Small Fermi energy effects are induced in MgB_2 by the low hole doping in the σ bands which are characterized by a Fermi energy E_ F^σ∼ 0.5 eV. We show that, due to the particularly strong deformation potential relative to the E_2g phonon mode, lattice fluctuations are reflected in strong fluctuations in the electronic band structure. Quantum fluctuations associated to the zero-point lattice motion are responsible for an uncertainty of the Fermi energy of the order of the Fermi energy itself,

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... ading to the breakdown of the adiabatic principle underlying the Born-Oppenheimer approximation in MgB_2 even if ω_ ph/E_ F∼ 0.1-0.2, where ω_ ph are the characteristic phonon frequencies. This amounts to a new nonadiabatic regime, which could be relevant to other unconventional superconductors.