# Fluctuations of collective coordinates and convexity theorems for energy surfaces

Abstract : Constrained energy minimizations of a many-body Hamiltonian return energy landscapes $e(b)$ where $b$\equiv \langle {B} \rangle representes the average value(s) of one (or several) collective operator(s), B, in an "optimized" trial state \Phi_b, and e$\equiv$ $\langle {H} \rangle$ is the average value of the Hamiltonian in this state $\Phi_b$. It is natural to consider the uncertainty, $\Delta e$, given that $\Phi_b$ usually belongs to a restricted set of trial states. However, we demonstrate that the uncertainty, $\Delta b$, must also be considered, acknowledging corrections to theoretical models. We also find a link between fluctuations of collective coordinates and convexity properties of energy surfaces.
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B.G. Giraud, S. Karataglidis, T. Sami. Fluctuations of collective coordinates and convexity theorems for energy surfaces. Annals of Physics, Elsevier Masson, 2017, 376, pp.296 - 310. ⟨10.1016/j.aop.2016.11.015⟩. ⟨in2p3-01468960⟩

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