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arXiv · 2305.00442

On the localization regime of certain random operators within Hartree-Fock theory

Rodrigo Matos
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Abstract

Localization results for a class of random Schr\"odinger operators within the Hartree-Fock approximation are proved in two regimes: large disorder and weak disorder/extreme energies. A large disorder threshold $\lambda_{\mathrm{HF}}$ analogous to the threshold $\lambda_{\mathrm{And}}$ obtained by Schenker in \cite{Schenkl} is provided. We also show certain stability results for this large disorder threshold by giving examples of distributions for which $\lambda_{\mathrm{HF}}$ converges to $\lambda_{\mathrm{And}}$, or to a number arbitrarily close to it, as the interaction strength tends to zero.

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Rodrigo Matos. 2023-04-30. On the localization regime of certain random operators within Hartree-Fock theory. https://arxiv.org/abs/2305.00442

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