Spectral fluctuations for Schrödinger operators with a random decaying potential

2019/12/11 by Breuer, Jonathan, Grinshpon, Yoel, White, Moshe
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1912.05254

Abstract

We study fluctuations of polynomial linear statistics for discrete Schrödinger operators with a random decaying potential. We describe a decomposition of the space of polynomials into a direct sum of three subspaces determining the growth rate of the variance of the corresponding linear statistic. In particular, each one of these subspaces defines a unique critical value for the decay-rate exponent, above which the random variable has a limit that is sensitive to the underlying distribution and below which the random variable has asymptotically Gaussian fluctuations.

Related

• Eigenvalue Fluctuations of 1-dimensional random Schrödinger operators
• Spectral fluctuations for the multi-dimensional Anderson model
• Spectral statistics of random Schrödinger operator with growing potential
• One-dimensional Discrete Dirac Operators in a Decaying Random Potential II: Clock, Schrödinger and Sine statistics
• Fluctuations of the eigenvalue number in the fixed interval for β-models with β=1,2,4