Abstract

Random Schrödinger operators are popular in solid-state quantum physics because they provide accurate mathematical models for transitional phenomena occurring at the border between ordered and disordered systems (localisation {\it vs} delocalisation of eigenstates). Mathematically, the problem is to analyse properties of the spectrum of such an operator: this presents a challenge since new ideas and methods are required, combining Probability, Functional Analysis and—occasionally—other mathematical disciplines.

In this talk, I’ll discuss new results on multi-particle random Schr\”odinger operators in a Euclidean space (joint works with several colleagues completed in 2010). The main result is that when the randomness is `strong’, the spectrum near its lower edge is pure point with probability one and the corresponding eigenfunctions are exponentially localised. No preliminary knowledge of Quantum Mechanics will be assumed.