2010/06/30 by J. Maćkowiak, Jan Maćkowiak, Maćkowiak, Jan +2
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1006.5825
24 pages, 10 figures
openalex publication_date 2010/06/30 · arxiv created 2010/11/03 · arxiv updated 2010/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The thermodynamics of a free Bose gas with effective temperature scale T and hard-sphere Bose gas with the T scale are studied. T arises as the temperature experienced by a single particle in a quantum gas with 2-body harmonic oscillator interaction V_\textrmosc, which at low temperatures is expected to simulate, almost correctly, the attractive part of the interatomic potential V_\textrmHe between 4\textrmHe atoms. The repulsive part of V_\textrmHe is simulated by a hard-sphere (HS) potential. The thermodynamics of this system of HS bosons, with the T temperature scale (HSET), is investigated, first, by the Bogoliubov-Huang method and next by a modified version of this method, which takes approximate account of those terms of the 2-body repulsion which are linear in the zero-momentum Bose operators a0, a^*0 (originally rejected by Bogoliubov). Theoretical heat capacity CV(T) exhibits good agreement, below 2.1 K, with the experimental heat capacity graph observed in 4\textrmHe at saturated vapour pressure. The phase transition to the low-temperature phase, with a Bose-Einstein condensate, occurs in the HSET at Tλ=2.17 K, and is accompanied, in the modified HSET version, by a singularity of CV(T). Other thermal properties of HSET, such as the momentum distribution function, the fraction of atoms in the momentum condensate and normal fluid density, agree qualitatively with those of 4\textrmHe, but improve those of the free Bose gas.