# Thermal BCS-BEC Crossovers in Finite Systems

## TL;DR

This paper explores how temperature can drive a transition between two quantum states in a finite system, similar to the BCS-BEC crossover in quantum gases.

## Contribution

The study shows that temperature alone can induce a BCS-BEC-like crossover in a finite system, without changing interaction strength.

## Key findings

- Thermal fluctuations can drive a transition from BCS-like to BEC-like states in a finite SU(2) × SU(2) model.
- Different quasi-spin multiplet structures become thermally accessible, mimicking crossover behavior.
- The results highlight the role of temperature in quantum pairing phenomena in mesoscopic systems.

## Abstract

We investigate the thermal evolution of fermionic pairings in a finite-size SU(2) × SU(2) complex model, drawing an analogy to the BCS-BEC crossover in interacting quantum gases. Unlike the conventional crossover, which is driven by tuning the interaction strength, our study suggests that temperature alone can induce a smooth transition from weakly bound Cooper pairs (BCS-like state) to tightly bound dimers (BEC-like state). Using an exactly solvable model with a finite number of fermions, we analyze the structure of eigenstates, pairing correlations, and thermodynamic response functions. We demonstrate that different multiplet structures, characterized by distinct quasi-spin quantum numbers, become thermally accessible, effectively mimicking the crossover behavior seen in ultracold Fermi gases. Our results provide new insights into the role of thermal fluctuations in quantum pairing phenomena and suggest alternative routes for exploring crossover physics in mesoscopic and strongly correlated systems.