Thermodynamics of pairing in mesoscopic systems

TL;DR

This paper investigates the thermodynamic behavior of pairing correlations in mesoscopic nuclear systems using exact solutions, comparing different statistical ensembles, and exploring phase transition characteristics and effects of magnetic fields.

Contribution

It provides a comprehensive analysis of pairing thermodynamics in small systems with exact methods, including ensemble comparisons and the impact of magnetic fields.

Findings

Identification of discontinuities in thermodynamic variables during phase transition.

Analysis of fluctuations and zeros of partition functions in complex plane.

Insights into the influence of magnetic fields on the pairing phase transition.

Abstract

Using numerical and analytical methods implemented for different models we conduct a systematic study of thermodynamic properties of pairing correlation in mesoscopic nuclear systems. Various quantities are calculated and analyzed using the exact solution of pairing. An in-depth comparison of canonical, grand canonical, and microcanonical ensemble is conducted. The nature of the pairing phase transition in a small system is of a particular interest. We discuss the onset of discontinuity in the thermodynamic variables, fluctuations, and evolution of zeros of the canonical and grand canonical partition functions in the complex plane. The behavior of the Invariant Correlational Entropy is also studied in the transitional region of interest. The change in the character of the phase transition due to the presence of magnetic field is discussed along with studies of superconducting thermodynamics.