Quantum field theory (QFT) is the main tool we use to understand the fundamental particles and their interactions. It also appears in the context of condensed matter physics, as an effective description. But it is unfortunately also a notoriously difficult subject: first because it is tricky to define non-trivial instances rigorously (it’s not known for any one that exists in Nature), and also because even assuming it can be done, it is then very difficult to solve to extract accurate predictions.

Les combustibles nucléaires usés issus des réacteurs électrogènes français sont recyclés. D’aucuns arguent que ce recyclage permet de récupérer 96% du combustible, l’industrie est très vertueuse et exemplaire ! D’autres disent au contraire que le recyclage ne permet qu'1% de réutilisation, le recyclage c’est du bullshit ! Qui a raison ?

Je trouve que cette controverse est un bon prétexte pour expliquer la physique associée, qui est intéressante. Mon objectif est d’expliquer en détails l’aval du cycle du combustible pour son intérêt propre, la résolution de la controverse étant ensuite un corollaire trivial. Au passage, c’est l’occasion d’apprendre un peu plus sur l’histoire civile et militaire du nucléaire, le principe d’un réacteur nucléaire, et les subtilités des différents isotopes de l’uranium et du plutonium.

These days I am trying to improve my understanding of quantum field theory with as little perturbation theory as possible. I came across videos from a workshop at IHES in Bures-sur-Yvette on Hamiltonian methods for QFT and videos from a semester at the Newton institute in Cambridge, which both happened about a year ago. Both events are quite well filmed (especially at IHES), most presentations are made on a blackboard, and most talks I checked were well explained and interesting so I definitely recommend them.

My smart friends have been doing great work recently and I think it deserves attention.

I Understanding deep neural networks theoretically

Jonathan Donier, who now works for Spotify in London after a PhD in applied maths in Paris, has put a series of 3 fundamental articles on theoretical machine learning:

1) Capacity allocation analysis of neural networks: A tool for principled architecture design – arXiv:1902.04485
2) Capacity allocation through neural network layers – arXiv:1902.08572
3) Scaling up deep neural networks: a capacity allocation perspective – arXiv:1903.04455