N-soliton statistics and condensate formation in dense quantum gases

Abstract

Statistics of N quantum density soliton waves [B. M. Mirza, Mod. Phys. Lett. B28 (2014) 1450148] is extended here to the case of systems with symmetric wave function. Since many such systems exhibit condensation phenomena, application is made of the soliton wave statistics to investigate condensation and phase transition in quantum gases such as 4 He and also dense systems such as the alkali atoms. Specific heat discontinuities are used to determine the condensation temperature for dense quantum gases and liquids. For the model case of helium the statistical theory is shown to predict not only the observed superfluid condensation temperature (2.17 ± 0.01 K) correctly but also the normal condensation temperature (4.21 ± 0.02 K), as well as the exact specific heat λ-profile.