# About small eigenvalues of Witten Laplacian

## TL;DR

This paper investigates the eigenvalues of the semiclassical Witten Laplacian in cases where the associated Arrhenius numbers are degenerate, extending understanding of spectral properties in such scenarios.

## Contribution

It provides new insights into the spectral analysis of the Witten Laplacian when the Arrhenius numbers are not strictly increasing, a case less explored in prior research.

## Key findings

- Analysis of eigenvalue behavior in degenerate Arrhenius number cases
- Extension of spectral theory for Witten Laplacian
- Identification of conditions affecting eigenvalue degeneracy

## Abstract

We study the eigenvalues of the semiclassical Witten Laplacian $\Delta_\phi$ associated to a potential $\phi$. We consider the case where the sequence of Arrhenius numbers $S_1\leq \ldots\leq S_n$ associated to $\phi$ is degenerated, that is the preceding inequality are not necessarily strict.