Conserving Gapless Mean-Field Theory for Weakly Interacting Rose Gases(Condensed Matter: Structure, Mechanical and Thermal Properties)

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概要

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• This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function ψ and the Nambu Green's function G for the quasiparticle field. Imposing its stationarity respect to ψ and G yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: "conserving" and "gapless." The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length a and particle mass m to clarify its basic thermodynamic properties under two complementary conditions of constant density n and constant pressure p. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near T_c inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature T_c shows quite a different interaction dependence between the n-fixed and p-fixed cases. In the former case T_c increases from the ideal gas value T_0 as T_c/T_0=1+2.33an^<1/3>, whereas it decreases in the latter as T_c/T_0=1-3.84a(mp/2πh^2)^<1/5>. Temperature dependences of basic thermodynamic quantities are clarified explicitly.

• 社団法人日本物理学会の論文
• 2006-04-15

著者

• KITA Takafumi

  Division of Physics, Hokkaido University

• Kita T

  Hokkaido Univ. Sapporo Jpn

• Kita T

  Hokkaido Univ. Sapporo

• Kita Takafumi

  Depertment Of Applied Physics Faculty Of Engineering The University Of Tokyo

• Kita Takafumi

  Division Of Physics Graduate School Of Science Hokkaido University

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