不同边界条件下电场对量子阱影响的比较分析。II。热力学性质
Comparative analysis of electric field influence on the quantum wells with different boundary conditions. II. Thermodynamic properties
摘要：
计算了一维量子阱在垂直于表面电场$\mathscr{E}$的边界上Dirichlet（D）和Neumann（N）边界条件混杂排列时的热力学性质.对于正则系综，涉及θ函数的分析表达式被发现的平均能量和热容量$c_V$的盒子，没有施加电压。明显的最大值伴随着相邻的最小值的比热依赖于温度$T$的纯Neumann量子阱和他们的缺席，其他BC的预测和解释的结构相应的能谱。外加场导致热容的增加和新的极值的形成或现有极值的修改，这由相关电势的影响定性地描述。费米巨正则系综的一个显著特征是，在零场中的任何BC组合下，对于一个粒子，在$T$轴上观察到$c_V$的显著最大值，而对于任何其他数量的$N$，都不存在该最大值。对这一现象的定性和定量解释采用了不同$N$的化学势及其温度依赖性的分析。证明了玻色-爱因斯坦凝聚的临界温度$T_{cr}$随外加电压的增加而增加，除了小强度下的ND情形$\mathscr{E}$，这又用相关能量场的修正来解释.结果表明，即使在温度小于$T_{cr}$的总偶极矩$\langle P\rangle$可能成为负的相当温和的$\mathscr{E}$。无论是费米体系还是BE体系，随着$N$的生长，电场对热容的影响被抑制.
英文摘要：
Thermodynamic properties of the one-dimensional (1D) quantum well (QW) with miscellaneous permutations of the Dirichlet (D) and Neumann (N) boundary conditions (BCs) at its edges in the perpendicular to the surfaces electric field $\mathscr{E}$ are calculated. For the canonical ensemble, analytical expressions involving theta functions are found for the mean energy and heat capacity $c_V$ for the box with no applied voltage. Pronounced maximum accompanied by the adjacent minimum of the specific heat dependence on the temperature $T$ for the pure Neumann QW and their absence for other BCs are predicted and explained by the structure of the corresponding energy spectrum. Applied field leads to the increase of the heat capacity and formation of the new or modification of the existing extrema what is qualitatively described by the influence of the associated electric potential. A remarkable feature of the Fermi grand canonical ensemble is, at any BC combination in zero fields, a salient maximum of $c_V$ observed on the $T$ axis for one particle and its absence for any other number $N$ of corpuscles. Qualitative and quantitative explanation of this phenomenon employs the analysis of the chemical potential and its temperature dependence for different $N$. It is proved that critical temperature $T_{cr}$ of the Bose-Einstein (BE) condensation increases with the applied voltage for any number of particles and for any BC permutation except the ND case at small intensities $\mathscr{E}$ what is explained again by the modification by the field of the interrelated energies. It is shown that even for the temperatures smaller than $T_{cr}$ the total dipole moment $\langle P\rangle$ may become negative for the quite moderate $\mathscr{E}$. For either Fermi or BE system, the influence of the electric field on the heat capacity is shown to be suppressed with $N$ growing.
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