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Level Spacing for Non-Monotone Anderson Models

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Abstract

We prove localization and probabilistic bounds on the minimum level spacing for a random block Anderson model without monotonicity. Using a sequence of narrowing energy windows and associated Schur complements, we obtain detailed probabilistic information about the microscopic structure of energy levels of the Hamiltonian, as well as the support and decay of eigenfunctions.

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Notes

  1. Combinatoric factors are a convenient bookkeeping device when estimating sums. If \(\sum _\alpha c_\alpha ^{-1} \le 1\) for some positive constants \(c_\alpha \), then \(\sum _\alpha X_\alpha \le \sup _\alpha |X_\alpha |c_\alpha \). We call \(c_\alpha \) a combinatoric factor.

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Acknowledgments

This research was conducted in part while the author was visiting the Institute for Advanced Study in Princeton, supported by The Fund for Math and The Ellentuck Fund.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904-4137, USA

    John Z. Imbrie & Rajinder Mavi

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  1. John Z. Imbrie
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  2. Rajinder Mavi
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Correspondence to John Z. Imbrie.

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Imbrie, J.Z., Mavi, R. Level Spacing for Non-Monotone Anderson Models. J Stat Phys 162, 1451–1484 (2016). https://doi.org/10.1007/s10955-016-1461-8

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