In this paper, the thermodynamics of a two-dimensional charged Bose gas with a gap excitation spectrum of translation-invariant bipolarons is considered. Analytical expressions are obtained for the Bose condensation temperature Tc, the chemical potential μ(T), the internal energy U(T), the heat capacity C_V(T), and the magnitude of the heat capacity jump ΔC_V at the critical point. A quantitative agreement between the model and the classical calorimetric data of Loram et al. (1994) is carried out for the optimally doped high-temperature superconductor YBa₂Cu₃O_6.92 (T_с ≈ 91.5). It is shown that the regime of a strong energy gap (w₀ ≫ T_с, w₀ -optical phonon frequency) allows one to describe with good accuracy the macroscopic λ-peak of the electron heat capacity with the participation of only a small concentration of TI bipolarons from the total concentration of the carrier density in the CuO₂ planes.

preformed pairs, bose-condensate, pseudogap, roton spectrum, Loram experiments

Mathematical modelling in actual problems of science and technics