arXiv:2203.14847 Abstract | arXiv Analytics

arXiv:2203.14847 [math.PR]Abstract References Reviews Resources

Correlation of local densities of states on mesoscopic energy scales in random band matrices

Published 2022-03-28, updated 2023-05-30Version 2

We are interested in the phase transition of the correlation function of local densities of states at mesoscopic scales of random band matrices of width $W$ in dimension $2$. As a result, we show that the local densities of states are alternately positively and negatively correlated in the diffusive regime $O(\log(L/W))$ times, $L$ being the size of he system.

Comments: 10 pages, 3 figures. Accepted for publication in Letters in Mathematical Physics

Categories: math.PR, math-ph, math.MP

Subjects: 15B52, 82B44, 33E99

Keywords: random band matrices, mesoscopic energy scales, local densities, phase transition, correlation function

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