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In this article we focus on a semiclassical Schr\"odinger equation withmatrix-valued potential presenting a symmetric conjoint crossing of threeeigenvalues. The potential we consider is well-known in the chemical literatureas a pseudo  Jahn-Teller potential. We analyze the energy transfers which occur betweenthe three modes in terms of Wigner measures.

Semi-classical analysis of a conjoint crossing of three symmetric modes