Test of a modified BCS theory performance in the Picket Fence Model

TL;DR

This paper evaluates the performance of a modified BCS theory in the Picket Fence Model at finite temperatures, revealing significant deviations from exact results and discussing thermodynamical inconsistencies.

Contribution

It provides a detailed analysis of the modified BCS theory's accuracy and limitations within the Picket Fence Model, including symmetric and asymmetric cases.

Findings

MBCS results deviate significantly from exact values at low temperatures.

Heating in MBCS predicts a thermal pairing gap component.

Thermodynamical inconsistency is identified in MBCS.

Abstract

Analyses of a modified BCS (MBCS) theory performance at finite temperatures in the Picket Fence Model (PFM) for light and heavy systems is presented. Both symmetric, $\Omega=N$ ($N$ particles on $\Omega$ twice-degenerate levels), and asymmetric, $\Omega\neq N$, versions of the PFM are considered. The quantities known exactly from particle-hole symmetry of the $\Omega=N$ PFM are calculated. Starting from very low temperatures, these quantities are found in dramatic deviation from the exact values in MBCS results. Consequences of the MBCS prediction that heating generates a thermal constituent of the pairing gap, are discussed. Thermodynamical inconsistency of the MBCS is also addressed.