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arXiv · 2409.08740

Another look at qualitative properties of eigenvalues using effective Hamiltonians

Idriss Mazari-Fouquer
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Abstract

The goal of this paper is to review several qualitative properties of well-known eigenvalue problems using a different perspective based on the theory of effective Hamiltonians, working exclusively on the Hopf-Cole transform of the equation. We revisit some monotonicity results as well as the derivation of several scaling limits by means of the Donsker-Varadhan formula, and we point out several differences between the case of quadratic Hamiltonians and non-quadratic ones.

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Idriss Mazari-Fouquer. 2024-09-13. Another look at qualitative properties of eigenvalues using effective Hamiltonians. https://arxiv.org/abs/2409.08740

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