1999/12/31 by Werner Fischer, Hajo Leschke, Peter Müller +1
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP
paper · pdf · doi:10.1023/a:1026425621261
published as J. Stat. Phys., vol. 101, pp. 935-985 (2000) · LaTeX, 54 pages, 4 figures; final version, to appear in slightly different form in Journal of Statistical Physics
arxiv created 2000/10/12 · openalex publication_date 2000/12/01 · arxiv updated 2009/11/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum particle in multi-dimensional Euclidean space under the influence of suitable random potentials has almost surely a pure-point component. The result applies in particular to a certain class of zero-mean Gaussian random potentials, which are homogeneous with respect to Euclidean translations. More precisely, for these Gaussian random potentials the spectrum is almost surely only pure point at sufficiently negative energies or, at negative energies, for sufficiently weak disorder. The proof is based on a fixed-energy multi-scale analysis which allows for different random potentials on different length scales.