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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?
Thermo dynamical prop erties of a three-dimensional free electron gas confined in a one-dimensional harmonical p otential
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摘要: 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。Abstract: We study the thermodynamical properties of a noninteracting electron gas confined in one dimension by a harmonic-oscillator potential. The exact analytical expression for the thermodynamical potential is obtained by using a formula of contour integration. The magnetizations, magnetic susceptibilities, and the specific heats are then studied each as a function of the strength of the magnetic field in different regimes of the temperature and effective thickness. It is shown at low temperature, the magnetization, magnetic susceptibility, and the specific heat oscillate as the strength of the magnetic field increases. Especially, there exist two modes of oscillations for the specific heat in certain regimes of low temperature and effective thickness.
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