Abstract
以安德生晶格模型 (Anderson lattice model) 在役使玻色子平均場(slave boson mean field) 為理論基礎，我們研究重費米子系統 (heavy-fermion systems 簡寫為HF) 以下兩種性質：類變磁轉變 (metamagnetic-like transition) 及彈性異常。實驗上發現一些HF ( 如CeRu2Si2及UPt3) 的磁化率在某一臨界磁場下有一高峰，稱為類變磁相變。當引進異向性混成能量後，在平均場近似下，理論的計算發現CeRu2Si2有類似類變磁相變的性質。在本論文中，我們發現在UPt3也有同樣的節論。另外一些HF的彈性係數在低溫時出現陡降的現象。因安德生晶格模型無法解析求解, 我們使用數值方法處理，發現結果與實驗在定性上是符合的。除此之外，我們也研究理想粒子在層狀結構的比熱性質，發現在古典與量子系統都有一個類夏特基異常 (Schottky-like anomaly)。這與一般的夏特基異常 (Schottky anomaly) 不同處在於層狀結構沒有電荷激發(charge excitation)。當層數很大時，玻色子會出現第二個高峰，此高峰是趨近玻色沉澱 (Bose condesation) 的趨勢。我們也研究一個二體問題：兩個粒子以彈簧聯結，再放入一維無窮位能井。兩種位能當個別處理時可以精確解，但合併時是相當的困難。我們使用變分法來求基態能量及其趨近表示式 (asymptotic expression) ，然後討論相關問題，如霍爾效應的finite-size effect及離子化的氫分子的能階。Based on the Anderson lattice model in the slave boson meanfield method, we study the heavy-fermion systems, HF, in twotopics: the anomalous metamagnetic-like transition and theelastic anomaly. Experimentally, the magnetic susceptbility inseveral HF including CeRu2Si2 and UPt3 shows a peak at somecritical field. This is called the metamagnetic-liketransition. Theoretically, a similar transition was found forCeRu2Si2 at the mean-field level when the anisotropy of thehybridization matrix element is considered. Here we find thatthe same conclusion applied to UPt3. On the other hand, theelastic constant exhibits a dip at low temperature in some HF.Since the Anderson lattice model can not be solvedanalytically, numerically means is used and its results fit theexperimental data qualitatively. Besides these, we mentionworks on the specific heat of ideal particles in multilayersystems, for which a Schottky-like anomaly is found bothclassical and quantum systems. This is different from the usualscenario for the Schottky anomaly since there is no energy gapfor the charge excitation. For bosons, we find a second peakwhen the layer number is large, which is ascribed to the trendtowards Bose condesation. We also study a two-body problemproblem in which two particles are linked by a spring and putin an one-dimensional infinite potential well. These twopotentials when seperated can each be solved exactly, but whencombined it becomes extremely difficult to solve. We use thevariational method to obtain the groundstate energy andasymptotic expressions, and discuss some related problems, suchas the finite-size effect in quantum Hall effect and the energylevel of an hydrogen molecule H2+.