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New results on spectra of multi-particle Schrödinger operators with random potentials.

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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.

This talk is part of the Probability series.

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