Transition temperature of the homogeneous and dilute Bose gas in D-dimensions

2007/07/10 by Sanghoon Kim, Sang-Hoon Kim, Kim, Sang-Hoon
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Strong Light-Matter Interactions #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.48550/arxiv.0707.1538

4 pages, 2 figure

openalex publication_date 2007/07/10 · arxiv created 2007/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The phase transition temperature of the homogeneous and dilute Bose gas in D-dimensions (2 ≤ D ≤ 3) is calculated by a mean field-based statistical method. The shift of the phase transition temperature is written up to the leading order as ΔT_c/T_c⁰ = c \gam^\al, where \gam=n^1/3a. We derived Huang's result of the phase transition temperature in the generalized dimensions. We show that c(D) is positive and \al(D)=2(D/2-1)² in the short-wavelength range. The origin of the difference between \al=1/2 and \al=1 at D=3 is discussed. The T_c at D=2 is calculated in the same scheme. The result is compared with Fisher and Hohenberg's KT temperature.

Related

• Transition temperature of the homogeneous imperfect Bose gas
• Transition Temperature of Dilute, Weakly Repulsive Bose Gas
• Critical Temperature Shift in Weakly Interacting Bose Gas
• Transition temperature and thermodynamic properties of homogeneous weakly interacting Bose gas in self-consistent Popov approximation
• Discontinuity in the specific heat of a weakly interacting Bose gas