限制在一维谐振势下的三维自由电子气的一些热力学性质

利用围路积分表达的计算系统热力学势的一个公式,得到被一维谐振子势限制、有垂直磁场作用的三维自由电子气的在任意温度下的热力学势的精确解析表达式.然后利用其研究了不同温度和尺度区域内磁化强度、磁化率和比热随磁场强度的变化情况.研究表明,低温下磁化强度、磁化率和比热随磁场强度变化出现振荡现象,其中比热还会出现两种不同的振荡模式.     

Analytical thermodynamical properties of a two-dimensional electron gas in a magnetic field

Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular magnetic field are derived.This is accomplished by first deriving the general expression for the thermodynamical potential,and then employing this result to obtain the corresponding expression for the two-dimensional gas.The chemical potential and magnetization are studied as a function of temperature and magnetic field,and shown to be in agreement with prior work.It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.