Matter, and more specifically molecules, are constantly moving... However, a mathematical model can explain this movement, which is both ordered and chaotic : the Langevin equation. So let Ω ⊂ R^d be a bounded smooth domain and b : Ω→ R^d be a smooth vector field. We focus on the associated overdamped Langevin equation : \partial_t Xt = b(Xt ) + h^1/2Bt in the low temperature regime h→ 0 and in the case where b admits the decomposition b = −∇ f− ℓ with ∇ f· ℓ= 0 on \partial Ω. To study this equation, we analyse the spectrum of the infinitesimal generator of the dynamics: Lh = −∆ + ∇ f · ∇ + ℓ · ∇ with Neumann boundary conditions. In this case, moving particles will remain trapped inside the domain and more precisely the process remains trapped, for some time, in a certain region of the domain before going to another area. These regions are called metastables and correspond to neighborhoods of minima of f. Finally, thanks to spectral theory and more specifically small eigenvalues of Lh , we can describe the return to equilibrium of this metastable dynamic.