| Summary: | 博士 === 國立清華大學 === 物理研究所 === 83 === Based on the Anderson lattice model in the slave boson mean
field method, we study the heavy-fermion systems, HF, in two
topics: the anomalous metamagnetic-like transition and the
elastic anomaly. Experimentally, the magnetic susceptbility in
several HF including CeRu2Si2 and UPt3 shows a peak at some
critical field. This is called the metamagnetic-like
transition. Theoretically, a similar transition was found for
CeRu2Si2 at the mean-field level when the anisotropy of the
hybridization matrix element is considered. Here we find that
the same conclusion applied to UPt3. On the other hand, the
elastic constant exhibits a dip at low temperature in some HF.
Since the Anderson lattice model can not be solved
analytically, numerically means is used and its results fit the
experimental data qualitatively. Besides these, we mention
works on the specific heat of ideal particles in multilayer
systems, for which a Schottky-like anomaly is found both
classical and quantum systems. This is different from the usual
scenario for the Schottky anomaly since there is no energy gap
for the charge excitation. For bosons, we find a second peak
when the layer number is large, which is ascribed to the trend
towards Bose condesation. We also study a two-body problem
problem in which two particles are linked by a spring and put
in an one-dimensional infinite potential well. These two
potentials when seperated can each be solved exactly, but when
combined it becomes extremely difficult to solve. We use the
variational method to obtain the groundstate energy and
asymptotic expressions, and discuss some related problems, such
as the finite-size effect in quantum Hall effect and the energy
level of an hydrogen molecule H2+.
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