Undecidability in physics… and its consequences

David Pérez-García (Universidad Complutense, Madrid) — March 16

Abstract :
The pioneering work of Goedel and Turing in the 30s showed that there exist problems in mathematics and computer science that cannot be solved. They are called undecidable. Since then, several problems in physics have been shown to be undecidable too. In this talk I will show that many interesting properties of a quantum many body system are indeed undecidable. This negative result has, however, a positive side. It predicts the existence of a new effect that we name "size-driven quantum phase transition”. I will present this effect, its characteristic features, as well as our recent ideas to try to observe it.
This is joint work with J. Bausch, T. Cubitt, B. Doucot, S. Iblisdir, A. Lucia and M.M. Wolf.

Biography :
David Pérez-García is Professor in the Department of Mathematical Analysis at Universidad Complutense de Madrid and director of the research group "Mathematics and Quantum Information". After a PhD in Mathematics at Universidad Complutense de Madrid, he moved to the Max Planck Institute of Quantum Optics in Garching, where he started working in Quantum Information Theory, his main research topic since then. David has been awarded the Young Researcher RAC-Endesa Prize in Mathematics in 2012 and an ERC-Consolidator Grant in 2015.

You can also watch this video on savoirs.ens.fr