In this paper, we report the ground state properties i.e. electron momentum density and X-ray structure factors of fcc-copper are presented. The Am241 Compton spectrometer, which uses 59.54 keV gamma-rays, has been us...In this paper, we report the ground state properties i.e. electron momentum density and X-ray structure factors of fcc-copper are presented. The Am241 Compton spectrometer, which uses 59.54 keV gamma-rays, has been used for the Compton profile measurement. To compare the experimental data, the Compton profiles within the framework of linear combination of atomic orbitals (LCAO) method using Hartree–Fock (HF), density functional (DF) and hybrid B3PW schemes embodied in the CRYSTAL06 code have been computed. Among the various theoretical calculations, it is found that the present experimental data is in very good agreement with the hybrid B3PW scheme. A real-space analysis of the experimental Compton profile shows the metal-like behavior of copper The structure factors for copper are computed using hybrid B3PW scheme and compared with available experimental and theoretical data.展开更多
The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various...The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter a = 1 - 2/γ, where γ, is the dimensionless interaction strength. We also discuss the Tan＇s adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in terms of the fractional statistical parameter.展开更多
When analyzing an Electron’s orbit’s and movements, a “classical” bare g-factor of “1” must be used, but when analyzing just the Electron itself, a bare g-factor and gyromagnetic ratio of twice the “classical”...When analyzing an Electron’s orbit’s and movements, a “classical” bare g-factor of “1” must be used, but when analyzing just the Electron itself, a bare g-factor and gyromagnetic ratio of twice the “classical” value is needed to fit reality. Nobody has fully explained this yet. By examining the electromagnetic wave nature of the electron, it is possible to show a simple reason why its bare g-factor must be 2, without resorting to superluminal velocities or dismissing it as mystically intrinsic. A simple charged electromagnetic wave loop (CEWL) model of the electron that maintains the same electromagnetic wave nature as the high-energy photons from which electron-positron pairs form, will have exactly half of its energy in the form of magnetic energy who’s field lines are perpendicular to the direction of the charge rotation, which leads to the conclusion that only half of the electron’s electromagnetic mass is rotational mass, from which it is easy to calculate a bare g-factor of 2 using Feynman’s equation for the electron’s g-factor.展开更多
文摘In this paper, we report the ground state properties i.e. electron momentum density and X-ray structure factors of fcc-copper are presented. The Am241 Compton spectrometer, which uses 59.54 keV gamma-rays, has been used for the Compton profile measurement. To compare the experimental data, the Compton profiles within the framework of linear combination of atomic orbitals (LCAO) method using Hartree–Fock (HF), density functional (DF) and hybrid B3PW schemes embodied in the CRYSTAL06 code have been computed. Among the various theoretical calculations, it is found that the present experimental data is in very good agreement with the hybrid B3PW scheme. A real-space analysis of the experimental Compton profile shows the metal-like behavior of copper The structure factors for copper are computed using hybrid B3PW scheme and compared with available experimental and theoretical data.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11374331 and 11534014)the National Key R&D Program of China(Grant No.2017YFA0304500)partially supported by CAS-TWAS President’s Fellowship for International PhD Students
文摘The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter a = 1 - 2/γ, where γ, is the dimensionless interaction strength. We also discuss the Tan＇s adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in terms of the fractional statistical parameter.
文摘When analyzing an Electron’s orbit’s and movements, a “classical” bare g-factor of “1” must be used, but when analyzing just the Electron itself, a bare g-factor and gyromagnetic ratio of twice the “classical” value is needed to fit reality. Nobody has fully explained this yet. By examining the electromagnetic wave nature of the electron, it is possible to show a simple reason why its bare g-factor must be 2, without resorting to superluminal velocities or dismissing it as mystically intrinsic. A simple charged electromagnetic wave loop (CEWL) model of the electron that maintains the same electromagnetic wave nature as the high-energy photons from which electron-positron pairs form, will have exactly half of its energy in the form of magnetic energy who’s field lines are perpendicular to the direction of the charge rotation, which leads to the conclusion that only half of the electron’s electromagnetic mass is rotational mass, from which it is easy to calculate a bare g-factor of 2 using Feynman’s equation for the electron’s g-factor.
