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It is generally believed that the high energy emissions from isolated pulsars are emitted from relativistic electrons/positrons\udaccelerated in outer magnetospheric accelerators (outergaps) via a curvature radiation mechanism, which has a simple\udexponential cut-off spectrum. However, many gamma-ray pulsars detected by the Fermi LAT (Large Area Telescope) cannot\udbe fitted by simple exponential cut-off spectrum, and instead a sub-exponential is more appropriate. It is proposed that\udthe realistic outergaps are non-stationary, and that the observed spectrum is a superposition of different stationary states\udthat are controlled by the currents injected from the inner and outer boundaries. The Vela and Geminga pulsars have the\udlargest fluxes among all targets observed, which allows us to carry out very detailed phase-resolved spectral analysis. We\udhave divided the Vela and Geminga pulsars into 19 (the off pulse of Vela was not included) and 33 phase bins, respectively.\udWe find that most phase resolved spectra still cannot be fitted by a simple exponential spectrum: in fact, a sub-exponential\udspectrum is necessary. We conclude that non-stationary states exist even down to the very fine phase bins

Probing Gamma-ray Emission of Geminga and Vela with Non-stationary Models