FIR Project
2014 – 2017

Condensed Matter in Mathematical Physics

COND-MATH is a multiple unit three-year research project on a number of mathematical problems arising in the rigorous treatment of models and phenomena of condensed matter physics.

It is a most remarkable and incontrovertible fact that the progress of the experimental techniques of condensed matter and cold atom physics is disclosing an unprecedented horizon of reciprocal interaction between mathematics and physics.

This research project moves precisely along this conceptual two-fold line, from modern experiments to their rigorous formalisation and back from such an understanding to the proof of consequences that are observed in the lab. Whence the title, COND-MATH, to represent our investigation at the crossroads of condense matter and mathematical physics.
The problems we aim at investigating concern quantum mechanical (QM) systems divided into these 3 macro-areas:

(1) rigorous set up and spectral analysis of specific quantum many-body models;
(2) derivation of effective theories in appropriate scaling limits;
(3) analysis of such effective theories.

We thus merge two complementary perspectives: (1) covers specific (and today fashionable) models on which exact statements can be proved (a fairly rare case in many-body QM), while (2) and (3) cover few-body effective descriptions of otherwise too complex many-body systems that can be understood in their essence through limiting procedure which still retain the essential physical features.

Our approach will be that of bridging mathematical rigour with effective treatments used in physics. This is intended to be the basis for the scientific impact and the potentialities for applications of our investigation: justification of ad-hoc formal methods, selection of suitable mathematical models based on actual physics, creation of new fruitful bridges among two scientific communities, development of initiatives for the divulgation of our results.

Four autonomous research units will work under the continual coordination of the PI through an integrated approach towards the scientific goals.

Updated 21/09/2016