Spectral statistics of random Schr\"{o}dinger operator with growing potential

Dhriti Ranjan Dolai; Anish Mallick

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arXiv · 1506.07132

Spectral statistics of random Schr\"{o}dinger operator with growing potential

Dhriti Ranjan Dolai·Anish Mallick

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Abstract

In this work we investigate the spectral statistics of random Schr\"{o}dinger operators $H^\omega=-\Delta+\sum_{n\in\mathbb{Z}^d}(1+|n|^\alpha)q_n(\omega)|\delta_n\rangle\langle\delta_n|$, $\alpha>0$ acting on $\ell^2(\mathbb{Z}^d)$ where $\{q_n\}_{n\in\mathbb{Z}^d}$ are i.i.d random variables distributed uniformly on $[0,1]$.

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BibTeX RIS

Dhriti Ranjan Dolai, Anish Mallick. 2015-06-23. Spectral statistics of random Schr\"{o}dinger operator with growing potential. https://arxiv.org/abs/1506.07132

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