A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresp...A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.展开更多
Calculations of properties of materials require performing numerical integrals over the Brillouin zone(BZ).Integration points in density functional theory codes are uniformly spread over the BZ(despite integration err...Calculations of properties of materials require performing numerical integrals over the Brillouin zone(BZ).Integration points in density functional theory codes are uniformly spread over the BZ(despite integration error being concentrated in small regions of the BZ)and preserve symmetry to improve computational efficiency.Integration points over an irreducible Brillouin zone(IBZ),a rotationally distinct region of the BZ,do not have to preserve crystal symmetry for greater efficiency.This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error,resulting in improved algorithmic efficiency.We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D.The algorithmuses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial.The algorithm is simple,general,and available as open-source software.展开更多
文摘A functional integral approach (FIA) is introduced to calculate the transition temperature of a uniform imperfect Bose gas. With this approach we find that the transition temperature is higher than that of the corresponding ideal gas. We obtain the expression of the transition temperature shift as , where n is the density of particle number and a is the scattering length. The result has never been reported in the literature.
文摘Calculations of properties of materials require performing numerical integrals over the Brillouin zone(BZ).Integration points in density functional theory codes are uniformly spread over the BZ(despite integration error being concentrated in small regions of the BZ)and preserve symmetry to improve computational efficiency.Integration points over an irreducible Brillouin zone(IBZ),a rotationally distinct region of the BZ,do not have to preserve crystal symmetry for greater efficiency.This freedom allows the use of adaptive meshes with higher concentrations of points at locations of large error,resulting in improved algorithmic efficiency.We have created an algorithm for constructing an IBZ of any crystal structure in 2D and 3D.The algorithmuses convex hull and half-space representations for the BZ and IBZ to make many aspects of construction and symmetry reduction of the BZ trivial.The algorithm is simple,general,and available as open-source software.
