Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime

TL;DR

This paper reviews an exact Bethe Ansatz method for analyzing pairing fluctuations in mesoscopic systems, bridging the gap between few-electron and thermodynamic regimes, and clarifying finite size effects.

Contribution

It introduces a Bethe Ansatz approach to compute pairing correlations in the canonical ensemble, connecting the discrete BCS model to integrable Gaudin magnets with boundary terms.

Findings

Finite size scaling behavior of pairing correlations clarified.

The approach enables analysis beyond formal calculations.

Applications to mesoscopic superconductivity are outlined.

Abstract

We review the exact treatment of the pairing correlation functions in the canonical ensemble. The key for the calculations has been provided by relating the discrete BCS model to known integrable theories corresponding to the so called Gaudin magnets with suitable boundary terms. In the present case the correlation functions can be accessed beyond the formal level, allowing the description of the cross-over from few electrons to the thermodynamic limit. In particular, we summarize the results on the finite size scaling behavior of the canonical pairing clarifying some puzzles emerged in the past. Some recent developments and applications are outlined.