Thermal and quantum ﬂuctuations in superconducting nanostructures
P. Ribeiro, MPI Dresden
I will report a study on the combined eﬀect of thermal and quantum ﬂuctuations in a zero dimensional superconductor.
Using path integral techniques, the expression for the partition function is obtained as well as the superconducting order parameter which include both types of ﬂuctuations.
These results are valid for any temperature and to leading order in $\delta/\Delta_0$ where $\delta$ is the mean level spacing and $\Delta_0$ is the bulk energy gap.
Divergences arising at low temperatures, previously reported in the literature, are avoided by identifying and treating non-perturbatively a low-energy collective mode.
In the low and high temperature limit our results agrees with those from the random phase (RPA) and the static path approximation (SPA) respectively.