分类: 物理学 >> 基本粒子与场物理学 提交时间: 2016-05-08
摘要: We calculate the Casimir force at a finite cut-off Lambda by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L Lambda -> infinity. There is a correction in the order of (L Lambda)(-2), when L Lambda is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale Lambda(-1). It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.
分类: 物理学 >> 基本粒子与场物理学 提交时间: 2016-05-08
摘要: The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation (MF). The matrix of the second derivatives of the grand canonical potential Omega with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase in stability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical end point with the reduced density rho* = rho sigma(3) = 0.224 and the reduced temperature T* = kT/epsilon = 1.87 (sigma is the diameter of Heisenberg hard sphere and epsilon is the coupling constant).