广义不确定性原理下广义外势中n维理想费米气体的热力学性质

发布时间：2018-12-20 13:52

【摘要】：采用Thomas-Fermi的半经典近似,研究了广义不确定性原理下广义外势中n维理想费米气体的热力学性质.解析计算出平均粒子数、内能和热容等热力学量,给出了低温条件下上述热力学量及化学势、费米能和基态能的解析表达式以及考虑广义不确定性原理的修正项;在低温条件下,数值分析了外势与广义不确定性原理对铜电子气体及电子密度更高的电子系统热力学性质的影响,发现:1)考虑广义不确定性原理时,外势对电子系统的影响很大,使广义不确定性原理的修正项增加了6~11个数量级.2)粒子数密度越大、粒子质量越小,广义不确定性原理的影响越大.3)广义不确定性原理导致内能随温度的增加先增大,当温度升到某一数值时(对三维谐振势中的铜电子气体,T/T_(F0)~0.22)时,增值为0,温度再增加内能减少;热容随温度的增加减少;化学势、费米能和基态能随温度的升高而增大.
[Abstract]:By using Thomas-Fermi 's semiclassical approximation, the thermodynamic properties of n-dimensional ideal Fermi gas in generalized external potential under generalized uncertainty principle are studied. The thermodynamic quantities such as average particle number, internal energy and heat capacity are calculated analytically. The analytical expressions of the thermodynamic quantities and chemical potential, Fermi energy and ground state energy at low temperature are given, as well as the correction terms considering the generalized uncertainty principle. At low temperature, the effects of external potential and generalized uncertainty principle on thermodynamic properties of copper electron gas and electron system with higher electron density are numerically analyzed. It is found that: 1) when the generalized uncertainty principle is considered, The external potential has a great influence on the electronic system, which increases the correction term of the generalized uncertainty principle by 6 ~ 11 orders of magnitude.) the larger the particle number density, the smaller the particle mass. The effect of generalized uncertainty principle is greater. 3) the generalized uncertainty principle causes the internal energy to increase with the increase of temperature, when the temperature rises to a certain value (for copper electron gas in 3D resonance potential, T / T _ (F _ 0) ~ 0.22), The increment is 0, and the internal energy decreases with the increase of temperature. The heat capacity decreases with the increase of temperature, and the chemical potential, Fermi energy and ground state energy increase with the increase of temperature.
【作者单位】：宁夏大学物理与电子电气工程学院;宁夏沙漠信息智能感知重点实验室;
【基金】：国家自然科学基金(61167002) 宁夏自然科学基金(NZ14055)
【分类号】：O414.1

【相似文献】