Thermal BCS-BEC Crossovers in Finite 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 quantumgases. Unlike the conventional crossover, which is driven by tuning the interaction strength,our study suggests that temperature alone can induce a smooth transition from weaklybound Cooper pairs (BCS-like state) to tightly bound dimers (BEC-like state). Using anexactly solvable model with a finite number of fermions, we analyze the structure ofeigenstates, pairing correlations, and thermodynamic response functions. We demonstratethat different multiplet structures, characterized by distinct quasi-spin quantum numbers,become thermally accessible, effectively mimicking the crossover behavior seen in ultracoldFermi gases. Our results provide new insights into the role of thermal fluctuations inquantum pairing phenomena and suggest alternative routes for exploring crossover physicsin mesoscopic and strongly correlated systems.