Efficient Anderson localization bounds for large multi-particle systems
Victor Chulaevsky
Université de Reims, FranceYuri Suhov
University of Cambridge, UK
![Efficient Anderson localization bounds for large multi-particle systems cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-7-issue-1.png&w=3840&q=90)
Abstract
We study multi-particle interactive quantum disordered systems on a polynomially growing countable connected graph (). The main novelty is to give localization bounds uniform in finite volumes (subgraphs) in as well as for the whole of . Such bounds are proved here by means of a comprehensive fixed-energy multi-particle multiscale analysis. We consider – for the first time in the literature – a discrete -particle model with an infinite-range, sub-exponentially decaying interaction, and establish (1) exponential spectral localization, and (2) strong dynamical localization with sub-exponential rate of decay of the eigenfunction correlators with respect to the natural symmetrized distance in the multi-particle configuration space.
Cite this article
Victor Chulaevsky, Yuri Suhov, Efficient Anderson localization bounds for large multi-particle systems. J. Spectr. Theory 7 (2017), no. 1, pp. 269–320
DOI 10.4171/JST/163