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The heat capacity $C_{p}$ of an array of independent aluminum rings has beenmeasured under an external magnetic field $\vec{H}$ using highly sensitiveac-calorimetry based on a silicon membrane sensor. Each superconducting vortexentrance induces a phase transition and a heat capacity jump and hence $C_{p}$oscillates with $\vec{H}$. This oscillatory and non-stationary behaviourmeasured versus the magnetic field has been studied using the Wigner-Villedistribution (a time-frequency representation). It is found that theperiodicity of the heat capacity oscillations varies significantly with themagnetic field; the evolution of the period also depends on the sweepingdirection of the field. This can be attributed to a different behavior betweenexpulsion and penetration of vortices into the rings. A variation of more than15% of the periodicity of the heat capacity jumps is observed as the magneticfield is varied. A description of this phenomenon is given using an analyticalsolution of the Ginzburg-Landau equations of superconductivity.

Fine frequency shift of sigle vortex entrance and exit in superconducting loops